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Control of Micro Air Vehicles Using Wing Morphing


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CONTR OL OF MICR O AIR VEHICLES USING WING MORPHING By HELEN MICHELLE GARCIA A THESIS PRESENTED T O THE GRADU A TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2003

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T ABLE OF CONTENTS page LIST OF T ABLES . . . . . . . . . . . . . . . . . iii LIST OF FIGURES . . . . . . . . . . . . . . . . . i v ABSTRA CT . . . . . . . . . . . . . . . . . . . vi CHAPTER1 INTR ODUCTION . . . . . . . . . . . . . . . . 1 2 MICR O AIR VEHICLES . . . . . . . . . . . . . . 5 3 MORPHING . . . . . . . . . . . . . . . . . 9 4 MODELING . . . . . . . . . . . . . . . . . 16 5 24 in MICR O AIR VEHICLE . . . . . . . . . . . . . 22 5.1 V ehicle Description . . . . . . . . . . . . . . 22 5.2 Morphing . . . . . . . . . . . . . . . . 23 5.3 Flight T esting . . . . . . . . . . . . . . . 24 5.4 Modeling . . . . . . . . . . . . . . . . 28 5.5 Ev aluation . . . . . . . . . . . . . . . . 31 6 12 in MICR O AIR VEHICLE . . . . . . . . . . . . . 33 6.1 V ehicle Description . . . . . . . . . . . . . . 33 6.2 Morphing . . . . . . . . . . . . . . . . 34 6.3 Flight T esting . . . . . . . . . . . . . . . 38 6.4 Modeling . . . . . . . . . . . . . . . . 40 6.5 Ev aluation . . . . . . . . . . . . . . . . 43 7 CONCLUSION . . . . . . . . . . . . . . . . . 44 REFERENCES . . . . . . . . . . . . . . . . . . 46 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . 48 ii

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LIST OF T ABLES T able page 5–1 Range of control ef fectors . . . . . . . . . . . . . 23 5–2 Properties of the 24 in MA V . . . . . . . . . . . . 23 5–3 Poles of a linear model of the 24 in MA V . . . . . . . . . 30 6–1 Properties of the 12 in MA V . . . . . . . . . . . . 33 6–2 Poles of a linear model of the 12 in MA V . . . . . . . . . 41 iii

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LIST OF FIGURES Figure page 1–1 MA Vs with 24 in (left) and 12 in (right) W ingspan . . . . . . . 3 2–1 Members of MA V Fleet at Uni v ersity of Florida . . . . . . . 7 3–1 A Gull (left) and Sno wy Owl (right) in Flight . . . . . . . . 12 3–2 Aspect Ratio of Bird W ings . . . . . . . . . . . . 13 5–1 Ov erhead V ie w of the 24 in MA V . . . . . . . . . . . 22 5–2 W ing with T orque Rod . . . . . . . . . . . . . . 23 5–3 Rear V ie w of the 24 in MA V with Undeected (left) and Morphed (right) W ing . . . . . . . . . . . . . . . . . . 24 5–4 Doublet Command to Rudder Serv o . . . . . . . . . . 25 5–5 Response to Rudder Doublet for Roll Rate(left) and Y a w Rate(right) . 25 5–6 Second Doublet Command to Rudder Serv o . . . . . . . . 26 5–7 Response to Second Rudder Doublet for Roll(left) and Y a w Rate(right) . 26 5–8 Doublet Command to Morphing Serv o . . . . . . . . . . 27 5–9 Response to Morphing Doublet for Roll(left) and Y a w Rate(right) . . 27 5–10 Second Doublet Command to Morphing Serv o . . . . . . . 28 5–11 Response to Second Morphing Doublet Command for Roll Rate(left) and Y a w Rate(right) . . . . . . . . . . . . . . 28 5–12 Simulated () and Actual (—) Roll Rate(left) and Y a w Rate(right) Responses to Morphing Doublet . . . . . . . . . . . 29 5–13 Simulated () and Actual (—) Roll Rate(left) and Y a w Rate(right) Responses to Morphing Doublets . . . . . . . . . . . 31 6–1 V ie w of the 12 in MA V . . . . . . . . . . . . . . 33 6–2 V ie w of the 10 in MA V . . . . . . . . . . . . . . 34 6–3 W ing with K e vlar Threads . . . . . . . . . . . . . 37 i v

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6–4 Front V ie w of the 12 in MA V with Undeected (left) and Morphed (right) W ing . . . . . . . . . . . . . . . . . . 37 6–5 Doublet Command to Morphing Serv o . . . . . . . . . . 39 6–6 Roll Rate(left) and Y a w Rate(right) in Response to Morphing Doublet . 39 6–7 Second Doublet Command to Morphing Serv o . . . . . . . 40 6–8 Response to Second Morphing Doublet Command for Roll Rate(left) and Y a w Rate(right) . . . . . . . . . . . . . . 40 6–9 Simulated() and Actual(-) Roll Rate(left) and Y a w Rate(right) Responses to a Doublet . . . . . . . . . . . . . . 41 6–10 Simulated () and Actual (—) Roll Rate(left) and Y a w Rate(right) Responses to Morphing Doublets . . . . . . . . . . . 42 v

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Abstract of Thesis Presented to the Graduate School of the Uni v ersity of Florida in P artial Fulllment of the Requirements for the De gree of Master of Science CONTR OL OF MICR O AIR VEHICLES USING WING MORPHING By Helen Michelle Garcia December 2003 Chair: Richard C. Lind, Jr Major Department: Mechanical and Aerospace Engineering A micro air v ehicle (MA V) is typically dened to ha v e a wingspan of 6 in and operates with airspeeds of less than 25 mph Recent attention has been de v oted to MA Vs because there is a v ariety of applications for which the y can be used. Specically the y are useful in missions within urban en vironments. These missions require MA Vs to be v ery small and highly agile. These characteristics are achie v ed with the use of light materials such as carbon ber airframes and plastic membrane wings; ho we v er this design also causes these v ehicles to be dif cult to operate. This construction mak es them strong with good aerodynamic properties; ho we v er hinges for con v entional control surf aces are not easily implemented on e xible wings. Therefore, these v ehicles are strong and light b ut ha v e limited control authority A dif ferent control ef fector is then necessary in order to pro vide control authority This thesis will consider using wing morphing as a control ef fector Simple techniques are used to change the shape of the wings during ight such as twisting the wings of a 24 in MA V and curling the wings of a 12 in MA V Flight tests are then performed and sho w that morphing is an ef fecti v e w ay to induce roll motion. The data are then analyzed to consider linear modeling techniques as well as control design. The use of morphing vi

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results in a more ef fecti v e roll motion than the use of the rudder and impro v es the maneuv erability of the v ehicles. vii

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CHAPTER 1 INTR ODUCTION Recent adv ances in technology ha v e made the use of smart v ehicles in a v ariety of applications possible. These adv ances ha v e led to the de v elopment of small unmanned air v ehicles (U A V) as well as micro air v ehicles (MA V) which ha v e mission capabilities. These v ehicles can range in size according to their specic application. Small U A Vs and MA Vs can be designed to operate within urban en vironments. Their design typically depends on the mission in which the y will be used and can range from ci vilian to military applications. F or e xample, these v ehicles might be assigned to military missions such as bomb damage assessment, which w ould in v olv e transmitting video after a bomb has been dropped at a specic location. These v ehicles could also be used in w arf are as a means to ha v e li v e video of what is occuring ahead before ground troops are sent into the battleeld. There are also some ci vilian applications to MA Vs, such as transmitting video for traf c/ne ws co v erage, and to look in specic places for search and rescue missions. Other scenarios where MA Vs w ould be useful include assessing the damage caused by chemical spills, in search and aiding in rescue missions and e v en in trafc/ne ws co v erage. Some of these applications might require MA Vs to w ork in collaboration with other MA Vs in order to co v er a lar ge area of surv eillance. Another application where a MA V w ould be useful is if for e xample, there is a biological agent released into a public area. A biohazard team w ould ha v e to suit up and prepare before being able to enter the area for testing and clearing of the biological agent. Instead, a MA V can be released from a nearby station which can ha v e 1

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2 sensors on board, and be able to detect the e xtent of the contamination and the type of biological agent which w as released before an y humans ha v e arri v ed at the scene. The recent concern for terrorism being planned in urban en vironments such as small apartments leads to specic situations where MA Vs could be useful. Current technology cannot k eep track and observ e these small suspected areas. A MA V w ould be useful in this situation because it could y up to windo ws or e v en indoors and send li v e video and audio of the suspect acti vities. In order to accomplish the e v olving missions for which MA Vs can be used, their designs ha v e to be considered accordingly F or most military missions, the requirements typically demand that these v ehicles be v ery small and highly agile. The y are constructed of v ery light materials, such as carbon ber airframes and e xible membrane sheeting for wings. Ho we v er this v ehicle design does not allo w for con v entional control surf aces due to the comple xity of implementing hinges along the e xible membrane wings. The lack of con v entional control surf aces mak es these v ehicles dif cult to y Se v eral benets can be achie v ed by the use of additional control ef fectors. The implementation of wing morphing as an additional control ef fector is considered to increase controllability Simple techniques are considered to study the benets of using morphing as compared to the current control ef fectors which are used on MA Vs. This thesis will consider morphing as a control ef fector for a pair of micro air v ehicles with dif ferent dimensions. The v ehicles sho wn in Figure 1–1 with a 24 in wingspan and a 12 in wingspan will be used to demonstrate morphing for control. These v ehicles will be referred to as MA Vs, though their wings are lar ger than the denition implies, due to the similarities in design and construction. The MA V is an ideal platform for morphing because the po wer required is v ery small due to the e xibility of the wings, and there are se v eral benets including increased controllability

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3 Figure 1–1: MA Vs with 24 in (left) and 12 in (right) W ingspan W ing morphing on the 12 in MA V is actuated by connecting a strand of K e vlar to a serv o inside the fuselage and then to a location on the wing. This initial design only allo wed for morphing at a single location, which w as the wing outboard. Further testing led to the consideration of more dramatic morphing. The morphing of the wing w as made more dramatic by then adjusting an e xtra K e vlar strand to the serv os. This allo ws for morphing about the span and the trailing edge at the same time. The morphing is actuated on the 24 in MA V by use of torque rods which are connected from the fuselage to the wing outboard. These torque rods are connected to the wings by being se wn along the plastic sheeting of the wing. These rods are then actuated and in turn change the shape of the wings. Data is then collected with a data acquisition system which pro vides information with 3 accelerometers and 3 gyros along an orthogonal coordinate system of the v ehicle. This data is then processed to consider the response of the aircraft to the input commands. A linear model approximation is then done using the roll rate and ya w rate responses. The approximation is done using an ARX technique in Matlab using the responses. The approximation results in a good correlation of the coef cients when compared to the data which w as collected. The linear model for the 24 in MA V can then be approximated b ut the model of the 12 in MA V requires further research. This is

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4 due to the f act that the 24 in MA V is being morphed symmetrically so that a linear approximation can be made, b ut the 12 in MA V is morphed asymmetrically which requires a nonlinear study to be done.

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CHAPTER 2 MICR O AIR VEHICLES Micro Air V ehicles(MA Vs) are typically dened as v ehicles with a wingspan of less than 6 in and which operate with airspeeds of less than 25 mph The idea for a MA V is to ha v e a platform which is small, ine xpensi v e and that can be used in situations which are not suitable for lar ger v ehicles [ 14 ]. The rst succesfull design of a micro air v ehicle w as achie v ed by AeroV ironment. The y designed the Black W ido w MA V with funding from D ARP A. The Black W ido w is a MA V with a 6 in wingspan, airspeed of about 30 mph and weighs under 100 gr ams [ 13 ]. This v ehicle also has the capability of carrying a video camera which transmits li v e video to the ground and has an endurance of 30 minutes. It is also equipped with an autopilot, which is capable of performing altitude, airspeed, and heading holds as well as a ya w damper The transmitter and actuators are some of the smallest and lightest systems a v ailable. This design led to further interest and research in the eld of MA Vs from se v eral countries and uni v ersities. The Uni v ersity of Florida has been v ery acti v e in the design and testing of micro air v ehicles. Dr Peter Ifju has led a successful research team at the Uni v ersity of Florida in the area of MA Vs. The y ha v e been able to win v arious aspects of the annual MA V competition, which is sponsored by the International Society of Structural and Multidisciplinary Optimization. The MA V team at the Uni v ersity of Florida has succeeded in this competition each year from 1999 to 2003 with the v arious designs that ha v e been tested and ha v e w on the o v erall rst place a w ard. The annual MA V competition typically includes entries from se v eral uni v ersities around the w orld. The 2003 competition consisted of entries from 15 uni v ersities. 5

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6 Current MA V designs are based on a e xible wing design used at the Uni v ersity of Florida [ 14 ]. The most common design is an airframe constructed entirely of composite carbon ber The fuselage is typically a tw o-piece monocoque structure designed to house ight components and instrumentation. The ight components include serv os and connectors, and some of the instrumentation used in ight includes orientation systems. A con v entional empennage is af x ed to the fuselage with ele v ators and rudders hinged to the horizontal and v ertical stabilizers. The MA Vs are equipped with sensors for measurement consisting of 3-axis gyros and 3-axis accelerometers along with the serv o command. The sensing and actuation data is recorded on an on board data acquisition board which weighs 7 gr ams and w as de v eloped by N ASA Langle y Research Center specically for MA V applications [ 1 ]. This micro data acquisition board is capable of recording 27 analog channels which is suf cient for the current sensor package. The data is then a v ailable at 50 to 100 Hz and is resolv ed using a 12-bit analog-digital con v erter The data is recorded in a 4 MB ash chip on board the data acquisition board and is then do wnloaded to a PC at the end of each ight. The v ehicles use an electric motor for propulsion and the duration of ights depend on the amount of batteries which can be carried and the throttle setting on the motor On a v erage, ights ranging from 10-15 minutes are easily achie v ed for the 24 in and 12 in MA Vs which are considered. Structures used in ight, both in biological and aircraft applications, are e xible by a certain amount. F or aircraft to be able to withstand the lar ge forces obtained during ight; ho we v er the wings ha v e to be strong enough. Flight of birds also consists of e xible wings which can adapt to the changing en vironments the y y in. Birds ha v e man y layers of feathers which can be mo v ed around in order to adjust to the specic maneuv er the y need to perform [ 22 ]. The use of apping for ight, such as done by birds, has not been e xtensi v ely studied. This has

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7 not been done due to the comple xity of the ight mechanics which includes changing geometry e xible surf aces and unsteady aerodynamics. The e xible membrane wings together with the size constraints of MA Vs mak e analysis and design of these v ehicles v ery challenging. Specically the aerodynamics of a MA V are complicated by lo w Re ynolds number ight, lar gely deforming structures, the ef fects of viscosity and o w separation at high angles of attack [ 22 ]. The f act that the MA Vs are challenging to design pro vides a good platform for research in the areas of dynamics and control, aeroserv oelasticity structures, microelectronics, small actuation and data acquisition systems, and other elds. The research and de v elopment of these v ehicles has progressed rapidly due to the a v ailability of smaller electronics as well as the adv ances in lighter materials. Se v eral of these v ehicles are sho wn in Figure 2–1 Figure 2–1: Members of MA V Fleet at Uni v ersity of Florida Adv ances in miniature digital electronics, communications and computer technologies ha v e made sensing capabilities on micro air v ehicles possible. A typical application of these miniature electronics is in a reconaissance mission where a small MA V w ould be preferred to a lar ger v ehicle in order to remain stealthy The use of inno v ati v e control ef fectors is an area being e xplored as an enabling technology for designing a stability augmentation system. The current generation of MA Vs uses traditional ef fectors, specically an ele v ator and rudder whose positions are commanded by the remote pilot. The ele v ator presents adequate ef fecti v eness for longitudinal control b ut the rudder presents some dif culty for lateral-directional control.

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8 The rudder mainly e xcites the dutch roll mode so steering and gust rejection are really accomplished using the coupled roll and ya w motion resulting from dutch roll dynamics. Such an approach is ob viously not optimal b ut traditional ailerons are not feasible on this type of aircraft. Actuation of the MA V control surf aces is accomplished with tw o control ef fectors or serv os mounted inside the fuselage. These de vices actuate the control surf aces by rotating an arm and pushing or pulling a pushrod when a deection is commanded. Research in the design and testing of these v ehicles has been done in se v eral countries and uni v ersities. Research of micro air v ehicles has also been done e xtensi v ely at N ASA. Specically N ASA has considered a control assesment and simulation of a micro air v ehicle with aeroelastic wings which adapt to the disturbances during ight [ 23 ]. This w as done using aerodynamic data which w as obtained in pre vious testing of a MA V [ 24 ].

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CHAPTER 3 MORPHING The concept of morphing is not an idea which has been strictly dened. A morphing aircraft is generally dened to be an aircraft whose shape changes during ight to optimize performance. T ypes of shape changes include span, chord, camber area, thickness, aspect ratio and planform. The morphing can also be applied to a control surf ace in order to eliminate hinges. Morphing can be used as a control ef fector by changing the shape of the aircraft in order to alter the ight dynamics. The concept of morphing has been look ed at by D ARP A and N ASA to sho w the aerodynamic benets; ho we v er the use of morphing for control design has not been studied e xtensi v ely The wing morphing techniques for the MA Vs in this project consider using serv os which are attached to the wings. Aircraft ha v e pre viously used techniques for adapting their shape depending on the specic ight characteristics desired. The use of morphing as a control ef fector w as used initially on the Wright Flyer where the pilot used cables to twist the wings in order to achie v e the desired motion. W ing w arping did not become a common technique; ho we v er due to the po wer which is required from actuators to change the shape of the wings [ 21 ]. Morphing is also used on the F-14 which has a v ariable sweep on the wing, therefore changing the shape of the wing during ight. The wings are swept in order to balance the range and speed by slo wing do wn the increase in drag which de v elops as v elocity increases [ 21 ]. There are dif ferent w ays that an aircraft can be morphed which are appropriate for control. The current research will focus on morphing of the wings in order to consider 9

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10 primarily control issues. The ight characteristics of birds will be considered as a guide since the y also change the shape of their wings to achie v e certain maneuv ers. Man y mechanisms which consider morphing ha v e been designed b ut ha v e not been tested in ight v ehicles. N ASA has designed a wing which changes the camber of the wing [ 6 ]. One of the wings considered is referred to as a Hyper -Elliptic Cambered Span (HECS) because the curv ature along the span is continuously changing. This pro vides a lar ger area which allo ws for greater lift. This v ehicle uses a hinge-less panel along the trailing edge of the wing as a form of a control surf ace for pitch and roll. The simulations demonstrated the aerodynamic benets b ut also sho w this v ehicle has unstable lateral-directional dynamics. The use of smart materials such as shape memory allo ys and piezos ha v e been considered in the design of morphing wings b ut there is still a limit in that not enough force can be produced in order to twist lar ge wings using these mechanisms. Ho we v er smart spars ha v e been b uilt which pro vide dif ferent types of morphing b ut ha v e not been tested on ight v ehicles [ 2 ]. Another mechanism for morphing which has been studied considers changing the sweep of the wings of a small unmanned air v ehicle (U A V) [ 7 ]. The morphing on this U A V is done in order to meet changing mission requirements. Actuation of the morphing is done by using inatable actuators which are po wered with compressed air One of the benets of this project is that the actuation mechanism used is much lighter than the typical hydraulic systems that are used on full scale aircraft. The ef fects of the sweep are then studied considering the change of aspect ratio, lift and drag. Similarly a study has been done considering an inatable telescopic spar which can be morphed spanwise [ 4 ]. This design allo ws for changes in the aspect ratio while still pro viding enough support from the spars for the airloads which are being applied. This is achie v ed because the telescopic spar is pressurized and the telescopic skins

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11 maintain the geometry of the airfoil as well as pro vide ef fecti v e storing and deplo yment of the mechanism. Also for the purpose of considering impro v ed maneuv erability and performance, roll maneuv ers ha v e been studied using a e xible wing [ 16 ]. Numerical studies were used to consider the aerodynamic loads on a e xible wing at high speeds. W ing twist is also considered in order to reco v er the rolling moment lost b ut has not been tested in ight. This is due to the challenges in v olv ed in implementing a functioning mechanism for wing twist on a full scale aircraft. Research has also been done considering the material aspects of shape changing with a nite element model of a wing [ 17 ]. This considered roll maneuv ers using a piezoelectric material as an actuation mechanism with aerodynamic loads being applied. Piezoelectric sensors and actuators are useful for this application because the y are light, ha v e a small v olume and can achie v e v arious shapes. This technique has not been tested; ho we v er due to the lar ge deections that are needed from such small actuators. Numerical studies ha v e considered structural and aerodynamic modeling for shape changing wings [ 12 ]. These considered a generic lambda wing such as used in unmanned combat air v ehicles (UCA V). The dif ferent mode shapes were studied to consider structural modeling. This model w as then used to study the roll performance of the morphing wing. It w as sho wn that this wing with hinge-less control surf aces sho ws impro v ed roll performance because of the aerodynamic and structural benets. As mentioned pre viously there are se v eral benets such as impro v ed performance due to the use of wing morphing. Also, morphing is easily achie v ed on MA Vs because the wings are constructed of e xible membrane material. The e xible wings can be grossly deformed via mechanical actuation yet are capable of withstanding ight loads. The e xible nature of the wing also gi v es rise to the mechanism of adapti v e w ashout which permits small changes in wing shape in response to gusty wind conditions.

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12 F or this project, morphing is limited to changing the shape of the wings, not of the entire airframe. This type of morphing can be studied with the use of biologically inspired techniques. The dif ferent w ays that birds change the shape of their wings during ight is studied and compared with morphing techniques. Consider for e xample, the birds in Figure 3–1 These birds typically change the shape of their wings depending on the types of maneuv ers that the y need to perform. Figure 3–1: A Gull (left) and Sno wy Owl (right) in Flight Certain techniques of morphing for aircraft can be designed by studying these birds. There are se v eral morphing techniques which are used by these birds that demonstrate ho w their ight maneuv ers can be changed, such as loitering, di ving and tak e-of f. The wings of birds are shaped similarly to airfoils and ha v e the same basic function [ 8 ]. Certain birds use their wings more often than others who just y for short periods of time. Also, the en vironment the birds are in can af fect the aerodynamics of the ight, therefore birds ha v e dif ferent shapes of wings. The aspect ratio of the wings of birds is measured as the square of the span of the wing di vided by the area of the wing. This ratio can v ary depending on the specic technique for ying of each bird. F or e xample, long wings pro vide a smoother gliding motion b ut it tak es more ener gy to ap them quickly therefore the y are not useful for increasing speed. Therefore, birds with longer wings tend to use gliding as their primary method of ight. W ing loading can also af fect ho w a bird ies since the ener gy required to ap their wings also depends on ho w hea vy the y are.

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13 Consider for e xample, Figure 3–2 which sho ws the wing design for four dif ferent birds [ 8 ]. The lo wer aspect ratio wings, such as for a pheasant, typically allo w for quick tak e of f and slo w ights, b ut are not useful for gliding. The slightly lar ger aspect ratio wings, such as for eagles, are typically longer and ha v e feathers which are adjusted as a type of control surf ace for more precise maneuv ering. The wings for w aders, with a typical aspect ratio of 12.5, are useful for f aster speeds and gliding b ut do not allo w for f ast tak e of f. This limit on a f ast tak e of f is because a lot of ener gy is required to ap these longer wings. The higher aspect ratio wings, as for gulls, are typically useful for gliding close to surf aces such as sea and land and tak e adv antage of the winds in order to conserv e ener gy These are only a fe w of the man y dif ferent designs of wings which v ary depending on the migration patterns of each bird. Figure 3–2: Aspect Ratio of Bird W ings Some biologically inspired techniques can be applied to MA Vs. The span of the wings, the horizontal distance from the tip of a wing to the tip of the other can be altered to create a shorter wing for e xample. Birds and bats are also capable of changing the span of their wings to decrease the area, therefore increasing the forw ard v elocity and reducing drag. The chord, which is the distance from the leading edge to the trailing edge, can also be altered. The wing can also be morphed by twisting or rotating parts of the wing in order to af fect aerodynamic performance.

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14 Another type of morphing is sweeping the wing either at an elbo w joint on the wing or at the root of the wing. This pro vides a type of wing sweep which tak es a similar shape change as seen in birds. The area of the wing can also be changed by e xtending the length or trailing edge as some birds do. The aspect ratio is also af fected by the morphing and can be used to consider lift and drag for aerodynamics. A simple form of morphing is a wing twist. This is currently being used for control on the Acti v e Aeroelastic W ing (AA W) as well as the v ehicles in this project. The morphing on the AA W causes the wings to be twisted in response to the moments induced by the control surf aces. Birds and bats also do this in order to obtain the required lift or thrust during ight. Morphing on the MA Vs is accomplished by actuation of control ef fectors located inside the fuselage. These serv os are connected to the wings by either use of a torque rod or K e vlar strand. The wing morphing is actuated by mo ving the arm which rotates the tube or pulls the strand and changes the shape of the wing. Certain maneuv ers are of interest when considering the ef fects of wing morphing on a MA V The ight test maneuv er of interest is a control doublet for both rudder and wing shaping controls. The rudder doublet is being applied only to the 24 in MA V since the 12 in MA V consists of only ele v ator and wing morphing control ef fectors. These maneuv ers are performed by commanding a constant left deection for a certain time period follo wed immediately by a right deection for the same time period and nally returning to the neutral position. Aircraft response characteristics to the control input are then determined by analysis of the serv o position and rate responses. W ing-shaping control doublets induce a dif ferent beha vior of the MA V The response of the airplane to wing shaping is similar in nature to responses from ailerons. Essentially the aircraft response to the morphing is predominantly roll motion with little ya w or pitch coupling. Thus, the doublets are performed without considerable directional or altitude de viation.

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15 F ollo wing the completion of the maneuv er which resembles rocking the wings, the airplane is in a bank ed attitude. Reco v ery from the wing shaping doublet is considerably easier than that of the rudder doublet. Such a response indicates the wing shaping e xcites the roll con v er gence mode. Clearly the MA V requires a stability augmentation system to f acilitate operation and greatly e xpand its mission capability In general, lateral maneuv ers are particularly dif cult because the MA V is so responsi v e. The introduction of a controller w ould lessen pilot w orkload for trajectory tracking. The design of a controller is the ne xt step in the research of f acilitating the ability to operate these MA Vs with the aid of acti v e wing morphing. Future research will also enable de v elopment of a vision-based autopilot system currently being studied [ 9 ]. Open-loop ight tests were performed using wing morphing as an actuation mechanism. These ight tests demonstrate the v alue of morphing for consideration of a stability augmentation system. The rudder can be used to generate lateral maneuv ers b ut the tight coupling of roll and ya w complicates the control needed for trajectory tracking. Con v ersely the morphing produces almost pure roll so an associated controller for tracking roll commands will be the rst to be implemented.

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CHAPTER 4 MODELING A model of a system can be described by comparing the relationship between the signals which are observ ed [ 19 ]. A model can be de v eloped with the use of data which is collected in e xperiments. System identication considers the de v elopment of the model of a system with the use of observ ed data. F or this purpose the signals typically considered are the output signals, which are measured, as well as the input signals, which consider the ef fect the observ er has on the response of a system. Other signals which can be considered are outside disturbances, which are signals that are produced from outside sources such as noise, wind gusts and sensor drift. A model is therefore a mathematical description of a system considering se v eral aspects b ut is not an e xact description of the physical system [ 19 ]. System identication is performed by rst collecting data which emphasizes the parameters that are to be considered in the model estimation. Therefore, the input and output signals as well as specic maneuv ers are selected prior to the data collection. F or some systems it is useful to describe the models using graphical interpretations. More specically the y can be described using impulse, step and frequenc y responses. Certain systems can also be described using mathematical models. These can include continuous-time and discrete-time systems as well as linear and nonlinear systems. A set of models can then be selected according to the specic application or dynamic system. A model which uses a black box approach is used for this project. This approach considers the input and output signals of the system in order to perform a t to the data without pro viding physical meaning to the v alues. This model is then 16

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17 compared with the v alues obtained in the e xperiment in order to determine whether it is a good estimation of the system response. The black box model structure which considers input and output signals can be e xpressed as the linear equation sho wn in 4.1 where e(t) is the noise error term. yta 1 yt1a n a ytn anb 1 ut1b n b utn bet(4.1) Then this equation can be e xpressed in terms of the initial output signal as sho wn in 4.2 yt a 1 yt1 a n a ytn ab 1 ut1b n b utn bet(4.2) This is typically referred to as an ARX model, which denes the autore gressi v e part to be the output terms in 4.2 and the input terms in 4.2 as the e xtra input. So the initial output v alues as well as the input and output terms on the right hand side of 4.2 are collected in matrix form for each time interv al. This mak es it possible to solv e for the re gression coef cients since the initial output and the input v alues are kno wn. The initial output v alues for each time interv al can be e xpressed as in 4.3 in terms of the input and output v alues as well .r y t y t1y tn r y t 1y t n a u t 1 u t n by t1 1y t1 n a u t1 1 u t1 n b y tn 1y tn n a u tn 1 u tn n b r a 1 a n ab n b (4.3)

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18 Then the re gression coef cients are obtained by using the matrix equation 4.4 and solving for the matrix of coef cients X as sho wn in 4.5 BAX (4.4) A1 BX (4.5) A transformation as sho wn in 4.6 is then applied to equation 4.1 in order to obtain a transfer function as sho wn in 4.7 In this transfer function the B term contains all the input coef cients from equation 4.6 and the A terms consists of all the coef cients in the output terms. yta 1 z1 yta n a zn a ytb 1 z1 ut b n b zn b utet(4.6) yu1B A1 (4.7) A T ustin transformation is then done using Matlab in order to create a continuous time v ersion of the discrete time system. This is done using a standard bilinear transformation such as sho wn in 4.8 z12sT22sT222sT23(4.8) The ARX model approximation is just one of se v eral types of model structures which can be used for system identication. An ARMAX model structure can similarly be used b ut w as not used in this project because an initial simple estimation w as desired. The ARMAX model considers the basic properties that the ARX model uses b ut also includes a mo ving a v erage term, which considers the noise in its coef cient calculations.

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19 Another modeling technique considers recursi v e identication methods. This considers calculating a model simultaneous to obtaining data. Ho we v er this is not a requirement for this specic project b ut can be useful in dif ferent applications. Certain applications include ha ving an up to date model in order to consider these parameters when making decisions about what the system is to do ne xt. This is typically referred to as an adapti v e modeling technique because the input and output signals are calculated in order to be used as the y become a v ailable. An e xample of a recursi v e model which can be used for system identication in Matlab is the RARMAX model. This uses a recursi v e technique of an ARMAX model which considers the noise in its calculations. Ho we v er this technique only pro vides models for single-input, single-output systems. Similarly another technique is the RARX model which estimates parameters recursi v ely of a single-output system. Therefore, for this project an initial linear approximation w as done using an ARX technique. The initial step w as to design an e xperiment which consisted of specied maneuv ers such as doublets to the morphing and rudder serv os. These were done in order to consider the roll and ya w rate responses of the system. The data is then collected and processed before considering it for modeling. The data processing included using an algorithm which plotted, ltered and remo v ed the bias in the data. The ltering w as done using a lo w pass Butterw orth lter on all the parameters and the bias w as remo v ed from the parameters by subtracting the mean. This processed data is then used in the ARX modeling approximation. The roll rate and ya w rate responses are then compared to the simulation responses. This is done for both the morphing and rudder serv os. The orders and delays are selected for the parameter estimation.

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20 The orders of the approximation are the orders of the polynomials A and B in equation 4.7 Therefore, the y are the orders of the polynomials in equation 4.9 and equation 4.10 Az1a 1 z1 a n a zn a (4.9) Bzb 1b 2 z1 b n b zn b1 (4.10) The delays which are referred to as nk are selected as the number of delays from input to output as sho wn in equation 4.11 Azyt Bzutnket(4.11) In multi-output systems, the orders of the polynomials ha v e as man y ro ws as outputs. This is then used to create the simulation and it is then con v erted to a continuous time system from a discrete time system. The roll rate and ya w rate responses are then compared and for this project sho w a good correlation between the estimated and the actual data for the doublet maneuv ers. The follo wing step in system identication w ould be to v alidate the model which w as chosen as the best approximation to the data. This is done by considering whether the model is a good enough approximation for what it will be used for In other w ords, whether the model can be trusted to reproduce the collected data. A model is typically not accepted as describing the actual true system, b ut simply as a good description of specic parts of the system which are of interest. The rst model obtained using these techniques typically has to be re vised because it may not describe a system considering se v eral dif ferent aspects. P articularly for this project the models were obtained by considering the inputs and outputs of the

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21 system and then reproducing that data. Ho we v er the model obtained does not describe physical parameters which can be used for purposes of further control design. A model which w ould be useful for control design w ould include approximations of certain aerodynamic parameters and time constants. These parameters can then be used to design a controller as well as considering the modes. Once the system is represented in physical parameters, controllers such as roll and ya w dampers can be designed by feeding back the appropriate angles. This can be done by using a simple proportional gain in the closed loop system.

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CHAPTER 5 24 in MICR O AIR VEHICLE 5.1 V ehicle Description One of the v ehicles considered is the micro air v ehicle with a 24 in wingspan sho wn in Figure 5–1 Figure 5–1: Ov erhead V ie w of the 24 in MA V The 24 in MA V consists of a carbon composite frame with a mylar membrane skin wing. The leading edge of the wings consist of carbon-ber wea v e with battens of unidirectional carbon attached to the underside and e xtending to the trailing edge. These battens pro vide the strength needed to support the airloads which are being applied while the membrane pro vides the lifting surf ace. The original control ef fectors for this MA V are the rudder and ele v ator The rudder and ele v ator each ha v e a single serv o for actuation. The control surf aces, the ele v ator and rudder are connected to the serv os using a spring steel pushrod. The approximate range of motion for each is gi v en in T able 5–1 22

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23 T able 5–1: Range of control ef fectors Ef fector Range of Motion ele v ator15 o to20 o rudder25 o to25 o The basic properties of the 24 in MA V are gi v en in T able 5–2 T able 5–2: Properties of the 24 in MA V Property V alue W ingspan 24” W ing Area 100 in 2 W ing Loading 20.32 ozf t 2 Aspect Ratio 5.76 Po werplant Electric motor w/ 4.75” propeller T otal W eight 400 g 5.2 Morphing W ing morphing is used as an additional control ef fector A simple technique is used to morph the wings of the 24 in MA V The morphing is actuated by tw o serv os, one for each wing. The technique used for morphing on this v ehicle consists of the use of a torque rod which produces the deection that is commanded. This torque rod lies along each wing connected to the serv os inside the fuselage as sho wn in Figure 5–2 Figure 5–2: W ing with T orque Rod The rods are se wn into the leading edge of the membrane therefore causing mo v ement of the membrane if the rods are actuated. The ef fect of the morphing is seen

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24 to act as a simple form of wing w arping. The wing deection due to the morphing actuators for the 24 in MA V is sho wn in Figure 5–3 Figure 5–3: Rear V ie w of the 24 in MA V with Undeected (left) and Morphed (right) W ing 5.3 Flight T esting Flight testing of the acti v e wing-shaping 24 in MA V is performed in the open area of a radio controlled (R/C) model eld during which wind conditions range from calm to 7 knots throughout the ights. Once the ight control and instrumentation systems are po wered and initialized, the MA V is hand-launched into the wind. This launch is an ef fecti v e method to quickly and reliably allo w the MA V to reach ying speed and be gin a climb to altitude. This airplane is controlled by a pilot on the ground who maneuv ers the airplane visually by operating an R/C transmitter There is a data acquisition system on board which be gins recording as soon as the motor is po wered. This D A Q system records accelerations and rates about the coordinate system which is centered on the MA V This aircraft design allo ws either rudder or wing shaping to be used as the primary lateral control for standard maneuv ering. The airplane is controlled in this manner through turns, climbs, and le v el ight until a suitable altitude is reached. At altitude, the airplane is trimmed for straight and le v el ight. This trim establishes a neutral reference point for all the control surf aces and f acilitates performing ight test maneuv ers.

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25 Open-loop data is tak en to indicate the ight characteristics of the MA V Specically the roll and ya w rates and accelerations about a body x ed axis are measured in response to doublets commanded separately to the serv os. Se v eral sets of doublets are commanded ranging in magnitude and duration to obtain a di v erse set of ight data. The dynamics of the MA V in response to rudder commands is in v estigated to indicate the performance of the traditional conguration for this MA V A representati v e doublet command is sho wn in Figure 5–4 The roll rate and ya w rate measured in response to this command are sho wn in Figure 5–5 The roll rate is lar ge and indicates the rudder is able to pro vide lateral-directional authority; ho we v er the ya w rate is clearly lar ger than the minimal amount which can be e xpected. Actually the ya w rate is close in magnitude to the roll rate so the lateral-directional dynamics are v ery tightly coupled. The ef fect of the rudder in e xciting the dutch roll dynamics is clearly seen in this response. 0 1 2 3 4 5 6 15 10 5 0 5 10 15 Time(sec)Rudder Command Figure 5–4: Doublet Command to Rudder Serv o 0 1 2 3 4 5 200 150 100 50 0 50 100 150 Time(sec)Roll Rate (deg/sec) 0 1 2 3 4 5 200 150 100 50 0 50 100 150 Time(sec)Yaw Rate (deg/sec) Figure 5–5: Response to Rudder Doublet for Roll Rate(left) and Y a w Rate(right)

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26 Another doublet is commanded to the rudder in order to consider its response. The rudder is commanded with a slightly lar ger magnitude and longer duratio doublet which is sho wn in Figure 5–6 The response to this doublet command is sho wn in Figure 5–7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 20 15 10 5 0 5 10 15 Time(sec)Rudder Command Figure 5–6: Second Doublet Command to Rudder Serv o 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 200 150 100 50 0 50 100 150 200 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 200 150 100 50 0 50 100 150 200 Time(sec)Yaw Rate (deg/sec) Figure 5–7: Response to Second Rudder Doublet for Roll(left) and Y a w Rate(right) This sho ws a similar response as with the rst doublet to the rudder serv o. It sho ws a roll rate response of similar magnitude as the ya w rate. This then describes a dutch roll motion instead of a pure roll motion e v en with a slightly lar ger command to the rudder Also, since the doublet w as of lar ger magnitude and longer duration, this w ould indicate that the v ehicle could be de viating f arther from trim than in the pre vious maneuv er which w ould result in greater nonlinearities such as increased ya w motion. Doublet commands such as sho wn in Figure 5–8 are used in order to actuate the morphing serv o. This maneuv er is done without an y input from the rudder in order to

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27 consider strictly commands to the morphing actuators. The amount of deection of the morphing; ho we v er is dif cult to interpret because it is a deection of the material and it is not e xpressed in a physical dimension such as de grees. 0 0.5 1 1.5 2 8 6 4 2 0 2 4 6 8 Time(sec)Morphing Command Figure 5–8: Doublet Command to Morphing Serv o 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)roll rate (deg/s) 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)yaw rate (deg/s) Figure 5–9: Response to Morphing Doublet for Roll(left) and Y a w Rate(right) The roll rate and ya w rate in Figure 5–9 are measured in response to the doublet commanded to the morphing serv o. These measurements indicate the roll rate is considerably higher than the ya w rate. Thus, the morphing is clearly an attracti v e approach for roll control because of the nearly-pure roll motion measured in response to the morphing commands. A separate morphing doublet is commanded at a dif ferent time as sho wn in Figure 5–10 in order to consider the modeling for a dif ferent maneuv er Similarly this maneuv er consists of strictly morphing actuation and no rudder input.

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28 0 0.5 1 1.5 2 2.5 8 6 4 2 0 2 4 6 8 Time(sec)Morphing Command Figure 5–10: Second Doublet Command to Morphing Serv o The roll rate and ya w rate responses to the second morphing doublet are sho wn in Figure 5–11 It can be seen that the morphing doublet commanded in the second maneuv er w as of a slightly lar ger magnitude than the rst maneuv er This results in a lar ger roll rate response due to a lar ger morphing deection. 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 200 150 100 50 0 50 100 150 200 Time(sec)Yaw Rate (deg/sec) Figure 5–11: Response to Second Morphing Doublet Command for Roll Rate(left) and Y a w Rate(right) It is also seen that there is a minimal ya w rate response from the actuation of a lar ger morphing deection. Therefore, it similarly resulted in an almost pure roll motion with a slightly f aster roll rate response than with the pre vious maneuv er 5.4 Modeling The data from open-loop ights is then used to approximate a linear time-domain model using an ARX approximation [ 18 ]. This model is generated by computing optimal coef cients to match properties observ ed in the data.

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29 The maneuv ers of interest are doublets ranging in magnitude and centered around a trim condition. Therefore, the assumption of linearity is reasonable since the maneuv ers are about trim. F or the approximation, the rates which are considered are roll and ya w rate because the y are of most interest for maneuv ers such as doublets. The accelerometers were considered b ut the data w as v ery noisy therefore, not allo wing for accurate approximations to be made. The simulated and measured v alues of roll rate and ya w rate are sho wn in Figure 5–12 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)Yaw Rate (deg/sec) Figure 5–12: Simulated ( ) and Actual (—) Roll Rate(left) and Y a w Rate(right) Responses to Morphing Doublet The simulated responses sho w good correlation with the actual data. The model is thus considered a reasonable representation of the aircraft dynamics as it is e xcited by the doublet. The e xistence of such a model is important for future design of autopilot controllers b ut it is also v aluable for interpreting the morphing. When using the ARX simulation in Matlab, a linear approximation could not be made on the maneuv ers which were not centered around trim. Therefore, not only are maneuv ers around trim desired for a linear approximation, b ut the y are also necessary in order for the simulation to be done. The model which will be used w as chosen because it produced the closest match to the maneuv er as compared to four other doublets. The maneuv ers compared were from the same data set, b ut the one that w as chosen resulted in a closer match due to

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30 the aircraft being closer to trim. The resulting model consists of six states and poles as sho wn in T able 5–3 The roll mode is clearly sho wn and the dutch roll mode indicates the slight oscillations which are present in the combined roll and ya w motion as sho wn in Figure 5–12 T able 5–3: Poles of a linear model of the 24 in MA V Poles V alue Dutch Roll3751384 Roll -4.03 In order to study whether this model is a good enough linear approximation of the dynamics of the 24 in MA V dif ferent inputs are considered for the same model. These inputs are doublet morphing commands at dif ferent times throughout the same set of data. The simulated and measured v alues of roll rate and ya w rate are sho wn in Figure 5–13 for se v eral inputs. It is clearly sho wn that the simulated and actual roll rate and ya w rate responses demonstrate good correlation. The simulations sho wn in Figure 5–13 sho w that the model which w as obtained from a doublet maneuv er responds well to dif ferent inputs. The rst input w as a small morphing doublet commanded from a separate data set. The follo wing tw o inputs were from a medium and lar ge morphing doublet, respecti v ely from the data set that w as used for obtaining the model.

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31 0 0.5 1 1.5 2 2.5 3 3.5 4 200 150 100 50 0 50 100 150 200 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 200 150 100 50 0 50 100 150 200 Time(sec)Yaw Rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 200 150 100 50 0 50 100 150 200 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 200 150 100 50 0 50 100 150 200 Time(sec)Yaw Rate (deg/sec) 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 200 150 100 50 0 50 100 150 200 Time(sec)Yaw Rate (deg/sec) Figure 5–13: Simulated ( ) and Actual (—) Roll Rate(left) and Y a w Rate(right) Responses to Morphing Doublets 5.5 Ev aluation If this MA V is to be used in surv eillance missions, the use of only rudder and ele v ator could pro vide suf cient control during turns. Ho we v er the resulting dutch roll motion creates dif culties if this MA V is to be used for a more demanding mission and also requires more pilot control. Therefore, this v ehicle requires further control in order to be used in situations such as in urban en vironments where more controlled turns are required.

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32 Using wing twisting as an additional control ef fector for roll impro v es the performance and controllability of the aircraft. Using wing twist additionally as compared to the traditional rudder and ele v ator results in impro v ed ight path tracking, especially when considering gusty weather en vironments. The ight characteristics of the 24 in v ehicle are actually quite impressi v e to vie w The measurements of roll rate and ya w rate indicate the mathematical nature of the characteristics; ho we v er a qualitati v e e v aluation is also useful. Such an e v aluation is best achie v ed in association with step commands gi v en to each serv o. The step to the rudder causes the airplane to roll b ut the coupled ya w results in a ight path similar to a corkscre w spiral. Con v ersely the step to the morphing causes the airplane to roll with a minimum of ya w so the ight path is nearly a straight line. In other w ords, the morphing induces almost pure roll and allo ws much more accurate tracking of desired ight paths. Also, the morphing results in considerably higher roll rates than the rudder This result is quite interesting gi v en that the rudder deection is quite lar ge b ut the morphing, as sho wn in Figure 5–10 is not o v erly commanded to deect. Thus, a small amount of morphing is suf cient to cause a dramatic response from the aircraft.

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CHAPTER 6 12 in MICR O AIR VEHICLE 6.1 V ehicle Description A dif ferent micro air v ehicle is also considered. This v ehicle has a wingspan of 12 in and is sho wn in Figure 6–1 Figure 6–1: V ie w of the 12 in MA V The basic properties of this v ehicle are gi v en in T able 6–1 T able 6–1: Properties of the 12 in MA V Property V alue W ingspan 12” W ing Area 44 in 2 W ing Loading 14.19 ozf t 2 Aspect Ratio 3.27 Po werplant Electric motor w/ 2.25” propeller T otal W eight 123g The 12 in MA V is designed to ha v e an ele v ator as its control ef fector The ele v ator is actuated by using a single serv o. Therefore, this v ehicle does not include a rudder and an additional control ef fector will be added. 33

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34 This v ehicle is constructed using the similar designs which are used at the Uni v er sity of Florida which consist of carbon ber airframes and e xible membrane wings. The composite wing on the 12 in MA V sk eleton is co v ered with an e xtensible membrane skin of late x rubber The late x material used in the 12 in MA V is considerably more e xible than the mylar sheeting which is used in the 24 in MA V 6.2 Morphing The 12 in MA V is designed with morphing as an additional control ef fector The morphing is implemented by actuating a single serv o which is connected to each wing. The use of a more e xible material for the wing surf ace of this v ehicle w as chosen on purpose in order to consider more dramatic shape changes of the wings. This is also done on a smaller airframe without a rudder to consider strictly the ef fects of morphing. Figure 6–2: V ie w of the 10 in MA V The initial implementation of this morphing strate gy w as originally attempted on a MA V with 10 in wingspan as sho wn in Figure 6–2 The 10 in MA V is designed with a similar carbon ber airframe and e xible membrane wings. The f act that this aircraft is smaller than the 12 in MA V allo ws for a smaller wing area and shorter more closely aligned wing battons. This v ehicle, lik e the current v ehicle, has late x co v ering on the wings so w as v ery easy to morph in ight. The 10 in MA V w as chosen for the initial

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35 study because it w as already constructed and could be readily adapted for the ne w study The ights of that v ehicle were quite promising and clearly indicated that the morphing pro vided an ef fecti v e form of control authority This MA V responded well to the wing morphing commands, ho we v er is restricted in the amount of ight testing which can currently be done due to its payload limitations. This led to the design of the 12 in MA V with the requirement of a lar ger aircraft in order to carry the required instrumentation to perform open-loop and closed-loop ight testing. The design of the 12 in MA V initially follo wed closely the design of the 10 in MA V with a similar airframe and wing design. The open-loop ights are similarly performed with a data acquisition board and the closed-loop ights will be done with a memory board. The 12 in v ehicle w as essentially a scaled v ersion of the original v ehicle e xcept for the wing construction. The original v ersion had a single structure for the wings that mounted atop the fuselage. The ne w v ersion had separate wings that attached to posts on each side of the fuselage. This separation of the wings allo wed for more e xibility due to the remo v al of the carbon ber structure. The leading edge of the 12 in MA V w as initially b uilt with a single layer of carbon ber This pro v ed to be f aulty during the rst attempts at ight when the leading edge w ould fold o v er when wing loads were applied. Therefore another layer of carbon ber w as applied to the wing making it stif fer and better capable of withstanding the wing loads. Another issue with the wing design w as using the same e xible late x material on this 12 in as on the 10 in MA V with the lar ger airframe requiring a lar ger wing area. The wing battons are not as closely aligned on the lar ger frame and the lar ger sheet of late x is weak er with lar ger loads. Therefore not allo wing for wing morphing as dramatic on the 12 in as on the 10 in MA V

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36 Further ight testing of the 12 in MA V indicated a problem with the thread connection. The morphing of the 10 in MA V used only a single thread attached to the outboard of the trailing edge and this style w as used for the 12 in MA V Unfortunately the battens on the lar ger MA V were spaced f arther apart than on the smaller MA V so the wing w as weak er The leading edge on the 12 in MA V w ould no w remain properly shaped b ut the trailing edge w ould collapse when loaded. This problem w as addressed by attaching a second thread to the trailing edge of the wing and allo wing the morphing actuation to pro vide strength to support the loads. The 12 in MA V is designed to allo w for a more complicated type of morphing than is used for the 24 in MA V The wings of this smaller v ehicle are constructed from late x sheeting whereas the wings of the lar ger v ehicle are made of mylar sheeting. Consequently the wings of the 12 in v ehicle are considerably more e xible, and thus easier to morph, than the wings of the 24 in v ehicle. This e xibility allo ws simple mechanisms to again be appropriate for generating morphing and allo w control issues to be in v estigated. The high e xibility of the wings for this MA V allo w consideration of morphing be yond basic w arping. More specically this v ehicle is used to consider morphing that af fects the twist and span of the wings. A torque rod, as used for the 24 in MA V w ould clearly not be appropriate for such a morphing. Instead, the rod w as replaced with threads. The morphing strate gy for this MA V is sho wn in Figure 6–3 K e vlar threads are strung between a serv o in the fuselage and points near the outboard of the wings. These threads are incredibly strong and the minor stress recei v ed during ight is not suf cient to cause an y stretching. The morphing achie v ed by this strate gy is directly dependent upon the attachment points of the threads. The attachment of the threads to the fuselage is near the leading edge of the wings. The corresponding attachment to the wings is actually at separate

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37 Figure 6–3: W ing with K e vlar Threads points. One attachment point is near the mid-chord point at the wing-tip outboard. Another attachment point is the trailing edge near the tw o-thirds span location. The morphing that results by actuating the serv o is sho wn in Figure 6–4 The serv o rotates and causes the threads to pull against the attachments on the wing. The morphing resulting from this strate gy is clearly be yond simple w arping. In this case, the pulling of the threads to w ard the leading-edge attachment at the fuselage causes the wing to both twist and bend. The ef fect is similar in nature to a curling of the wings. The basic parameters that are readily observ ed to change are the twist, camber chord, and span. Figure 6–4: Front V ie w of the 12 in MA V with Undeected (left) and Morphed (right) W ing The morphing is designed for a biologically-inspired ef fect. The displacement of the wing resembles shapes observ ed in birds lik e gulls. F or instance, the bending along the span is concentrated around a single point which correlates to the elbo w in

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38 birds. The twist is concentrated near the trailing-edge outboard which correlates with the feathers near the wrist of birds. A more formal approach to this concept is being designed by N ASA b ut this current v ehicle is suf cient to in v estigate control issues [ 6 ]. Only a single wing is altered in Figure 6–4 The v ehicle actually contains separate serv os for each wing that allo w the morphing to act simultaneously on both wings; ho we v er this thesis will restrict attention to morphing a single wing. The current objecti v e considers roll control b ut the longitudinal issues will be in v estigated in the future. Also, this v ehicle is ideal for the focus of this thesis. Specically the morphing strate gy is quite simple b ut the morphing ef fect is complicated. This approach allo ws the control issues associated with morphing to be easily studied. The v ehicle is not designed to study the optimal strate gies for morphing; rather the v ehicle is designed to study the optimal strate gies for control. 6.3 Flight T esting Flight testing is also done on the 12 in MA V in an open area for R/C airplanes. The ight tests for this MA V are performed in similar conditions as the tests for the 24 in MA V This MA V is equiped with a data acquisition board which be gins logging when the motor is turned on. This MA V is then similarly hand launched into the incoming wind for tak eof f. The primary forms of control for this MA V are the ele v ator and wing morphing. The airplane is controlled with these surf aces for tak eof f, turns, climbs, and le v el ight. The airplane is then trimmed for straight and le v el ight. Achie ving trimmed ight is necessary as a neutral reference point for the control surf aces and in performing dif ferent ight test maneuv ers. This MA V is then tested by commanding doublets to the morphing serv os. A representati v e doublet command is sho wn in Figure 6–5 The units of this command

PAGE 46

39 are just count commands to the serv o because the actual deection caused by morphing is dif cult to quantify 0 0.5 1 1.5 2 2.5 30 20 10 0 10 20 30 40 Time(sec)Morphing Command Figure 6–5: Doublet Command to Morphing Serv o The responses to the morphing doublets are measured by the on-board data acquisition system. The roll rate and ya w rate are presented in Figure 6–6 0 0.5 1 1.5 2 2.5 60 40 20 0 20 40 60 80 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 60 40 20 0 20 40 60 80 Time(sec)Yaw Rate (deg/sec) Figure 6–6: Roll Rate(left) and Y a w Rate(right) in Response to Morphing Doublet The roll rate is clearly correlating well with the commanded doublet and demonstrates the morphing is capable of commanding roll maneuv ers. The ya w rate is some what more dif cult to understand. Notably the aircraft b uilds up ya w rate approximately 0.5 seconds after the onset of the doublet command. This ight characteristic results from the single-sided nature of the morphing. Essentially the wing that is morphed loses lift b ut also increases drag. The loss of lift immediately causes rolling and the increase of drag causes a slight delay in b uilding up the ya w rate.

PAGE 47

40 A separate morphing doublet is commanded at a dif ferent time as sho wn in Figure 6–7 in order to consider the modeling for a dif ferent maneuv er This maneuv er consists of strictly morphing actuation. 0 0.5 1 1.5 2 2.5 3 3.5 30 20 10 0 10 20 30 40 Time(sec)Morphing Command Figure 6–7: Second Doublet Command to Morphing Serv o The roll rate and ya w rate responses to the second morphing doublet are sho wn in Figure 6–8 It can be seen that the morphing doublet commanded in the second maneuv er w as of a slightly smaller magnitude than the rst maneuv er This results in a smaller roll rate response due to a smaller morphing deection. 0 0.5 1 1.5 2 2.5 3 3.5 20 0 20 40 60 80 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 20 0 20 40 60 80 Time(sec)Yaw Rate (deg/sec) Figure 6–8: Response to Second Morphing Doublet Command for Roll Rate(left) and Y a w Rate(right) 6.4 Modeling A linear model is identied from the ight data. A 6-state model w as originally identied b ut reduced to a 3-state model as sho wn in T able 6–2 The simulated responses of this model are compared with measured v alues of roll rate and ya w rate in Figure 6–9

PAGE 48

41 0 0.5 1 1.5 20 0 20 40 60 80 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 20 0 20 40 60 80 Time(sec)Yaw Rate (deg/sec) Figure 6–9: Simulated( ) and Actual(-) Roll Rate(left) and Y a w Rate(right) Responses to a Doublet T able 6–2: Poles of a linear model of the 12 in MA V Poles V alue Dutch Roll3670414732 Roll -7.521 The responses of the model are reasonably close to the measured responses. The roll rate sho ws a good correlation although the ya w rate is some what less accurate. The model contains a roll con v er gence mode which, based on the accurac y of roll simulations, is accepted. The model also contains a dutch roll mode which attempts to capture the dynamics associated with ya w rate. The inability of this mode to represent the ya w dynamics may indicate some nonlinearity is associated with the v ehicle. Such nonlinear dynamics w ould not be une xpected gi v en the e xtreme nature of the morphing and the asymmetry resulting from morphing a single wing. In order to study whether this model is a good enough linear approximation of the dynamics of the 12 in MA V dif ferent inputs are considered for the same model. These inputs are doublet morphing commands at dif ferent times throughout the same set of data. The simulated and measured v alues of roll rate and ya w rate are sho wn in Figure 6–10 for se v eral inputs. It is clearly sho wn that the simulated and actual roll rate and ya w rate responses demonstrate good correlation. The simulations sho wn in Figure 6–10 sho w that the model which w as obtained from a doublet maneuv er responds well to dif ferent

PAGE 49

42 inputs. The ya w rate; ho we v er is dif cult to model because the v ehicle is morphed asymmetrically and this introduces nonlinearities. These nonlinearities ha v e to be considered in an approximation in order to obtain an accurate model. 0 0.5 1 1.5 2 2.5 3 3.5 4 100 50 0 50 100 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 80 60 40 20 0 20 40 60 80 Time(sec)Yaw Rate (deg/sec) 0 0.5 1 1.5 2 60 40 20 0 20 40 60 80 Time(sec)Roll Rate (deg/sec) 0 0.5 1 1.5 2 10 5 0 5 10 15 20 25 30 35 Time(sec)Yaw Rate (deg/sec) Figure 6–10: Simulated ( ) and Actual (—) Roll Rate(left) and Y a w Rate(right) Responses to Morphing Doublets

PAGE 50

43 6.5 Ev aluation When using the ARX simulation in Matlab, a linear approximation could not be made on the maneuv ers which were not centered around trim. Therefore, not only are maneuv ers around trim desired for a linear approximation, b ut the y are also necessary in order for the simulation to be done. It is particularly dif cult to nd maneuv ers to use for a linear approximation for this specic v ehicle due to the f act that it is v ery hard to trim. Therefore, before most maneuv ers there is an indication in the data that there are some oscillations about the roll axis. Similarly the data indicates that se v eral seconds after a maneuv er has been initiated, a component of ya w rate be gins to de v elop. The b uild up of ya w rate after a morphing maneuv er has been initiated can be attrib uted to the f act that the shape of the wing is being altered. The wings on this v ehicle are being curled underneath, one at a time resulting in an asymmetric morphing actuation. This leads to nonlinearities in the ight characteristics of the v ehicle which can e xplain the oscillations and the b uild up of ya w seconds after a maneuv er has been initiated. The modeling is a linear approximation of coef cients, and when considering nonlinear beha vior it might not pro vide data that can be trusted. The 24 in MA V is morphed by twisting the wings symmetrically which can be approximated as a linear beha vior Ho we v er the 12 in MA V is being morphed asymmetrically and therefore requires further studies to obtain a better approximation of the model.

PAGE 51

CHAPTER 7 CONCLUSION Current micro air v ehicles are designed with the common features of carbon ber airframes and e xible membrane wings. The typical control surf aces which can be implemented on MA Vs consist of rudder and ele v ator The con v entional control surf aces such as ailerons can not be easily included in the design of the common MA Vs due to the f act that the wings are made of e xible material. A dif ferent form of actuation is necessary in order to impro v e maneuv erability and performance for MA Vs if the y will be assigned to e v olving missions. A particularly demanding mission is one which tak es place in an urban en vironment which requires these v ehicles to ha v e adv anced maneuv ering capabilities. A simple approach to increasing maneuv erability is to include an additional control ef fector such as wing morphing. This paper has demonstrated that morphing can be an ef fecti v e means to achie v e roll control for a micro air v ehicle. The e xible nature of the wings enables their shapes to be easily altered. Simple mechanisms, such as a torque rod and K e vlar threads, are used on a 24 in MA V and a 12 in MA V In each case, the v ehicle w as o wn using morphing as the primary ef fector for roll maneuv ers. The ight data clearly sho ws the morphing produces signicant roll rates and pro vides signicant controllability These v ehicles are o wn in an R/C eld and are equipped with a data acquisition system(D AS). This D AS consists of gyros and accelerometers for the three axis. The data is then retrie v ed and the accelerations and rates of the three axis can be studied. This data is then used for a linear modeling technique. 44

PAGE 52

45 A linear approximation is then considered using an ARX modeling technique in Matlab This sho ws a good correlation with the data for the 24 in and the 12 in MA V Ho we v er further studies ha v e to be considered for the modeling of the 12 in MA V since it is being morphed asymmetrically by curling one wing at a time. This then introduces nonlinearities in the ight characteristics which ha v e to be considered in modeling approximations. The 24 in MA V can be approximated linearly since the morphing is being induced with symmetric wing twisting.

PAGE 53

REFERENCES [1] M. Abdulrahim,H. Garcia,J. Dupuis, and R. Lind,“Flight Characteristics of W ing Shaping for a Micro Air V ehicle with Membrane W ings, ” International F orum on Aer oelasticity and Structur al Dynamics IF ASD-US-24, June 2003. [2] M. Amprikidis and J.E. Cooper ,“De v elopment of Smart Spars for Acti v e Aeroelastic Structures, ” AIAA-2003-1799, 2003. [3] J. Bo wman,“ Af fordability Comparison of Current and Adapti v e and Multifunctional Air V ehicle Systems, ” AIAA-2003-1713, 2003. [4] J. Blondeau,J. Richeson and D.J. Pines,“Design, De v elopment and T esting Of A Morphing Aspect Ratio W ing Using An Inatable T elescopic Spar ” AIAA-20031718, 2003. [5] C.E.S. Cesnik and E.L. Bro wn, “ Acti v e W arping Control of A Joined-W ing Airplane Conguration, ” AIAA-2003-1715, 2003. [6] J.B. Da vidson,P Chw alo wski and B.S. Lazos,“Flight Dynamic Simulation Assessment of a Morphable Hyper -Elliptic Cambered Span W inged Conguration, ” AIAA-2003-5301, 2002. [7] P de Marmier and N.M. W erele y “Morphing W ings of a Small Scale U A V Using Inatable Actuators for Sweep Control, ” AIAA-2003-1802, 2003. [8] Ecobirds, ”Putting Birds Back Into Ecology ” http://birds.ecoport.or g, 10/15/2003. [9] S.M. Ettinger M.C. Nechyba, P .G. Ifju and M. W aszak,“V ision-Guided Flight Stability and Control for Micro Air V ehicles, ” Pr oceedings of the IEEE Confer ence on Intellig ent Robots and Systems 2002, pp. 2134-2140. [10] S.W Gano,J.E. Renaud,S.M. Batill and A. T o v ar ,“Shape Optimization for Conforming Airfoils, ” AIAA-2003-1579, 2003. [11] H. Garcia,M. Abdulrahim and R. Lind,“Roll Control for a Micro Air V ehicle using Acti v e W ing Morphing, ” AIAA Guidance Navigation and Contr ol Confer ence AIAA-2003-5347, 2003. [12] F .H. Gern, D.J. Inman and R.K. Kapania, ”Structural and Aeroelastic Modeling of General Planform W ings with Morphing Airfoils, ” AIAA J ournal V ol 40,No. 4,2002, pp. 628-637. 46

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47 [13] J.M. Grasme yer and M.T K eennon,“De v elopment of the Black W ido w Micro Air V ehicle, ” AIAA-2001-0127, 2001. [14] P .G. Ifju,D.A. Jenkins,S. Ettinger ,Y Lian and W Shyy ,“Fle xible-W ing Based Micro Air V ehicles, ” AIAA-2002-0705, 2002. [15] C.O. Johnston,D.A. Neal,L.D. W iggins,H.H. Robertsha w W .H. Mason and D.J. Inman,“ A Model T o Compare The Flight Control Ener gy Requirements Of Morphing And Con v entionally Actuated W ings, ” AIAA-2003-1716, 2003. [16] N.S. Khot, F .E. Eastep, and R.M. K olonay “Method for Enhancement of the Rolling Maneuv er of a Fle xible W ing, ” J ournal of Air cr aft V ol. 34, No. 5, 1997, pp. 673-678. [17] S.K. Kw ak and R.K. Y eda v alli, ”Ne w Modeling and Control Design T echniques for Smart Deformable Aircraft Structures”, J ournal of Guidance Contr ol and Dynamics V ol 24, No. 4, 2001, pp. 805-815. [18] L. Ljung, User s Manual for System Identication T oolbox The Math W orks, Inc, Natick, MA, 1991. [19] L. Ljung, System Identication: Theory for the User Prentice Hall, Engle w ood Clif fs, NJ,1987. [20] S.L. P adula,J.L. Rogers and D.L. Rane y ,“Multidisciplinary T echniques And No v el Aircraft Control Systems, ” AIAA-2000-4848, 2000. [21] B. Sanders, F .E. Eastep and E. F orster ”Aerodynamic and Aeroelastic Character istics of W ings with Conformal Control Surf aces for Morphing Aircraft”, J ournal of Air cr aft V ol 40, No. 1, 2003, pp. 94-99. [22] W Shyy M. Ber g and D. Ljungqvist, “Flapping and Fle xible W ings F or Biological And Micro Air V ehicles, ” Pr o gr ess in Aer ospace Sciences V ol. 35, No. 5, 1999, pp. 455-506. [23] M.R. W aszak,J.B. Da vidson and P .G. Ifju, “Simulation and Flight Control of an Aeroelastic Fix ed W ing Micro Aerial V ehicle, ” AIAA-2002-4875, 2002. [24] M.R. W aszak,L.N. Jenkins and P Ifju, “Stability and Control Properties of an Aeroelastic Fix ed W ing Micro Aerial V ehicle, ” AIAA-2001-4005, 2001. [25] R.W Wlezien,G.C. Horner ,A.R. McGo w an,S.L. P adula,M.A. Scott, R.J. Silcox and J.O. Simpson,“The Aircraft Morphing Program, ” AIAA-98-1927, 1998.

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BIOGRAPHICAL SKETCH Helen Garcia w as born in Santo Domingo, Dominican Republic, on May 22, 1979. Her f amily mo v ed to Miami, FL, in 1990. She recei v ed her high school diploma from Miami Coral P ark Senior High School in Miami, FL. She then attended the Uni v ersity of Florida and recei v ed her bachelor' s de gree in aerospace engineering in May 2002. She has w ork ed in the dynamics and control research group under Dr Rick Lind and will recei v e her master of science de gree in aerospace engineering in December 2003. 48


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Title: Control of Micro Air Vehicles Using Wing Morphing
Physical Description: Mixed Material
Copyright Date: 2008

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CONTROL OF MICRO AIR VEHICLES USING WING MORPHING


By

HELEN MICHELLE GARCIA


















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2003

















TABLE OF CONTENTS


LIST OF TABLES .........

LIST OF FIGURES .........

ABSTRACT ............

CHAPTER

1 INTRODUCTION ......

2 MICRO AIR VEHICLES ..

3 MORPHING .........

4 MODELING .........

5 24 in MICRO AIR VEHICLE

5.1 Vehicle Description .
5.2 Morphing .......
5.3 Flight Testing .....
5.4 Modeling .......
5.5 Evaluation .......

6 12 in MICRO AIR VEHICLE

6.1 Vehicle Description .
6.2 Morphing .......
6.3 Flight Testing .....
6.4 Modeling .......
6.5 Evaluation .......

7 CONCLUSION ........

REFERENCES ..........

BIOGRAPHICAL SKETCH .. .


...............

...............

...............
















Table

5-1 Range of control effectors .

5-2 Properties of the 24 in MAV

5-3 Poles of a linear model of the

6-1 Properties of the 12 in MAV

6-2 Poles of a linear model of the


LIST OF TABLES


24 n M AV ...............



12 in M AV . . . . .















LIST OF FIGURES
Figure page

1-1 MAVs with 24 in(left) and 12 in(right) Wingspan ........... .. 3

2-1 Members of MAV Fleet at University of Florida ....... ....... 7

3-1 A Gull (left) and Snowy Owl (right) in Flight ................ 12

3-2 Aspect Ratio of Bird Wings ................... ..... 13

5-1 Overhead View of the 24 in MAV .................. 22

5-2 Wing with Torque Rod ............... . . ... 23

5-3 Rear View of the 24 in MAV with Undeflected (left) and Morphed (right)
W ing . .. .. . .. ... ... .... 24

5-4 Doublet Command to Rudder Servo .......... ....... .... 25

5-5 Response to Rudder Doublet for Roll Rate(left) and Yaw Rate(right) 25

5-6 Second Doublet Command to Rudder Servo ..... . . ..... 26

5-7 Response to Second Rudder Doublet for Roll(left) and Yaw Rate(right) 26

5-8 Doublet Command to Morphing Servo .......... ....... .... 27

5-9 Response to Morphing Doublet for Roll(left) and Yaw Rate(right) . 27

5-10 Second Doublet Command to Morphing Servo ....... ....... 28

5-11 Response to Second Morphing Doublet Command for Roll Rate(left)
and Yaw Rate(right) ...... .. ......... ...... 28

5-12 Simulated ( ) and Actual (-) Roll Rate(left) and Yaw Rate(right) Re-
sponses to Morphing Doublet .................. ...... 29

5-13 Simulated ( ) and Actual (-) Roll Rate(left) and Yaw Rate(right) Re-
sponses to Morphing Doublets .................. .. ..31

6-1 View of the 12 in MAV ............ . . ..... 33

6-2 View of the 10 in MAV ........ .... ............... 34

6-3 Wing with Kevlar Threads .......... ....... 37









6-4 Front View of the 12 in MAV with Undeflected (left) and Morphed (right)
W ing . . . . . .. .. ... .... 37

6-5 Doublet Command to Morphing Servo .......... ....... .... 39

6-6 Roll Rate(left) and Yaw Rate(right) in Response to Morphing Doublet .39

6-7 Second Doublet Command to Morphing Servo . . . 40

6-8 Response to Second Morphing Doublet Command for Roll Rate(left)
and Yaw Rate(right) ........ ................. 40

6-9 Simulated(- -) and Actual(-) Roll Rate(left) and Yaw Rate(right) Re-
sponses to a Doublet ............ . . ...... 41

6-10 Simulated ( ) and Actual (-) Roll Rate(left) and Yaw Rate(right) Re-
sponses to Morphing Doublets .................. .. ..42















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

CONTROL OF MICRO AIR VEHICLES USING WING MORPHING

By

Helen Michelle Garcia

December 2003

Chair: Richard C. Lind, Jr.
Major Department: Mechanical and Aerospace Engineering

A micro air vehicle (MAV) is typically defined to have a wingspan of 6 in and

operates with airspeeds of less than 25 mph. Recent attention has been devoted

to MAVs because there is a variety of applications for which they can be used.

Specifically, they are useful in missions within urban environments. These missions

require MAVs to be very small and highly agile. These characteristics are achieved

with the use of light materials such as carbon fiber airframes and plastic membrane

wings; however, this design also causes these vehicles to be difficult to operate. This

construction makes them strong with good aerodynamic properties; however, hinges for

conventional control surfaces are not easily implemented on flexible wings. Therefore,

these vehicles are strong and light but have limited control authority. A different

control effector is then necessary in order to provide control authority. This thesis

will consider using wing morphing as a control effector. Simple techniques are used

to change the shape of the wings during flight such as twisting the wings of a 24 in

MAV and curling the wings of a 12 in MAV. Flight tests are then performed and show

that morphing is an effective way to induce roll motion. The data are then analyzed to

consider linear modeling techniques as well as control design. The use of morphing









results in a more effective roll motion than the use of the rudder and improves the


maneuverability of the vehicles.















CHAPTER 1
INTRODUCTION

Recent advances in technology have made the use of smart vehicles in a variety

of applications possible. These advances have led to the development of small

unmanned air vehicles (UAV) as well as micro air vehicles (MAV) which have mission

capabilities. These vehicles can range in size according to their specific application.

Small UAVs and MAVs can be designed to operate within urban environments. Their

design typically depends on the mission in which they will be used and can range from

civilian to military applications.

For example, these vehicles might be assigned to military missions such as bomb

damage assessment, which would involve transmitting video after a bomb has been

dropped at a specific location. These vehicles could also be used in warfare as a means

to have live video of what is occurring ahead before ground troops are sent into the

battlefield. There are also some civilian applications to MAVs, such as transmitting

video for traffic/news coverage, and to look in specific places for search and rescue

missions.

Other scenarios where MAVs would be useful include assessing the damage

caused by chemical spills, in search and aiding in rescue missions and even in traf-

fic/news coverage. Some of these applications might require MAVs to work in

collaboration with other MAVs in order to cover a large area of surveillance.

Another application where a MAV would be useful is if for example, there is

a biological agent released into a public area. A biohazard team would have to suit

up and prepare before being able to enter the area for testing and clearing of the

biological agent. Instead, a MAV can be released from a nearby station which can have







2

sensors on board, and be able to detect the extent of the contamination and the type of

biological agent which was released before any humans have arrived at the scene.

The recent concern for terrorism being planned in urban environments such as

small apartments leads to specific situations where MAVs could be useful. Current

technology cannot keep track and observe these small suspected areas. A MAV would

be useful in this situation because it could fly up to windows or even indoors and send

live video and audio of the suspect activities.

In order to accomplish the evolving missions for which MAVs can be used,

their designs have to be considered accordingly. For most military missions, the

requirements typically demand that these vehicles be very small and highly agile.

They are constructed of very light materials, such as carbon fiber airframes and

flexible membrane sheeting for wings. However, this vehicle design does not allow for

conventional control surfaces due to the complexity of implementing hinges along the

flexible membrane wings.

The lack of conventional control surfaces makes these vehicles difficult to fly.

Several benefits can be achieved by the use of additional control effectors. The

implementation of wing morphing as an additional control effector is considered to

increase controllability. Simple techniques are considered to study the benefits of using

morphing as compared to the current control effectors which are used on MAVs.

This thesis will consider morphing as a control effector for a pair of micro air

vehicles with different dimensions. The vehicles shown in Figure 1-1 with a 24 in

wingspan and a 12 in wingspan will be used to demonstrate morphing for control.

These vehicles will be referred to as MAVs, though their wings are larger than the

definition implies, due to the similarities in design and construction.

The MAV is an ideal platform for morphing because the power required is very

small due to the flexibility of the wings, and there are several benefits including

increased controllability.





















Figure 1-1 MAVs with 24 in(left) and 12 zn(right) Wingspan


Wing morphing on the 12 in MAV is actuated by connecting a strand of Kevlar

to a servo inside the fuselage and then to a location on the wing This initial design

only allowed for morphing at a single location, which was the wing outboard Further

testing led to the consideration of more dramatic morphing The morphing of the wing

was made more dramatic by then adjusting an extra Kevlar strand to the serves This

allows for morphing about the span and the trailing edge at the same time

The morphing is actuated on the 24 in MAV by use of torque rods which are

connected from the fuselage to the wing outboard These torque rods are connected to

the wings by being sewn along the plastic sheeting of the wing These rods are then

actuated and in turn change the shape of the wings

Data is then collected with a data acquisition system which provides information

with 3 accelerometers and 3 gyros along an orthogonal coordinate system of the

vehicle This data is then processed to consider the response of the aircraft to the input

commands A linear model approximation is then done using the roll rate and yaw rate

responses The approximation is done using an ARX technique in Matlab using the

responses

The approximation results in a good correlation of the coefficients when compared

to the data which was collected The linear model for the 24 in MAV can then be

approximated but the model of the 12 in MAV requires further research This is







4

due to the fact that the 24 in MAV is being morphed symmetrically so that a linear

approximation can be made, but the 12 in MAV is morphed asymmetrically which

requires a nonlinear study to be done.















CHAPTER 2
MICRO AIR VEHICLES

Micro Air Vehicles(MAVs) are typically defined as vehicles with a wingspan

of less than 6 in and which operate with airspeeds of less than 25 mph. The idea

for a MAV is to have a platform which is small, inexpensive and that can be used in

situations which are not suitable for larger vehicles [14].

The first succesfull design of a micro air vehicle was achieved by AeroViron-

ment. They designed the Black Widow MAV with funding from DARPA. The Black

Widow is a MAV with a 6 in wingspan, airspeed of about 30 mph and weighs under

100 grams [13]. This vehicle also has the capability of carrying a video camera which

transmits live video to the ground and has an endurance of 30 minutes. It is also

equipped with an autopilot, which is capable of performing altitude, airspeed, and

heading holds as well as a yaw damper. The transmitter and actuators are some of the

smallest and lightest systems available. This design led to further interest and research

in the field of MAVs from several countries and universities.

The University of Florida has been very active in the design and testing of micro

air vehicles. Dr. Peter Ifju has led a successful research team at the University of

Florida in the area of MAVs. They have been able to win various aspects of the

annual MAV competition, which is sponsored by the International Society of Structural

and Multidisciplinary Optimization. The MAV team at the University of Florida has

succeeded in this competition each year from 1999 to 2003 with the various designs

that have been tested and have won the overall first place award. The annual MAV

competition typically includes entries from several universities around the world. The

2003 competition consisted of entries from 15 universities.









Current MAV designs are based on a flexible wing design used at the University

of Florida [14]. The most common design is an airframe constructed entirely of

composite carbon fiber. The fuselage is typically a two-piece monocoque structure

designed to house flight components and instrumentation. The flight components

include servos and connectors, and some of the instrumentation used in flight includes

orientation systems. A conventional empennage is affixed to the fuselage with elevators

and rudders hinged to the horizontal and vertical stabilizers.

The MAVs are equipped with sensors for measurement consisting of 3-axis gyros

and 3-axis accelerometers along with the servo command. The sensing and actuation

data is recorded on an on board data acquisition board which weighs 7 grams and was

developed by NASA Langley Research Center specifically for MAV applications [1].

This micro data acquisition board is capable of recording 27 analog channels which is

sufficient for the current sensor package. The data is then available at 50 to 100 Hz

and is resolved using a 12-bit analog-digital converter. The data is recorded in a 4 MB

flash chip on board the data acquisition board and is then downloaded to a PC at the

end of each flight.

The vehicles use an electric motor for propulsion and the duration of flights

depend on the amount of batteries which can be carried and the throttle setting on

the motor. On average, flights ranging from 10-15 minutes are easily achieved for the

24 in and 12 in MAVs which are considered.

Structures used in flight, both in biological and aircraft applications, are flexible by

a certain amount. For aircraft to be able to withstand the large forces obtained during

flight; however, the wings have to be strong enough.

Flight of birds also consists of flexible wings which can adapt to the changing

environments they fly in. Birds have many layers of feathers which can be moved

around in order to adjust to the specific maneuver they need to perform [22]. The use

of flapping for flight, such as done by birds, has not been extensively studied. This has









not been done due to the complexity of the flight mechanics which includes changing

geometry, flexible surfaces and unsteady aerodynamics.

The flexible membrane wings together with the size constraints of MAVs make

analysis and design of these vehicles very challenging. Specifically, the aerodynamics

of a MAV are complicated by low Reynolds number flight, largely deforming struc-

tures, the effects of viscosity and flow separation at high angles of attack [22]. The fact

that the MAVs are challenging to design provides a good platform for research in the

areas of dynamics and control, aeroservoelasticity, structures, microelectronics, small

actuation and data acquisition systems, and other fields.

The research and development of these vehicles has progressed rapidly due to the

availability of smaller electronics as well as the advances in lighter materials. Several

of these vehicles are shown in Figure 2-1.







Figure 2-1 h Iclibci of NI.A Fleet at University of Florida


Advances in miniature digital electronics, communications and computer tech-

nologies have made sensing capabilities on micro air vehicles possible. A typical

application of these miniature electronics is in a reconnaissance mission where a small

MAV would be preferred to a larger vehicle in order to remain stealthy.

The use of innovative control effectors is an area being explored as an enabling

technology for designing a stability augmentation system. The current generation of

MAVs uses traditional effectors, specifically an elevator and rudder, whose positions

are commanded by the remote pilot. The elevator presents adequate effectiveness

for longitudinal control but the rudder presents some difficulty for lateral-directional

control.









The rudder mainly excites the dutch roll mode so steering and gust rejection are

really accomplished using the coupled roll and yaw motion resulting from dutch roll

dynamics. Such an approach is obviously not optimal but traditional ailerons are not

feasible on this type of aircraft.

Actuation of the MAV control surfaces is accomplished with two control effectors

or servos mounted inside the fuselage. These devices actuate the control surfaces by

rotating an arm and pushing or pulling a pushrod when a deflection is commanded.

Research in the design and testing of these vehicles has been done in several

countries and universities. Research of micro air vehicles has also been done exten-

sively at NASA. Specifically, NASA has considered a control assessment and simulation

of a micro air vehicle with aeroelastic wings which adapt to the disturbances during

flight [23]. This was done using aerodynamic data which was obtained in previous

testing of a MAV [24].















CHAPTER 3
MORPHING

The concept of morphing is not an idea which has been strictly defined. A

morphing aircraft is generally defined to be an aircraft whose shape changes during

flight to optimize performance. Types of shape changes include span, chord, camber,

area, thickness, aspect ratio and planform. The morphing can also be applied to a

control surface in order to eliminate hinges.

Morphing can be used as a control effector by changing the shape of the aircraft

in order to alter the flight dynamics. The concept of morphing has been looked at by

DARPA and NASA to show the aerodynamic benefits; however, the use of morphing

for control design has not been studied extensively. The wing morphing techniques for

the MAVs in this project consider using servos which are attached to the wings.

Aircraft have previously used techniques for adapting their shape depending on

the specific flight characteristics desired. The use of morphing as a control effector

was used initially on the Wright Flyer, where the pilot used cables to twist the wings

in order to achieve the desired motion. Wing warping did not become a common

technique; however, due to the power which is required from actuators to change the

shape of the wings [21].

Morphing is also used on the F-14 which has a variable sweep on the wing,

therefore changing the shape of the wing during flight. The wings are swept in order to

balance the range and speed by slowing down the increase in drag which develops as

velocity increases [21].

There are different ways that an aircraft can be morphed which are appropriate for

control. The current research will focus on morphing of the wings in order to consider









primarily control issues. The flight characteristics of birds will be considered as a

guide since they also change the shape of their wings to achieve certain maneuvers.

Many mechanisms which consider morphing have been designed but have not

been tested in flight vehicles. NASA has designed a wing which changes the camber of

the wing [6]. One of the wings considered is referred to as a Hyper-Elliptic Cambered

Span (HECS) because the curvature along the span is continuously changing. This

provides a larger area which allows for greater lift. This vehicle uses a hinge-less panel

along the trailing edge of the wing as a form of a control surface for pitch and roll.

The simulations demonstrated the aerodynamic benefits but also show this vehicle has

unstable lateral-directional dynamics.

The use of smart materials such as shape memory alloys and piezos have been

considered in the design of morphing wings but there is still a limit in that not enough

force can be produced in order to twist large wings using these mechanisms. However,

smart spars have been built which provide different types of morphing but have not

been tested on flight vehicles [2].

Another mechanism for morphing which has been studied considers changing

the sweep of the wings of a small unmanned air vehicle (UAV) [7]. The morphing on

this UAV is done in order to meet changing mission requirements. Actuation of the

morphing is done by using inflatable actuators which are powered with compressed air.

One of the benefits of this project is that the actuation mechanism used is much lighter

than the typical hydraulic systems that are used on full scale aircraft. The effects of the

sweep are then studied considering the change of aspect ratio, lift and drag.

Similarly, a study has been done considering an inflatable telescopic spar which

can be morphed spanwise [4]. This design allows for changes in the aspect ratio while

still providing enough support from the spars for the airloads which are being applied.

This is achieved because the telescopic spar is pressurized and the telescopic skins









maintain the geometry of the airfoil as well as provide effective storing and deployment

of the mechanism.

Also for the purpose of considering improved maneuverability and performance,

roll maneuvers have been studied using a flexible wing [16]. Numerical studies were

used to consider the aerodynamic loads on a flexible wing at high speeds. Wing twist

is also considered in order to recover the rolling moment lost but has not been tested in

flight. This is due to the challenges involved in implementing a functioning mechanism

for wing twist on a full scale aircraft.

Research has also been done considering the material aspects of shape changing

with a finite element model of a wing [17]. This considered roll maneuvers using

a piezoelectric material as an actuation mechanism with aerodynamic loads being

applied. Piezoelectric sensors and actuators are useful for this application because they

are light, have a small volume and can achieve various shapes. This technique has

not been tested; however, due to the large deflections that are needed from such small

actuators.

Numerical studies have considered structural and aerodynamic modeling for

shape changing wings [12]. These considered a generic lambda wing such as used in

unmanned combat air vehicles (UCAV). The different mode shapes were studied to

consider structural modeling. This model was then used to study the roll performance

of the morphing wing. It was shown that this wing with hinge-less control surfaces

shows improved roll performance because of the aerodynamic and structural benefits.

As mentioned previously, there are several benefits such as improved performance

due to the use of wing morphing. Also, morphing is easily achieved on MAVs because

the wings are constructed of flexible membrane material. The flexible wings can be

grossly deformed via mechanical actuation yet are capable of withstanding flight loads.

The flexible nature of the wing also gives rise to the mechanism of adaptive washout

which permits small changes in wing shape in response to gusty wind conditions.









For this project, morphing is limited to changing the shape of the wings, not of

the entire airframe This type of morphing can be studied with the use of biologically

inspired techmques The different ways that birds change the shape of their wings

during flight is studied and compared with morphmg techniques Consider, for

example, the birds m Figure 3-1 These birds typically change the shape of their wings

depending on the types of maneuvers that they need to perform









Figure 3-1 A Gull (left) and Snowy Owl (nght) m Fhght


Certain techmques of morphing for aircraft can be designed by studymg these

birds There are several morphing techmques which are used by these birds that

demonstrate how their flight maneuvers can be changed, such as loitermg, diving and

take-off

The wings of birds are shaped similarly to airfoils and have the same basic

function [8] Certain birds use their wings more often than others who just fly for short

periods of time Also, the enviromnent the birds are in can affect the aerodynamics of

the flight, therefore birds have different shapes of wings

The aspect ratio of the wings of birds is measured as the square of the span of the

wing divided by the area of the wing Tius ratio can vary depending on the specific

technique for flying of each bird For example, long wings provide a smoother ghding

motion but it takes more energy to flap them quickly, therefore they are not useful

for increasing speed Therefore, birds with longer wings tend to use ghding as their

primary method of flight Wmg loading can also affect how a bird flies since the

energy required to flap their wings also depends on how heavy they are









Consider, for example, Figure 3-2 which shows the wing design for four different

birds [8] The lower aspect ratio wings, such as for a pheasant, typically allow for

quick take off and slow flights, but are not useful for gliding The slightly larger

aspect ratio wings, such as for eagles, are typically longer and have feathers which are

adjusted as a type of control surface for more precise maneuvenng

The wings for waders, with a typical aspect ratio of 12 5, are useful for faster

speeds and gliding but do not allow for fast take off This limit on a fast take off is

because a lot of energy is required to flap these longer wings The higher aspect ratio

wings, as for gulls, are typically useful for gliding close to surfaces such as sea and

land and take advantage of the winds in order to conserve energy These are only a few

of the many different designs of wings which vary depending on the migration patterns

of each bird

Pheasant
Eagle


,,

Aspect ratio 68 Aspe atio 9.3
Wader G-- u
Gull


Aspect ratlo 12 Aspect ratio -1t ;
Figure 3-2 Aspect Rato ofBird Wings


Some biologically inspired techniques can be applied to MAVs The span of

the wings, the horizontal distance from the tip of a wing to the tip of the other, can

be altered to create a shorter wing for example Birds and bats are also capable of

changing the span of their wings to decrease the area, therefore increasing the forward

velocity and reducing drag The chord, which is the distance from the leading edge to

the trailing edge, can also be altered The wing can also be morphedby twisting or

rotating parts of the wing in order to affect aerodynamic performance









Another type of morphing is sweeping the wing either at an elbow joint on the

wing or at the root of the wing. This provides a type of wing sweep which takes a

similar shape change as seen in birds. The area of the wing can also be changed by

extending the length or trailing edge as some birds do. The aspect ratio is also affected

by the morphing and can be used to consider lift and drag for aerodynamics.

A simple form of morphing is a wing twist. This is currently being used for

control on the Active Aeroelastic Wing (AAW) as well as the vehicles in this project.

The morphing on the AAW causes the wings to be twisted in response to the moments

induced by the control surfaces. Birds and bats also do this in order to obtain the

required lift or thrust during flight.

Morphing on the MAVs is accomplished by actuation of control effectors located

inside the fuselage. These servos are connected to the wings by either use of a torque

rod or Kevlar strand. The wing morphing is actuated by moving the arm which rotates

the tube or pulls the strand and changes the shape of the wing.

Certain maneuvers are of interest when considering the effects of wing morphing

on a MAV. The flight test maneuver of interest is a control doublet for both rudder and

wing shaping controls. The rudder doublet is being applied only to the 24 in MAV

since the 12 in MAV consists of only elevator and wing morphing control effectors.

These maneuvers are performed by commanding a constant left deflection for a certain

time period followed immediately by a right deflection for the same time period and

finally returning to the neutral position. Aircraft response characteristics to the control

input are then determined by analysis of the servo position and rate responses.

Wing-shaping control doublets induce a different behavior of the MAV. The

response of the airplane to wing shaping is similar in nature to responses from ailerons.

Essentially, the aircraft response to the morphing is predominantly roll motion with

little yaw or pitch coupling. Thus, the doublets are performed without considerable

directional or altitude deviation.









Following the completion of the maneuver, which resembles rocking the wings,

the airplane is in a banked attitude. Recovery from the wing shaping doublet is

considerably easier than that of the rudder doublet. Such a response indicates the wing

shaping excites the roll convergence mode.

Clearly, the MAV requires a stability augmentation system to facilitate operation

and greatly expand its mission capability. In general, lateral maneuvers are particularly

difficult because the MAV is so responsive. The introduction of a controller would

lessen pilot workload for trajectory tracking.

The design of a controller is the next step in the research of facilitating the ability

to operate these MAVs with the aid of active wing morphing. Future research will also

enable development of a vision-based autopilot system currently being studied [9].

Open-loop flight tests were performed using wing morphing as an actuation mech-

anism. These flight tests demonstrate the value of morphing for consideration of a

stability augmentation system. The rudder can be used to generate lateral maneuvers

but the tight coupling of roll and yaw complicates the control needed for trajec-

tory tracking. Conversely, the morphing produces almost pure roll so an associated

controller for tracking roll commands will be the first to be implemented.















CHAPTER 4
MODELING

A model of a system can be described by comparing the relationship between the

signals which are observed [19]. A model can be developed with the use of data which

is collected in experiments. System identification considers the development of the

model of a system with the use of observed data. For this purpose the signals typically

considered are the output signals, which are measured, as well as the input signals,

which consider the effect the observer has on the response of a system. Other signals

which can be considered are outside disturbances, which are signals that are produced

from outside sources such as noise, wind gusts and sensor drift.

A model is therefore a mathematical description of a system considering several

aspects but is not an exact description of the physical system [19]. System identifica-

tion is performed by first collecting data which emphasizes the parameters that are to

be considered in the model estimation. Therefore, the input and output signals as well

as specific maneuvers are selected prior to the data collection.

For some systems it is useful to describe the models using graphical interpre-

tations. More specifically, they can be described using impulse, step and frequency

responses. Certain systems can also be described using mathematical models. These

can include continuous-time and discrete-time systems as well as linear and nonlinear

systems.

A set of models can then be selected according to the specific application or

dynamic system. A model which uses a black box approach is used for this project.

This approach considers the input and output signals of the system in order to perform

a fit to the data without providing physical meaning to the values. This model is then









compared with the values obtained in the experiment in order to determine whether it is

a good estimation of the system response.

The black box model structure which considers input and output signals can be

expressed as the linear equation shown in 4.1 where e(t) is the noise error term.




y(t)+aly(t--1)+...+an y(t-na) = blu(t- 1)+...+bnbu(t-nb)+e(t) (4.1)


Then this equation can be expressed in terms of the initial output signal as shown

in 4.2.




y(t) = -aly(t 1) -... -ay(t na) + blu(t- 1) +...+ bu(t --nb) +e(t) (4.2)


This is typically referred to as an ARX model, which defines the autoregressive

part to be the output terms in 4.2, and the input terms in 4.2 as the extra input.

So the initial output values as well as the input and output terms on the right hand

side of 4.2 are collected in matrix form for each time interval. This makes it possible

to solve for the regression coefficients since the initial output and the input values are

known.

The initial output values for each time interval can be expressed as in 4.3 in terms

of the input and output values as well .

I --11 --r U Ut
nb al
/ l /l1 _/ 1 ; 1 1 an (4.3)



/n-" yiI" _-" '/" 9 n
y \ na U1 p









Then the regression coefficients are obtained by using the matrix equation 4.4 and

solving for the matrix of coefficients X as shown in 4.5.



B =AX (4.4)



A"-B =X (4.5)

A transformation as shown in 4.6 is then applied to equation 4.1 in order to obtain

a transfer function as shown in 4.7. In this transfer function the B term contains all the

input coefficients from equation 4.6 and the A terms consists of all the coefficients in

the output terms.




y(t) at) + t) +... + az y(t) = blzlu(t) +... + b,,z u(t) + e(t) (4.6)



yu 1 =BA1 (4.7)

A Tustin transformation is then done using Matlab in order to create a continuous

time version of the discrete time system. This is done using a standard bilinear

transformation such as shown in 4.8.



z = 1 + 2(sT/2) + 2(sT/2)2 + 2(sT/2)3 +... (4.8)

The ARX model approximation is just one of several types of model structures

which can be used for system identification. An ARMAX model structure can similarly

be used but was not used in this project because an initial simple estimation was

desired. The ARMAX model considers the basic properties that the ARX model uses

but also includes a moving average term, which considers the noise in its coefficient

calculations.









Another modeling technique considers recursive identification methods. This

considers calculating a model simultaneous to obtaining data. However, this is not

a requirement for this specific project but can be useful in different applications.

Certain applications include having an up to date model in order to consider these

parameters when making decisions about what the system is to do next. This is

typically referred to as an adaptive modeling technique because the input and output

signals are calculated in order to be used as they become available.

An example of a recursive model which can be used for system identification in

Matlab is the RARMAX model. This uses a recursive technique of an ARMAX model

which considers the noise in its calculations. However, this technique only provides

models for single-input, single-output systems. Similarly, another technique is the

RARX model which estimates parameters recursively of a single-output system.

Therefore, for this project an initial linear approximation was done using an ARX

technique. The initial step was to design an experiment which consisted of specified

maneuvers such as doublets to the morphing and rudder servos. These were done in

order to consider the roll and yaw rate responses of the system.

The data is then collected and processed before considering it for modeling. The

data processing included using an algorithm which plotted, filtered and removed the

bias in the data. The filtering was done using a low pass Butterworth filter on all the

parameters and the bias was removed from the parameters by subtracting the mean.

This processed data is then used in the ARX modeling approximation. The roll

rate and yaw rate responses are then compared to the simulation responses. This is

done for both the morphing and rudder servos. The orders and delays are selected for

the parameter estimation.









The orders of the approximation are the orders of the polynomials A and B in

equation 4.7. Therefore, they are the orders of the polynomials in equation 4.9 and

equation 4.10.



A(z) = 1 +aiz-1 +...+anz-n (4.9)



B(z) = b + b2Z + + bnbzb+l (4. 10)

The delays which are referred to as nk are selected as the number of delays from

input to output as shown in equation 4.11.



A(z)y(t) = B(z)u(t nk) + e(t) (4.11)

In multi-output systems, the orders of the polynomials have as many rows

as outputs. This is then used to create the simulation and it is then converted to

a continuous time system from a discrete time system. The roll rate and yaw rate

responses are then compared and for this project show a good correlation between the

estimated and the actual data for the doublet maneuvers.

The following step in system identification would be to validate the model which

was chosen as the best approximation to the data. This is done by considering whether

the model is a good enough approximation for what it will be used for. In other words,

whether the model can be trusted to reproduce the collected data. A model is typically

not accepted as describing the actual true system, but simply as a good description of

specific parts of the system which are of interest.

The first model obtained using these techniques typically has to be revised because

it may not describe a system considering several different aspects. Particularly, for

this project the models were obtained by considering the inputs and outputs of the







21

system and then reproducing that data. However, the model obtained does not describe

physical parameters which can be used for purposes of further control design.

A model which would be useful for control design would include approximations

of certain aerodynamic parameters and time constants. These parameters can then

be used to design a controller as well as considering the modes. Once the system is

represented in physical parameters, controllers such as roll and yaw dampers can be

designed by feeding back the appropriate angles. This can be done by using a simple

proportional gain in the closed loop system.















CHAPTER 5
24 MICRO AIR VEHICLE

5 1 VehicleDescripion

One of the vehicles cosdeed is the micro ar vehicle with a 24 n wingspan

shown m Figue 5-1















Figure 5-1 Ovehead View of the 24 MAV


The 24 ai MAV consists of a carbon composite frame with a mylar membrane

sltn wing The leadig edge of the wings consst cf carbon-fiber weave wth battens

cf undirectconal ca rbon attached to the undersdendextendgto he tiling edge

These battens provde the stengh needed to support the roads whch ae bemg

appliedwhlle the membrane provides the hliflng surface The oginal cont ol effectcrs

for tis MAY ae the tudder and elevator The udder and elevator each have a single

servo for actation

The control surfaces, the elevator and rudder, axe connected to the serves using a

spring steel puslrod The approximate range cf motion fr each is weninTable 5-1









Table 5-1 Range of control effectors

Effector Range of Motion
elevator 150 to -200
rudder 250 to -250


The basic properties of the 24 in MAV are given m Table 5-2

Table 5-2 Properties of the 24 in MAV

Property Value
Wingspan 24"
Wing Area 100 in
Wing Loading 20 32 oz/ft2
Aspect Ratio 5 76
Powerplant Electric motor w/ 4 75" propeller
Total Weight 400 g


5 2 Morphing

Wing morphing is used as an additional control effector A simple techmque is

used to morph the wings of the 24 n MAV The morphing is actuated by two servos,

one for each wing The techmque used for morphing on this vehicle consists of the use

of a torque rod which produces the deflection that is commanded This torque rod lies

along each wing connected to the servos inside the fuselage as shown in Figure 5-2













Figure 5-2 Wing with Torque Rod


The rods are sewn into the leading edge of the membrane therefore causing

movement of the membrane if the rods are actuated The effect of the morphing is seen









to act as a simple form of wing warping The wing deflection due to the morphing

actuators for the 24 in MAV is show in Figure 5-3













Figure 5-3 Rear View of the 24 in MAV with Undeflected (left) and Morphed (right)
Wing


5 3 Flight Testing

Flight testing of the active wing-shaping 24 in MAV is performed in the open area

of a radio controlled (R/C) model field during which wind conditions range from calm

to 7 knots throughout the flights Once the flight control and instrumentation systems

are powered and initialized, the MAV is hand-launched into the wind This launch is

an effective method to quickly and reliably allow the MAV to reach flying speed and

begin a climb to altitude

This airplane is controlled by a pilot on the ground who maneuvers the airplane

visually by operating an R/C transmitter There is a data acquisition system on board

which begins recording as soon as the motor is powered This DAQ system records

accelerations and rates about the coordinate system which is centered on the MAV

This aircraft design allows either rudder or wing shaping to be used as the

primary lateral control for standard maneuvering The airplane is controlled in this

manner through turns, climbs, and level flight until a suitable altitude is reached At

altitude, the airplane is trimmed for straight and level flight This trim establishes a

neutral reference point for all the control surfaces and facilitates performing flight test

maneuvers










Open-loop data is taken to indicate the flight characteristics of the MAV. Specifi-

cally, the roll and yaw rates and accelerations about a body fixed axis are measured in

response to doublets commanded separately to the servos. Several sets of doublets are

commanded ranging in magnitude and duration to obtain a diverse set of flight data.

The dynamics of the MAV in response to rudder commands is investigated to

indicate the performance of the traditional configuration for this MAV. A representative

doublet command is shown in Figure 5-4. The roll rate and yaw rate measured in

response to this command are shown in Figure 5-5. The roll rate is large and indicates

the rudder is able to provide lateral-directional authority; however, the yaw rate is

clearly larger than the minimal amount which can be expected. Actually, the yaw rate

is close in magnitude to the roll rate so the lateral-directional dynamics are very tightly

coupled. The effect of the rudder in exciting the dutch roll dynamics is clearly seen in

this response.

15






15150[--------- 150---------
10

25






0 1 2 3 4 5 6
Time(sec)
Figure 5-4: Doublet Command to Rudder Servo





-50 -50







Tlme(sec) Time(sec)
Figure 55: Response to Rudder Doublet for Roll Rate(left) and Yaw Rate(right)












Another doublet is commanded to the rudder in order to consider its response.


The rudder is commanded with a slightly larger magnitude and longer duratio doublet

which is shown in Figure 5-6. The response to this doublet command is shown in

Figure 5-7.


-e


o
0
c-i
LU
F0
-e






Figure 5-6:


010





-15
20
0 05 1 15 2 25 3 35 4 45
Time(sec)
Second Doublet Command to Rudder Servo


200-
150
100
50




-100
-150


0 05 1 15 2 25 3 35 4 45 0 05
Time(sec)
Figure 5-7: Response to Second Rudder Doublet for


1 15 2 25 3 35
Time(sec)
Roll(left) and Yaw


4 45

Rate(right)


This shows a similar response as with the first doublet to the rudder servo. It

shows a roll rate response of similar magnitude as the yaw rate. This then describes

a dutch roll motion instead of a pure roll motion even with a slightly larger command


to the rudder. Also, since the doublet was of larger magnitude and longer duration,

this would indicate that the vehicle could be deviating farther from trim than in the


previous maneuver which would result in greater nonlinearities such as increased yaw

motion.


Doublet commands such as shown in Figure 5-8 are used in order to actuate the


morphing servo. This maneuver is done without any input from the rudder in order to


150
100
50




100
150











consider strictly commands to the morphing actuators. The amount of deflection of the

morphing; however, is difficult to interpret because it is a deflection of the material and

it is not expressed in a physical dimension such as degrees.


Figure 5


1 15
Time(sec)


Servo


200
150
100
50

0
-50
-100
150


25 0


05 1 15
Time(sec)


Figure 5-9: Response to Morphing Doublet for Roll(left) and Yaw Rate(right)



The roll rate and yaw rate in Figure 5-9 are measured in response to the doublet

commanded to the morphing servo. These measurements indicate the roll rate is

considerably higher than the yaw rate. Thus, the morphing is clearly an attractive

approach for roll control because of the nearly-pure roll motion measured in response

to the morphing commands.

A separate morphing doublet is commanded at a different time as shown in

Figure 5-10 in order to consider the modeling for a different maneuver. Similarly, this


maneuver consists of strictly morphing actuation and no rudder input.
















0
00






0 05 1 15 2 25
Time(sec)
Figure 5-10: Second Doublet Command to Morphing Servo


The roll rate and yaw rate responses to the second morphing doublet are shown

in Figure 5-11. It can be seen that the morphing doublet commanded in the second

maneuver was of a slightly larger magnitude than the first maneuver. This results in a

larger roll rate response due to a larger morphing deflection.


200 200
150 150
0 100 100
M 50


0 50
0100

150 \ -150
200 200
0 05 1 15 2 25 0 05 1 15 2
Time(sec) Time(sec)
Figure 5-11: Response to Second Morphing Doublet Command for Roll Rate(left) and
Yaw Rate(right)



It is also seen that there is a minimal yaw rate response from the actuation of

a larger morphing deflection. Therefore, it similarly resulted in an almost pure roll

motion with a slightly faster roll rate response than with the previous maneuver.

5.4 Modeling

The data from open-loop flights is then used to approximate a linear time-domain

model using an ARX approximation [18]. This model is generated by computing

optimal coefficients to match properties observed in the data.











The maneuvers of interest are doublets ranging in magnitude and centered

around a trim condition. Therefore, the assumption of linearity is reasonable since the

maneuvers are about trim. For the approximation, the rates which are considered are

roll and yaw rate because they are of most interest for maneuvers such as doublets.

The accelerometers were considered but the data was very noisy, therefore, not

allowing for accurate approximations to be made.

The simulated and measured values of roll rate and yaw rate are shown in

Figure 5-12.

200 200
150i 150
100 100
50 50
0 0
4 -50 \- -50
-100 -100
150 150
-200 -------------------- 200--------------------
0 05 1 15 22 25 0 05 1 1 5 2 25
Time(sec) Time(sec)
Figure 5-12: Simulated (- ) and Actual (-) Roll Rate(left) and Yaw Rate(right)
Responses to Morphing Doublet


The simulated responses show good correlation with the actual data. The model is

thus considered a reasonable representation of the aircraft dynamics as it is excited by

the doublet. The existence of such a model is important for future design of autopilot

controllers but it is also valuable for interpreting the morphing.

When using the ARX simulation in Matlab, a linear approximation could not be

made on the maneuvers which were not centered around trim. Therefore, not only are

maneuvers around trim desired for a linear approximation, but they are also necessary

in order for the simulation to be done.

The model which will be used was chosen because it produced the closest match

to the maneuver as compared to four other doublets. The maneuvers compared were

from the same data set, but the one that was chosen resulted in a closer match due to









the aircraft being closer to trim. The resulting model consists of six states and poles as

shown in Table 5-3. The roll mode is clearly shown and the dutch roll mode indicates

the slight oscillations which are present in the combined roll and yaw motion as shown

in Figure 5-12.

Table 5-3: Poles of a linear model of the 24 m MAV

Poles Value
Dutch Roll -3.75 13.841
Roll -4.03


In order to study whether this model is a good enough linear approximation of

the dynamics of the 24 m MAV, different inputs are considered for the same model.

These inputs are doublet morphing commands at different times throughout the same

set of data. The simulated and measured values of roll rate and yaw rate are shown in

Figure 5-13 for several inputs.

It is clearly shown that the simulated and actual roll rate and yaw rate responses

demonstrate good correlation. The simulations shown in Figure 5-13 show that the

model which was obtained from a doublet maneuver responds well to different inputs.

The first input was a small morphing doublet commanded from a separate data set. The

following two inputs were from a medium and large morphing doublet, respectively

from the data set that was used for obtaining the model.


















50-


-50

100

150

0 05 1 15 2 25 3 35 4
Time(sec)
200

150

100

50

150 /'


100

150


0 05 1 15 2 25
Time(sec)


0 05 1 15
Time(sec)
Figure 5-13: Simulated (

Responses to Morphing Doublets


3 35 4


2 25

) and Actual


0 05 1 15 2 25 3 35 4
Time(sec)


ThU
0 05 1 15 2 25 3 35 4
Time(sec)
200

150

100

50

s0-
-50

-100

150
200]
0 05 1 15 2 25
Time(sec)
(-) Roll Rate(left) and Yaw Rat


e(right)


5.5 Evaluation


If this MAV is to be used in surveillance missions, the use of only rudder and


elevator could provide sufficient control during turns. However, the resulting dutch roll


motion creates difficulties if this MAV is to be used for a more demanding mission and


also requires more pilot control. Therefore, this vehicle requires further control in order


to be used in situations such as in urban environments where more controlled turns are


required.


0C-- -









Using wing twisting as an additional control effector for roll improves the

performance and controllability of the aircraft. Using wing twist additionally, as

compared to the traditional rudder and elevator results in improved flight path tracking,

especially when considering gusty weather environments.

The flight characteristics of the 24zn vehicle are actually quite impressive to view.

The measurements of roll rate and yaw rate indicate the mathematical nature of the

characteristics; however, a qualitative evaluation is also useful. Such an evaluation is

best achieved in association with step commands given to each servo.

The step to the rudder causes the airplane to roll but the coupled yaw results in a

flight path similar to a corkscrew spiral. Conversely, the step to the morphing causes

the airplane to roll with a minimum of yaw so the flight path is nearly a straight line.

In other words, the morphing induces almost pure roll and allows much more accurate

tracking of desired flight paths.

Also, the morphing results in considerably higher roll rates than the rudder.

This result is quite interesting given that the rudder deflection is quite large but the

morphing, as shown in Figure 5-10, is not overly commanded to deflect. Thus, a small

amount of morphing is sufficient to cause a dramatic response from the aircraft.















CHAPTER 6
12 m MICRO AIR VEHICLE

6 1 Vehicle Description


This vehicle has a wngspan of


12 n and is show in Figure 6-1


Fgure 6-1


The basic properties of this vehicle are given in Table 6-1

Table 6-1 Properties of the 12 xn MAV

Property Value
Wingspan 12"
Wing Area 44n2
Wing Loading 14 19 oz/ft2
Aspect Ratio 3 27
Powerplant Electric motor w/ 2 25" propeller
Total Weight 123g


The 12 n MAV is designed to have an elevator as its control effector The

elevator is actuated by using a single servo Therefore, this vehicle does not include a

rudder and an additional control effector will be added









Thi s vehcl i constcted using the similar designs which are used at the Univer-

sity of Flcrida which consist of carbon fiber aifraines and flexible membrane wings

The composite wmig on the 12 i MAV skeleton is covered with an extensible m m-

brane skm of latex uibber The latex matenal used m the 120 MAV is considerably

moe flexible e han the mylar sheeting whhis used m the 24 in MAV

6 2 Morphing

The 12 in MAV is designed with m ophing as an additional control effector The

m ophing is implemented y actuatng a singe servo which is connected to each wing

The use of a oe flexly le m material for the wing surface of this vehicle was chosen

on purpose m order to consider m e dramatic shape changes of the wings Ths is

also done on a smaller ar fr me without a Mudder to consider stnctly the effects of

morphing

















Figure 6-2 View of the 10 i MAV


The initial implementaton of this morphing strategy was ongnally attempted on a

MAV with 10 oi wingspan as shown in Figue 6-2 The 10 in MAV is designed with a

similar carbon fibi er a frae and fle le membrane wings The fact that ths craft

is smaller than the 12 in MAV allows for a smaller wing aea and shorter, more closely

aligned wing batts This vehicle, like the current vehicle, has latex coveng o the

wings so was very easy to morphine fliit The 10 1 n MAV was chosen for the itial









study because it was already constructed and could be readily adapted for the new

study. The flights of that vehicle were quite promising and clearly indicated that the

morphing provided an effective form of control authority.

This MAV responded well to the wing morphing commands, however, is restricted

in the amount of flight testing which can currently be done due to its payload limita-

tions. This led to the design of the 12 in MAV with the requirement of a larger aircraft

in order to carry the required instrumentation to perform open-loop and closed-loop

flight testing.

The design of the 12 in MAV initially followed closely the design of the 10 in

MAV with a similar airframe and wing design. The open-loop flights are similarly

performed with a data acquisition board and the closed-loop flights will be done with a

memory board.

The 12 in vehicle was essentially a scaled version of the original vehicle except

for the wing construction. The original version had a single structure for the wings that

mounted atop the fuselage. The new version had separate wings that attached to posts

on each side of the fuselage. This separation of the wings allowed for more flexibility

due to the removal of the carbon fiber structure.

The leading edge of the 12 in MAV was initially built with a single layer of

carbon fiber. This proved to be faulty during the first attempts at flight when the

leading edge would fold over when wing loads were applied. Therefore another

layer of carbon fiber was applied to the wing making it stiffer and better capable of

withstanding the wing loads.

Another issue with the wing design was using the same flexible latex material

on this 12 in as on the 10 in MAV with the larger airframe requiring a larger wing

area. The wing battons are not as closely aligned on the larger frame and the larger

sheet of latex is weaker with larger loads. Therefore not allowing for wing morphing

as dramatic on the 12 in as on the 10 in MAV.









Further flight testing of the 12 in MAV indicated a problem with the thread

connection. The morphing of the 10 in MAV used only a single thread attached to the

outboard of the trailing edge and this style was used for the 12 in MAV. Unfortunately

the battens on the larger MAV were spaced farther apart than on the smaller MAV

so the wing was weaker. The leading edge on the 12 in MAV would now remain

properly shaped but the trailing edge would collapse when loaded. This problem was

addressed by attaching a second thread to the trailing edge of the wing and allowing

the morphing actuation to provide strength to support the loads.

The 12 in MAV is designed to allow for a more complicated type of morphing

than is used for the 24 in MAV. The wings of this smaller vehicle are constructed from

latex sheeting whereas the wings of the larger vehicle are made of mylar sheeting.

Consequently, the wings of the 12 in vehicle are considerably more flexible, and thus

easier to morph, than the wings of the 24 in vehicle. This flexibility allows simple

mechanisms to again be appropriate for generating morphing and allow control issues

to be investigated.

The high flexibility of the wings for this MAV allow consideration of morphing

beyond basic warping. More specifically, this vehicle is used to consider morphing

that affects the twist and span of the wings. A torque rod, as used for the 24 in MAV,

would clearly not be appropriate for such a morphing. Instead, the rod was replaced

with threads.

The morphing strategy for this MAV is shown in Figure 6-3. Kevlar threads

are strung between a servo in the fuselage and points near the outboard of the wings.

These threads are incredibly strong and the minor stress received during flight is not

sufficient to cause any stretching.

The morphing achieved by this strategy is directly dependent upon the attachment

points of the threads. The attachment of the threads to the fuselage is near the leading

edge of the wings. The corresponding attachment to the wings is actually at separate























points One attachment point is near the mid-chord point at the wing-tip outboard

Another attachment point is the trailing edge near the two-thirds span location

The morphing that results by actuating the servo is shown in Figure 6-4 The

servo rotates and causes the threads to pull against the attachments on the wing The

morphing resulting from this strategy is clearly beyond simple warping In this case,

the pulling of the threads toward the leading-edge attachment at the fuselage causes the

wing to both twist and bend The effect is similar in nature to a curling of the wings

The basic parameters that are readily observed to change are the twist, camber, chord,

and span













Figure 6-4 Front View of the 12 in MAV with Undeflected (left) and Morphed (right)
Wing


The morphing is designed for a biologically-inspired effect The displacement

of the wing resembles shapes observed in birds like gulls For instance, the bending

along the span is concentrated around a single point which correlates to the elbow in









birds. The twist is concentrated near the trailing-edge outboard which correlates with

the feathers near the wrist of birds. A more formal approach to this concept is being

designed by NASA but this current vehicle is sufficient to investigate control issues [6].

Only a single wing is altered in Figure 6-4. The vehicle actually contains separate

servos for each wing that allow the morphing to act simultaneously on both wings;

however, this thesis will restrict attention to morphing a single wing. The current

objective considers roll control but the longitudinal issues will be investigated in the

future.

Also, this vehicle is ideal for the focus of this thesis. Specifically, the morphing

strategy is quite simple but the morphing effect is complicated. This approach allows

the control issues associated with morphing to be easily studied. The vehicle is not

designed to study the optimal strategies for morphing; rather, the vehicle is designed to

study the optimal strategies for control.

6.3 Flight Testing

Flight testing is also done on the 12 in MAV in an open area for R/C airplanes.

The flight tests for this MAV are performed in similar conditions as the tests for the

24 in MAV. This MAV is equipped with a data acquisition board which begins logging

when the motor is turned on.

This MAV is then similarly hand launched into the incoming wind for takeoff.

The primary forms of control for this MAV are the elevator and wing morphing. The

airplane is controlled with these surfaces for takeoff, turns, climbs, and level flight.

The airplane is then trimmed for straight and level flight. Achieving trimmed flight

is necessary as a neutral reference point for the control surfaces and in performing

different flight test maneuvers.

This MAV is then tested by commanding doublets to the morphing servos. A

representative doublet command is shown in Figure 6-5. The units of this command












are just count commands to the servo because the actual deflection caused by morphing

is difficult to quantify.

40

30
-0


o 10


-10

-20

301
0 05 1 15 2 25
Time(sec)
Figure 6-5: Doublet Command to Morphing Servo



The responses to the morphing doublets are measured by the on-board data

acquisition system. The roll rate and yaw rate are presented in Figure 6-6.

80 80

60 60

40 40


S20 \ 20
0 0


-40 40

60 60
0 05 1 15 2 25 0 05 1 15 2 25
Time(sec) Time(sec)
Figure 6-6: Roll Rate(left) and Yaw Rate(right) in Response to Morphing Doublet



The roll rate is clearly correlating well with the commanded doublet and demon-

strates the morphing is capable of commanding roll maneuvers. The yaw rate is

somewhat more difficult to understand. Notably, the aircraft builds up yaw rate approx-

imately 0.5 seconds after the onset of the doublet command. This flight characteristic

results from the single-sided nature of the morphing. Essentially, the wing that is

morphed loses lift but also increases drag. The loss of lift immediately causes rolling

and the increase of drag causes a slight delay in building up the yaw rate.








40


A separate morphing doublet is commanded at a different time as shown in

Figure 6-7 in order to consider the modeling for a different maneuver. This maneuver

consists of strictly morphing actuation.

40

30




-0


3O -10
-20

0 05 1 15 2 25 3 35
Time(sec)
Figure 6-7: Second Doublet Command to Morphing Servo


The roll rate and yaw rate responses to the second morphing doublet are shown

in Figure 6-8. It can be seen that the morphing doublet commanded in the second

maneuver was of a slightly smaller magnitude than the first maneuver. This results in a

smaller roll rate response due to a smaller morphing deflection.

80-- 80-

S60 60


0 0
-20 202



-20 -20


0 05 1 15 2 25 3 35
Time(sec)
Figure 6-8: Response to Second Morphing
Yaw Rate(right)


0 05 1 15 2 25 3 35
Time(sec)
Doublet Command for Roll Rate(left) and


6.4 Modeling

A linear model is identified from the flight data. A 6-state model was originally

identified but reduced to a 3-state model as shown in Table 6-2. The simulated

responses of this model are compared with measured values of roll rate and yaw rate in

Figure 6-9.










80--------------------- 80---------------------

0 60
bt 40 40





-20 R -7.520
0 05 1 15 0 05 1 15
Time(sec) Time(sec)
Figure 6 9: Simulated(- -) and Actual(-) Roll Rate(left) and Yaw Rate(right) Re-
sponses to a Doublet

Table 6 2: Poles of a linear model of the 12 mv MAV

Poles Value
Dutch Roll -3.6704 14.7321
Roll -7.521


The responses of the model are u nexpected givento the measured responses. The

roll rate shows a good correlation although the yaw rate is somewhat less accurate.

The model contains a roll convergence mode which, based on the accuracy of roll

simulations, is accepted. The model also contains a dutch roll mode which attempts to

capture the dynamics associated with yaw rate. The inability of this mode to represent

the yaw dynamics may indicate some nonlinearity is associated with the vehicle. Such

nonlinear dynamics would not be unexpected given the extreme nature of the morphing

and the asymmetry resulting from morphing a single wing.

In order to study whether this model is a good enough linear approximation of

the dynamics of the 12 m MAV, different inputs are considered for the same model.

These inputs are doublet morphing commands at different times throughout the same

set of data. The simulated and measured values of roll rate and yaw rate are shown in

Figure 6-10 for several inputs.

It is clearly shown that the simulated and actual roll rate and yaw rate responses

demonstrate good correlation. The simulations shown in Figure 6-10 show that

the model which was obtained from a doublet maneuver responds well to different













inputs. The yaw rate; however, is difficult to model because the vehicle is morphed


asymmetrically and this introduces nonlinearities. These nonlinearities have to be


considered in an approximation in order to obtain an accurate model.


Time(sec)


40

20



20

-40
'


-60-


Figure 6 10:


05 1
Time(sec)
Simulated (


S0 25
20
15
4 o
-d



5l
-5
-10
15 2 o

-) and Actual (


05 1 15 2
Time(sec)
) Roll Rate(left) and Yaw Rate(right)


Responses to Morphing Doublets









6.5 Evaluation

When using the ARX simulation in Matlab, a linear approximation could not be

made on the maneuvers which were not centered around trim. Therefore, not only are

maneuvers around trim desired for a linear approximation, but they are also necessary

in order for the simulation to be done.

It is particularly difficult to find maneuvers to use for a linear approximation for

this specific vehicle due to the fact that it is very hard to trim. Therefore, before most

maneuvers there is an indication in the data that there are some oscillations about the

roll axis. Similarly, the data indicates that several seconds after a maneuver has been

initiated, a component of yaw rate begins to develop.

The build up of yaw rate after a morphing maneuver has been initiated can be

attributed to the fact that the shape of the wing is being altered. The wings on this

vehicle are being curled underneath, one at a time resulting in an asymmetric morphing

actuation. This leads to nonlinearities in the flight characteristics of the vehicle which

can explain the oscillations and the build up of yaw seconds after a maneuver has been

initiated.

The modeling is a linear approximation of coefficients, and when considering

nonlinear behavior it might not provide data that can be trusted. The 24 in MAV is

morphed by twisting the wings symmetrically, which can be approximated as a linear

behavior. However, the 12 in MAV is being morphed asymmetrically, and therefore

requires further studies to obtain a better approximation of the model.















CHAPTER 7
CONCLUSION

Current micro air vehicles are designed with the common features of carbon

fiber airframes and flexible membrane wings. The typical control surfaces which can

be implemented on MAVs consist of rudder and elevator. The conventional control

surfaces such as ailerons can not be easily included in the design of the common

MAVs due to the fact that the wings are made of flexible material.

A different form of actuation is necessary in order to improve maneuverability and

performance for MAVs if they will be assigned to evolving missions. A particularly

demanding mission is one which takes place in an urban environment which requires

these vehicles to have advanced maneuvering capabilities. A simple approach to

increasing maneuverability is to include an additional control effector such as wing

morphing.

This paper has demonstrated that morphing can be an effective means to achieve

roll control for a micro air vehicle. The flexible nature of the wings enables their

shapes to be easily altered. Simple mechanisms, such as a torque rod and Kevlar

threads, are used on a 24 in MAV and a 12 in MAV. In each case, the vehicle was

flown using morphing as the primary effector for roll maneuvers. The flight data

clearly shows the morphing produces significant roll rates and provides significant

controllability.

These vehicles are flown in an R/C field and are equipped with a data acquisition

system(DAS). This DAS consists of gyros and accelerometers for the three axis. The

data is then retrieved and the accelerations and rates of the three axis can be studied.

This data is then used for a linear modeling technique.







45

A linear approximation is then considered using an ARX modeling technique

in Matlab. This shows a good correlation with the data for the 24 in and the 12 in

MAV. However, further studies have to be considered for the modeling of the 12 in

MAV since it is being morphed asymmetrically by curling one wing at a time. This

then introduces nonlinearities in the flight characteristics which have to be considered

in modeling approximations. The 24 in MAV can be approximated linearly since the

morphing is being induced with symmetric wing twisting.















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BIOGRAPHICAL SKETCH

Helen Garcia was born in Santo Domingo, Dominican Republic, on May 22, 1979.

Her family moved to Miami, FL, in 1990. She received her high school diploma from

Miami Coral Park Senior High School in Miami, FL. She then attended the University

of Florida and received her bachelor's degree in aerospace engineering in May 2002.

She has worked in the dynamics and control research group under Dr. Rick Lind and

will receive her master of science degree in aerospace engineering in December 2003.