DYNAMIC CHARACTERISTICS OF MORPHING MICRO AIR VEHICLES
By MUJAHID ABDULRAHIM
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 2004 In the name of Allah, the Gracious, the Merciful.
My thesis in its entirety (apart from one sentence in the beginning of Chapter 4) is dedicated to my loving family, who have put up with my outrageous silliness in pursuit of academic achievements. To my father, who first led me down the path of innovation by helping me build my own toys. To my mother, who from the very beginning has been my advisor, counselor, and best friend. To my brother, who is my co-pilot in the clouded airspace of life. And to my sister, who is my ultimate role model for writing style and literary wit. The single outstanding sentence in Chapter 4 is dedicated to my rubber chicken, who provides irrelevant comic amusement like no other inanimate domestic animal can.
Looks real, feels real, stretchable. Hells yeah. ACKNOWLEDGMENTS The work presented in this thesis was heavily supported by a large group of highly supportive people. The bulk of the mentoring, advice, suggestions, and orders came from my research advisors, Dr. Richard Lind and Dr. Peter Ifju. Dr. Lind has helped me develop an understanding of flight test objectives, modeling strategies, and, more importantly, the effect of our work on the future of aerospace. Dr. Ifju has been the ultimate source for creative inspiration in aircraft design and fabrication technique.
Martin Waszak of NASA Langley Research Center has supported the UF micro air vehicle research effort for many years. In addition to providing the funding for all the research presented here, he has hosted me at LaRC for two summers on MAV design and flight testing internships. Mark Motter, also from LaRC, has provided considerable expertise in related projects. His influence carries over to the current research.
Several students have also been kind enough to support the research with time, knowledge and hardware. Jason W. Grzywna and Jason Plew have provided much of the electronics hardware support for the MAVs. Jos Cocquyt, Baron Johnson, Kenneth Boothe, Shawn Mytrik, and Dan Claxton have helped extensively in solving design problems and supporting flight tests. Finally, Alfred, my rubber chicken, helped pull me through the low times when even singing ”Always Look On the Bright Side of Life” could not cheer me up.
iii TABLE OF CONTENTS page ACKNOWLEDGMENTS ...... iii LIST OF TABLES ...... vi LIST OF FIGURES ...... vii ABSTRACT ...... x
1 INTRODUCTION ...... 1 2 BIOLOGICAL INSPIRATION ...... 4 3 MORPHING ON SMALL FLIGHT VEHICLES ...... 8 4 ASYMMETRIC WING SHAPING FOR ROLL CONTROL ...... 13
4.1 Aircraft Design ...... 13 4.2 Morphing Mechanism ...... 14 4.3 Flight Performance ...... 17 4.4 Nonlinear Modeling of Lateral and Longitudinal Dynamics ...... 19 5 SYMMETRIC WING TWISTING FOR ROLL CONTROL ...... 22 5.1 Aircraft Design ...... 22 5.2 Morphing Mechanism ...... 23 5.3 Flight Performance ...... 24 5.4 Linear Modeling of Lateral Dynamics ...... 25 5.5 Spin Characteristics of Wing Twist Morphing ...... 27 6 MULTI-POINT WING SHAPING ...... 33 6.1 Aircraft Design ...... 33 6.2 Morphing Mechanism ...... 33 6.3 Flight Performance ...... 35 7 VARIABLE GULL-WING ANGLE MORPHING ...... 37 7.1 Aircraft Design ...... 37 7.2 Morphing Mechanism ...... 38 7.3 Flight Performance ...... 41 7.3.1 Gliding Performance ...... 42 7.3.2 Climb Performance ...... 43
iv 7.3.3 Stall Characteristics ...... 44 7.4 Lateral-Directional Dynamics ...... 45 7.4.1 Roll Convergence ...... 45 7.4.2 Dutch Roll Mode ...... 50 7.5 Longitudinal Dynamics ...... 56 8 FOLDING WING AND TAIL MORPHING ...... 59
8.1 Aircraft Design ...... 59 8.2 Morphing Mechanism ...... 59 8.3 Flight Trials ...... 61
9 SUMMARY ...... 63 9.1 Recommendations ...... 63 9.2 Conclusions ...... 64 REFERENCES ...... 65
BIOGRAPHICAL SKETCH ...... 68
v LIST OF TABLES Table page 4–1 Properties of the 10 in and 12 in wing shaping MAVs ...... 14 5–1 Properties of the 24 in wing twisting MAV ...... 23 7–1 Wing geometry change over variable gull-wing morphing range ...... 38 7–2 Dutch roll modes for 0o gull-wing ...... 54
7–3 Dutch roll modes for 15o gull-wing ...... 55 7–4 Dutch roll mode eigenvectors for 0o gull-wing ...... 55 7–5 Dutch roll mode eigenvectors for 15o gull-wing ...... 56 7–6 Longitudinal modes for 0o gull-wing ...... 57
7–7 Longitudinal modes for 15o gull-wing ...... 57 8–1 Properties of the folding wing-tail aircraft in two configurations ...... 60
vi LIST OF FIGURES Figure page 1–1 Variable gull-wing morphing aircraft ...... 2 2–1 A bird alters its gull-wing angle to affect gliding angle ...... 5 2–2 A seagull uses differential wing extension (left) and differential wing sweep (right) ...... 6 2–3 A seagull extends its wings for cruising flight (left) and descends at a steep angle using gull-wing morphing (right) ...... 7 3–1 Micro data acquisition system ...... 10
3–2 Roll, pitch and yaw rate sensor board ...... 11 4–1 Wing shaping morphing MAVs - 10 in wingspan high-wing aircraft (left) and 12 in span mid-wing aircraft (right) ...... 14
4–2 Top, front, and side views of computer-aided design drawings for 12 in MAV ...... 15 4–3 Kevlar cables ...... 15 4–4 Front view showing undeflected wing (left) and morphed wing (right) . . . 16
4–5 Measured and predicted responses for roll rate (left), pitch rate (middle) and yaw rate (right) ...... 21 5–1 Wing-twisting MAV ...... 22 5–2 Underside view of wing showing torque rod ...... 23
5–3 Rear view of the 24 in MAV with undeflected (left) and morphed (right) Wing ...... 24 5–4 Doublet command to rudder (left), roll rate response (middle), and yaw rate response (right) ...... 26 5–5 Doublet command to wing twist morphing (left), roll rate response (mid- dle), and yaw rate response (right) ...... 27
5–6 Pilot commands (left) and responses (right) during conventional spin . . . 28 5–7 Pilot commands (left) and responses (right) during spin ...... 30
vii 5–8 Pilot commands (left) and responses (right) during cyclic spin ...... 31 6–1 Top, side, and front views of the 24 in span multiple-position wing shap- ing vehicle ...... 34 6–2 Wing shaping MAV showing neutral position (top left), wingtip morph- ing (top right), and full wing morphing (bottom) ...... 35 6–3 Spar torque-tube morphing actuators. The 4 front servos rotate concen- tric spar sections, aft 2 control rudder and elevator ...... 35
7–1 Top and side view of variable gull-wing aircraft ...... 38 7–2 Vehicle undergoing neutral (top), positive (center), and negative (bottom) gull-wing morphing ...... 39
7–3 Variable gull-wing spar structure and control linkage, linear actuator vis- ible inside fuselage at left ...... 40 7–4 Underside view of left wing showing wing twist effector ...... 41 7–5 Wing-twist command and response from flight data ...... 47
7–6 Pole migration with gull-wing morphing angle ...... 48 7–7 B-matrix value for first-order roll mode systems ...... 49 7–8 Wing-twist command (top) at 0o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) ...... 50
7–9 Wing-twist command (top) at 15o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) ...... 50 7–10 Wing-twist command (top) at 30o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) ...... 51 7–11 Wing-twist command (top) at -20o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) ...... 51
7–12 Rudder control pulse at 0o gull-wing angle with measured data (:) and simulated response (-) ...... 52 7–13 Rudder control pulse at 15o gull-wing angle with measured data (:) and simulated response (-) ...... 52 7–14 Open-loop Dutch roll mode pole migration for two morphing positions . . 55 7–15 Frequency response diagram for 0o gull-wing (:) and 15o gull-wing (-) . . 56 7–16 Elevator pulse command (left), measured (:) and simulated( -) pitch rate responses (right) ...... 58
viii 7–17 15o gull-wing elevator pulse command (left), measured (:) and simu- lated( -) pitch rate responses (right) ...... 58 8–1 Top view of unswept (left) and swept (right) configurations ...... 59 8–2 Side view of unswept (top) and swept (bottom) configurations ...... 60
8–3 Envisioned dynamic pitch up maneuver for forward to reverse flight tran- sition ...... 62
ix 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 DYNAMIC CHARACTERISTICS OF MORPHING MICRO AIR VEHICLES By Mujahid Abdulrahim
December 2004 Chair: Richard Lind Major Department: Mechanical and Aerospace Engineering The research presented in this thesis is an approach to the study of flight dynamics of morphing vehicles. Case studies of several strategies are addressed in order to determine some of the basic flight characteristics of dynamically and quasi-statically morphing aircraft. These strategies include a flexible membrane wing that uses tensioned cables to shape the wing for roll control. The wing shaping for this vehicle improves roll tracking and decreases coupling compared to a rudder, even though the morphing is asymmetric. Active morphing is also implemented by using torque-rods and torque-tubes to anti-symmetrically twist a flexible wing surface. This form of morphing provided aileron-like control without a hingeline. Quasi-static morphing is used to change the gull-wing angle of an aircraft in flight. This biologically-inspired shape change alters the performance characteristics and dynamics of the vehicle and allows it to fly in several distinct flight modes. The vehicles are equipped with sensors and data logging devices and flight tested using a variety of maneuvers and techniques. Data from these maneuvers are used to estimate longitudinal and lateral-directional models for the aircraft morphing systems. Stability and controllability of the vehicles
x are examined in the context of the high-agility and aerodynamic performance changes caused by the morphing.
xi CHAPTER 1 INTRODUCTION
As envisioned morphing designs become increasingly complex, the need for accu- rate flight dynamic analysis becomes even more important [38]. The complex shapes achievable by the new generation of actuators and structures can create difficulties in representing the vehicle using existing methods. For instance, an aircraft that morphs asymmetrically can undergo aerodynamic and inertial changes that violate assump- tions used to simplify the commonly used equations of motion. Existing modeling approaches typically do not account for time-varying vehicle geometry or large changes in the aircraft configuration. The modeling predicament underscores one of the current realities of morphing research; namely, the majority of morphing is being conducted in optimal aerodynamic shapes and static aeroelastic effects. The field of morphing vehicle flight dynamics is still highly underdeveloped. Part of this void is understandable since few, if any, morphing aircraft exist today to perform flight test experiments. However, the lack of work also points to potential future problems in morphing research. Flight dynamics must be developed in parallel to other morphing efforts in order to assess and control prototype vehicles. The work presented in this thesis represents an initial foray into such an effort. The flight dynamics of simple morphing vehicles, such as the aircraft shown in Figure
1–1, are discussed. Design of the morphing effectors is based on observations of biological systems. Dynamic effectors such as wing twisting and wing curling are tested on several vehicles. Such effectors are replacements to ailerons, which cannot be mounted to a flexible membrane wing. Such forms of morphing are similar to the roll control effectors used on the NASA F/A-18 AAW [27]. Other effectors are operated
1 2 quasi-statically, such as a gull-wing morphing and a folding wing-tail system. These systems also include dynamic morphing effectors, but are intended to address the larger problem of changing flight modes. Vehicle design and morphing actuators are considered only enough to develop testbeds for flight dynamics experiments. No claim is made as to the optimality of the vehicle shapes or morphing methods. It is sufficient to consider that the morphing causes a change in the flight performance, which is then the basis for studying any accompanying change in stability and control characteristics.
Figure 1–1: Variable gull-wing morphing aircraft
The enabling factor for this work is rapid prototyping of aircraft designs at the University of Florida Center for Micro Air Vehicles. Developing an experimental unmanned air vehicle from concept to initial flight test occurs within one or two weeks [18]. Fabrication tools such as CNC milling and composite lay-up facilities allow the entire airframe to be manufactured in-house [17]. Small instrumentation and avionics are commercially available, reducing development time and cost significantly. Using these resources, inexpensive testbeds can be produced quickly to test new concepts in aircraft design and flight control. The material presented in this thesis is from flight tests of several morphing micro air vehicles. A variety of modeling approaches are used to identify the flight dynamics of the vehicles. The initial modeling approach taken is based on simple transfer 3 function approaches. Initial models are developed under the assumption of linearity in order to understand the broad effect of the variable geometry on the aircraft dynamics. Nonlinear modeling is considered for vehicles with complex, asymmetric morphing. CHAPTER 2 BIOLOGICAL INSPIRATION
Early aviators of the 20th century were largely inspired in their designs by natural flight systems such as birds, insects, and seeds. This inspiration is evident in the design shapes they chose, which featured wing and tail planforms that were highly similar to birds. Even the early airplane attempts were constructed using a rigid skeleton frame covered in a cloth skin, to resemble the wings of birds and bats. With the eventual success of the Wright Brothers and the modernization of the airplane, designs became more faceted and less-birdlike than their predecessors. Contemporary aircraft now have little apparent similarities to birds. The divergence of aircraft designs from early biological inspiration is likely a result of the vastly different flight regimes encountered in natural and engineered systems. In particular, large, high-speed aircraft share very little in common with a typical bird, which is neither large nor high speed by comparison. The stiff, fixed geometry of airplanes are opposite to the physiology of birds, which incorporate many
flexible and variable-shape members. Modern aircraft design is then based entirely on derived aeronautical sciences and very little on direct biological-inspiration. The continued miniaturization of electronics has fueled a movement opposite to that of the large, supersonic jets. A new generation of small air vehicles is under development using micro sensors and instruments. These vehicles are getting smaller and lighter, such that they are now in a class highly similar to the birds and bats which motivated the early aeronautical efforts. Furthermore, with an emergent need for multi-role, shape-changing vehicles, biological-inspiration is coming to the forefront of design philosophy.
4 5
Morphing is under consideration as a means to adapt a flight vehicle to changing mission requirements or flight conditions. This type of adaptability has always been present with biological systems. Birds are forced to alter their wing shapes dramatically in order to accomplish cruise glides, steep descents, and aggressive maneuvering as shown in Figure 2–1. Conversely, conventional aircraft are generally of fixed configuration and are optimized for a very specific flight condition. Outside of this condition, aircraft usually suffer from poor efficiency and poor aerodynamic performance. By changing the vehicle shape in flight, an aircraft can re-optimize itself for a variety of tasks, as birds do constantly. Thus, morphing through biological- inspiration for small vehicles is both extremely relevant and highly desirable.
Figure 2–1: A bird alters its gull-wing angle to affect gliding angle
Biological-inspiration in aircraft flight systems presents considerable challenges to the aircraft designer. Natural and engineered systems differ greatly in structural composition, performance requirements, and available components. For instance, birds rely on strong muscles, hollow skeletons, flexible joints, and feathers to achieve the necessary motions and shapes for flight. Aircraft use motors, propellers, hinge lines, and mostly rigid structures to sustain flight. The differences between the two systems means that direct emulation is not practical or even desirable. Thus, it is not the goal of this research to mimic bird kinematics. Rather, the objective is to use select 6 biologically-inspired systems to improve the range of achievable flying conditions for conventional aircraft. Birds use a variety of morphing techniques in their wings and tail to accomplish dynamic maneuvering and stabilization. Differential wing twist, wing extension, and wing sweep are used for primary lateral-direction control. Differential wing extension is observed on seagulls during steep bank turns, as shown in Figure 2–2. Differential wing sweep is also shown, here used for roll and yaw control. Collective variations of these morphing motions are used in conjunction to the tail for longitudinal control. These strategies present an initial starting point for implementing morphing on a small vehicle.
Figure 2–2: A seagull uses differential wing extension (left) and differential wing sweep (right)
In addition to morphing for maneuvering, birds also implement a quasi-static morphing of gull-wing angle during glide and steep descent phases. Figure 2–3 shows a bird at two different gull-wing positions for different phases of flight. The gull-wing action depends on a set of parallel bones connecting the shoulder and elbow joints of a bird wing. A rotation of the shoulder joint in the vertical plane results in an extension or contraction of the entire wing. The skeletal mechanism provides a geometric ratio between the extension of the inner and outer bones. Such a mechanism allows the bird 7
Figure 2–3: A seagull extends its wings for cruising flight (left) and descends at a steep angle using gull-wing morphing (right) to morph into a variety of positions using a single movement. Each of the positions is largely stable and affords a unique capability within the flight envelope. The purpose of this variable gull-wing action in birds is likely for a variety of reasons, including static aerodynamic [9], physiology, and for flapping control. However, it is studied here solely to investigate the quasi-static aerodynamic benefit and the corresponding effect on the vehicle dynamic response. This type of morphing is considered on a small vehicle, exploring the potential benefits to the cruise, steep descent, and approach phases of flight. CHAPTER 3 MORPHING ON SMALL FLIGHT VEHICLES
Implementing basic forms of morphing on micro air vehicles involves iden- tifying morphing strategies that can be readily adapted to the vehicles. Identified forms of morphing in birds are adapted to aircraft using existing actuators or simple mechanisms. In this manner, the focus has been placed on flight testing the morph- ing concepts as opposed to developing optimal morphing shapes or actuators. This approach provides an essential look at the flight dynamics and controllability issues without depending on actuator and material technology. Despite the simplicity of the approach to morphing, the vehicles have demon- strated improved performance and control characteristics compared to aircraft with conventional control effectors. For instance, morphing can be used to provide roll control on an aircraft with flexible wings without the use of hinges. This method re- tains the beneficial characteristics of the flexible wing [22] [37], without compromising control [14].
The work presented in this thesis summarizes the development and flight testing of several morphing aircraft. Each aircraft type is essentially designed around a particular type of morphing. Although the essence of each design is based on several generations of non-morphing vehicles, each is adapted in structure, shape, and material to host the morphing mechanism. For several of the initial attempts at morphing, this adaptation is quite minimal and is limited to drilling holes in the airframe and attaching the actuator arm or cable to the wing. However, as the morphing shapes became increasingly complex, the vehicle shape and structure are then designed specifically for the purpose of morphing.
8 9
The aircraft design shapes are quite different from one another. Two primary scales are considered for morphing actuators, micro air vehicles of approximately 12 in span and larger vehicles with 24 in wingspans. Most of the vehicles differ in fuselage shape, empennage planform, actuators, and weight. Thus, each vehicle exhibits absolute performance metrics quite different than the others. The differing geometry and differing performance metrics make direct comparison between the vehicles impractical. As stated earlier, the goal of the research is not to determine optimal morphing methods, but rather to investigate the effect of any shape change on the vehicle dynamics. This does not require comparisons between the vehicles and morphing strategies, as each case study is addressed as a separate experiment. The cumulative result of the individual studies helps formulate a basic knowledge base of morphing vehicle flight dynamics. The experimental procedure is mostly similar for all the test vehicles. The basic process includes design, fabrication, instrumentation, flight testing, data recovery, and modeling stages. Apart from the instrumentation, these stages are covered in detail for each aircraft case study. Details of the instrumentation procedures are covered here, as the same sensors and data acquisition devices are used for all the flight tests.
A partial suite of flight test instruments are used on-board the aircraft to gather flight data. Inertial measurements include roll rate, pitch rate, yaw rate, and 3-axis linear accelerations. The remaining inertial aircraft states, Euler angles and position are not included due to a lack of small instrumentation. Estimates of the Euler angles are computed over small time periods by integrating angular rate data. Position measurements, as would be provided by a GPS sensor, are not important for the type of flight testing conducted. Pressure sensors for airspeed and altitude measurement are included for some flight tests, although the data is not used in the analysis. The primary deficiency in the instrumentation is the lack of angle of attack and angle of sideslip data. Potentiometer-based vanes were considered for use, but the rotational 10 friction prevented the sensors from providing any useful information. Finally, the control deflections are measured for all the hinged and morphing effectors. The primary element of the instrumentation system is a micro data acquisition system (microDAS) developed by NASA Langley Research Center. The microDAS has 30 analog voltage input channels measured with a 12-bit resolution. Sampling frequency is adjustable from 50 Hz to 500 Hz, allowing continuous data measurements from 20 minutes to 2 minutes respectively. Later versions of the board increased the storage capacity considerably. Data presented in this thesis is collected at 50 or 100 Hz. The board weight including the wiring harness is approximately 12 grams, although this varies depending upon the length of wire used to connect the sensors. Figure 3–1 shows the micro data acquisition system with the wiring harness connected. Leads from the harness are connected to sensor outputs and communication ports. Three linear accelerometers are integral to the board, allowing 3-axis measurement within +/- 50G.
Figure 3–1: Micro data acquisition system
Data from the newest version of the microDAS is stored in a 128MB flash memory chip. As long as the unit retains power, the measurement can be turned on or off from the remote transmitter. This permits the data to cover only the flight test maneuvers and exclude non-research phases of flight, such as launch, climb, trim, and 11 landing. Flight data is recovered to a laptop via a USB communications cable. An entire data set is downloaded in 6 minutes using the software provided with the device. Roll, pitch, and yaw rates are measured using muRata ENC-03J piezoelectric angular rate gyros. Each gyro sensor measures a single axis of rotation, requiring three orthogonally-oriented gyros for full rate measurement. A two-piece copper-plated circuit board fabricated at UF’s ECE department is used to align the gyros and provide signal outputs, as shown in Figure 3–2. The total weight of the board and the three gyros is 6 grams, making it suitable suitable for the smaller MAVs. The signal output from the gyros are stable enough such that no hardware filtering is required to achieve
high signal to noise ratios and stable mean values. The rate measurement range for
each gyro is specified by the manufacturer as +/-300o s, although calibration tests suggest that linear output exists over +/-1000o s.
Figure 3–2: Roll, pitch and yaw rate sensor board
Control surface deflections are measured at the rotary actuator. For conventionally hinged surfaces, a nominally rigid linkage connects the actuator output arm to the control surface. For morphing effectors, the actuator is connected to some hardpoint on the wing surface. In either case, the actuator position is directly representative of the command input and the surface deflection. For simplicity in quantifying the morphing 12 command, the actuator position is used to define the magnitude of the control input, although the actual geometry may be too complex to specify using a single parameter. The rotary servo actuators used in the vehicles are commercial off-the-shelf devices. The position of the servos is commanded using control sticks and knobs on a remote transmitter. A pilot input on the sticks generates a pulse-width modulated signal to the servos, where the width of the pulse is proportional to the commanded position. The internal circuitry in the servo controls the rotation of the output arm to the commanded position by using a motor-gear system and a rotary potentiometer. The voltage feedback from the potentiometer is used to create an error signal to drive the position control system. This voltage feedback is also a convenient measure of actuator position. The center pin of each feedback potentiometer is connected to an analog input channel of the microDAS, resulting in a time-synchronized measure of control deflection with the inertial data. CHAPTER 4 ASYMMETRIC WING SHAPING FOR ROLL CONTROL
4.1 Aircraft Design
Small vehicles having wingspans of less than 12in are being developed for military and civilian reconnaissance missions. Flexible wings are typically used in conjunction with conventional elevator and rudder control surfaces. The lateral-directional control effectiveness of the rudder is suitable for open-loop control, but suffers from significant coupling and saturation issues that preclude its use for fine flight path tracking. Wing curling is an attractive type of morphing for this class of MAV. The attraction lies in both its simplicity of implementation and its effectiveness for morphing. In this case, a MAV will simply be retrofitted to accommodate a basic type of wing curling. The objective of this study is to investigate the effect of wing shape on basic maneuvering. Specifically, the roll performance and associated coupling with pitch and yaw will be studied for wings which curl into asymmetric configurations. The effects of reduced area and increased camber, along with their corresponding changes in lift and drag on each wing, are of particular interest. Two MAVs, shown in Figure 4–1, are the platforms used to investigate wing curling. The only control surface on the 12 in wingspan MAV is an elevator for longitudinal control; therefore, morphing will be used as the only effector to control the lateral-directional dynamics. The 10 in includes a rudder control surface in order to compare with the effectiveness of the morphing for lateral-directional control. The fuselage of each aircraft houses a 3-axis gyro and 3-axis accelerometer along with a data logger to record flight responses. The airfoil used on the wings is similar to a competition airfoil developed by Dr. Mark Drela. The airfoil was modified using XFOIL to improve lift magnitude at low
13 14
Figure 4–1: Wing shaping morphing MAVs - 10 in wingspan high-wing aircraft (left) and 12 in span mid-wing aircraft (right) angles of attack. The modifications included increasing the camber to 8% and moving the maximum camber position forward along the chord to the 29% position. The wings are fabricated with no appreciable thickness using thin carbon-fiber and latex membrane. The shape of the airfoil on the physical wing is in line with the XFOIL modeling, which assumes a thin, undercambered airfoil. A 3-view schematic of the 12 in aircraft geometry is shown in Figure 4–2. Aircraft properties for the 10in and 12in vehicles are shown in Table 4–1. Table 4–1: Properties of the 10 in and 12 in wing shaping MAVs
Property 10 in high-wing MAV 12 in mid-wing MAV Wing Span 10 in 12 in
Wing Area 31 in2 44 in2
Wing Loading 13.93 oz ft2 14.19 oz ft2 Aspect Ratio 3.27 3.27 Powerplant coreless motor - 2.5in prop geared motor - 3.5in prop Total Weight 3.00 oz 4.33 oz
4.2 Morphing Mechanism
Wing curling is accomplished using rotary actuators connected to the wing structure by tensioned Kevlar cables as shown in Figure 4–3. As the actuator adjusts the tension on the cable, the wing deforms into a twisted form that is appropriate for flight control. Namely, the resulting shape increases the angle of incidence of the morphed wing and increases the lifting force produced. When one wing side is morphed, a lift differential is created which causes the aircraft to incur a roll rate. 15
Figure 4–2: Top, front, and side views of computer-aided design drawings for 12 in MAV
Figure 4–3: Kevlar cables 16
The morphing achieved by this strategy is directly dependent upon the attachment points of the threads. The threads attach to servos by passing through the fuselage near the leading edge of the wings. The corresponding attachment to the wings is actually at separate hardpoints. 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 4–4. 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 4–4: Front view showing undeflected wing (left) and morphed wing (right)
The extent and shape of the morphing can be adjusted by varying the amount of tension in the Kevlar lines or adjusting the location of the attachment hardpoint on the wing. The shape is also dependent on the direction of the tensile force from the Kevlar, which is determined by the position of the actuator arm with respect to the wing hardpoint. A large vertical separation between these two points, as on this MAV, 17 causes the tensile force to be applied in a more spanwise direction so the wing exhibits the predominantly curled motion in Figure 4–4. The extent and shape of the morphing can be adjusted by varying the amount of tension in the Kevlar lines or adjusting the location of the attachment hardpoint on the wing. The shape is also dependent on the direction of the tensile force from the Kevlar, which is determined by the position of the actuator arm with respect to the wing hardpoint. A large vertical separation between these two points, as on this MAV, causes the tensile force to be applied in a more spanwise direction so the wing exhibits the predominantly curled motion in Figure 4–4.
4.3 Flight Performance
A series of flight tests are performed to evaluate wing curling for roll performance.
The vehicle actually contains separate servos that allow symmetric curling; however, the current discussion only considers asymmetric morphing. As such, the flight test considers maneuvers in response to a single wing being curled while the other wing remains undeflected.
The wing curling causes a significant roll moment. The direction of roll is determined by an increase in lift on the curled wing. Essentially, the curling causes a greater angle of incidence and angle of attack on the morphed wing. This effect causes a lift increase on the left wing, and consequently a positive roll moment, when the left wing is curled. Of course, some amount of coupling to pitch and yaw results from the asymmetric configuration [14]. An immediate benefit from the morphing is realized when comparing this MAV to similar types that do not have morphing. This shape of vehicle, with a range of wing span, has been previously flown using only elevator and rudder for control. The vehicle is noticeably easier to pilot using elevator and morphing. The wing morphing generates roll moments that facilitate flight path tracking beyond the rudder over the majority of the flight envelope. 18
The wing-curling morphing exhibits good control response near the neutral, trim position. Small inputs are necessary in performing turns and in making slight adjustments to the flight path. The morphing provides an adequate level of control under these circumstances The aircraft responds predictably to various magnitudes of control input, although the physical deformation of the wing surface is not necessarily linear. In particular, the morphing is suitable for both commanding turns and for correcting for attitude perturbations from wind gusts or other disturbances. Roll controllability remains satisfactory throughout the airspeed range encountered during cruise, high-speed dives, and landing or approach phases.
Although turns and rolls are easily accomplished with the wing curling, aggressive maneuvers are considerably more difficult. The aircraft is quite sensitive to departure when morphing is commanded while the aircraft is at high loading conditions, such as in a steep turn or during a large pitch angle change. The wing deflection incurred during wing curling generates large incidence angles near the deformed region of the wing. The incidence angles generate the requisite change in aerodynamic forces and moments to control the aircraft during level or cruise flight conditions. Also, if the aircraft is already at a large angle of attack, such as during an aggressive maneuver, large morphing commands can exceed the critical angle of attack and force a stall on the deformed wing. Such a situation generates a rolling moment opposite to the commanded direction. For instance, during high angle of attack flight, deforming the left wing slightly increases the angle of attack and lift on the left wing and causes a roll rate to the right. However, large morphing commands cause a stall over portions of the left wing, reducing the lift compared to the right wing, and causing a stall-spin departure to the left. Departures caused by stall due to morphing are generally terminal on this type of aircraft, as the morphing can be controlled only in a single direction for each wing. Once a spin has developed, the morphing provides 19 insufficient control power to generate the required anti-spin forces and recover to level flight. Finally, roll handling qualities tend to be quite sensitive to the location of the hardpoint on the wing and to the tension in the cable. Slight asymmetries in the right and left side cable tensions often contribute to difficulties in control and non-zero trim condition. Unintentional variations in the control linkage tension cause control responses to change slightly over a series of flights. Additionally, deterioration of the latex membrane noticeably reduces the wing surface tension. The natural rubber used in the latex material decays when exposed to the sun. The reduced tension of the decayed latex prevents the deformation from propagating smoothly throughout the wing structure. In turn, the twist deformation caused by the buckling remains localized around the hardpoint and reduces control effectiveness.
4.4 Nonlinear Modeling of Lateral and Longitudinal Dynamics
Flight data from the vehicle is analyzed to estimate models of the flight dynamics.
Several techniques were attempted to estimate these models, including system identi- fication [24] and parameter estimation [19], but with limited success. This vehicle is particularly difficult to model because the morphing causes time-varying asymmetries which violate many assumptions used by standard routines.
Furthermore, the estimation is difficult because of limited flight data. The MAV is equipped with gyros and accelerometers but the flight data from the accelerometers is actually too noisy to be useful for modeling. Thus, several critical measurements, such as angle of attack and angle of sideslip, are not available. Some dynamics are not easily observable, especially in the presence of noise, using only the available sensors.
A nonlinear auto-regressive model is used to represent the flight dynamics. The
general form of this model is shown in Equation 4.1. This model relates the gyro
¢ ¡ ¢ ¡ ¢ measures of roll rate, p ¡ k , pitch rate, q k , and yaw rate, r k , to the morphing
20
¢ ¡ ¢
command, δm ¡ k , and elevator command, δe k , at the sampling instance of k. The ¤
3 ¤ 3 3 2 £
matrices, Ai £ R and Bi R , represent the dynamics.
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¨ ¢
p ¡ k 1
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¨ ¢
q ¡ k 1
§
¨ ¢
r ¡ k 1
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¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢
p ¡ k p k 1 p k p k p k 1 p k 1
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¨ ¨ ¨
¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢
A1 q ¡ k A2 q k 1 A3 q k q k A4 q k 1 q k 1
§ § § §
¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢
r ¡ k r k 1 r k r k r k 1 r k 1
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¢ ¡ ¢ ¡ ¢ ¡ ¢
p ¡ k q k p k 1 q k 1
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A5 q ¡ k r k A6 q k 1 r k 1
§ §
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r ¡ k p k r k 1 p k 1
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¢ ¡ ¢ ¡ ¢ ¡ ¢
δm ¡ k δm k δm k δe k
¨ ¨ ¨
§ §
B1 § B2 B3 (4.1)
¢ ¡ ¢ ¡ ¢ ¡ ¢ δm ¡ k 1 δm k 1 δm k 1 δe k 1
The model in Equation 4.1 contains quadratic terms of the rates and commands. Such quadratic terms are included to account for unknown relationships between the wing shape and the aerodynamics. In this case, the terms utilize an absolute value to allow the contributions from the quadratics to change in sign. The model in Equation 4.1 also contains coupling terms. These terms multiply the gyro measurements by each other. The standard equations of motion for a rigid-body aircraft include coupling terms which scale by the moments of inertia [26]. This MAV is obviously asymmetric during the morphing so the coupling is essential.
Finally, Equation 4.1 computes the update to the gyro measurements as a function of the measurements from two previous sampling times. These terms are included to account for the time-varying nature of the dynamics which arise by altering the wing 21 shape. The dynamics are assumed to be sufficiently described by two sampling times although a rigorous study of the sampling times was not conducted.
The values of the matrices, Ai and Bi, in Equation 4.1 are determined by a least- squares fit to the flight data. The resulting model is used to simulate the responses to the morphing and elevator commands. Such responses are shown in Figure 4–5.
15 5 8 data data data sim sim 6 sim 10 4
5 0 2
0 0 −2 −5 −5 Yaw Rate (deg/s) Roll Rate (deg/s) Pitch Rate (deg/s) −4 −10 −6
−15 −10 −8 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Time (s) Time (s) Time (s)
Figure 4–5: Measured and predicted responses for roll rate (left), pitch rate (middle) and yaw rate (right)
The responses in Figure 4–5 demonstrate the model captures the basic trend of the dynamics but is not completely accurate. The predicted responses are not perfect matches to the measured responses but yet they clearly show similarities. Thus, the model indicates the time-varying asymmetries associated with the morphing causes nonlinearities and coupling in the flight dynamics of this MAV. CHAPTER 5 SYMMETRIC WING TWISTING FOR ROLL CONTROL
5.1 Aircraft Design
Wing twisting is another type of morphing that is particularly interesting, and suitable, for a MAV. The concept of wing twisting is an obvious choice based on its use as a control effector for the Wright Flyer. It is also being adopted for the Active Aeroelastic Wing [27]. Wing twisting will be investigated for a MAV in a similar fashion as those previous aircraft; namely, wing twisting will be used to generate roll moments.
A mechanism for wing twisting is implemented on the MAV shown in Figure 5–1. This aircraft has an elevator and rudder as control surfaces. Also, the fuselage is large enough to house the sensor package comprised of gyros and accelerometers along with the data logger.
Figure 5–1: Wing-twisting MAV
The wing has several features advantageous to twisting. The leading-edge strip is a relatively thin piece of uni-directional carbon fiber. Also, the wing surface is a nylon film which is not overly extensible. These properties result in a wing which smoothly
22 23 and continuously deforms across the entire surface due to a small perturbation at a single point. Several basic properties of the vehicle are given in Table 5–1.
Table 5–1: Properties of the 24 in wing twisting MAV
Property Wing Twisting MAV Wing Span 24 in
Wing Area 100 in2
Wing Loading 20.32 oz ft2 Aspect Ratio 5.76 Powerplant Brushless motor - 4.75 in prop Total Weight 14.11 oz
5.2 Morphing Mechanism
Morphing is accomplished using an steel torque-rod affixed to a batten at ap- proximately the 66% span position. Actuating this rod with a servo forces the wing to undergo a twisting deformation. Although the actuating point is localized to a single wing batten, the wing surface distributes the deformation over the entire wing. The magnitude of the twist deformation is largest at the actuation point and is tapered toward the wing tip and wing root.
Figure 5–2: Underside view of wing showing torque rod
The use of torque-rods admits a bi-directional wing twisting that resists the effects of loading. The bi-directionality of twist results from actuating the wing to twist in either trailing-edge up and trailing-edge down directions. The resistance to loading 24 results from the stiffness of the aluminum rod, along with stiffness of the leading-edge strip, to maintain shape unless excessive loads are encountered. Thus, the control of the wing shape is largely a function of the actuator position with only small effects from response to airloads. Figure 5–3 compares the 24 in MAV wing in undeflected and morphed configurations.
Figure 5–3: Rear view of the 24 in MAV with undeflected (left) and morphed (right) Wing
5.3 Flight Performance
The wing twisting aircraft exhibits highly desirable control characteristics in flight [14]. Roll control is extremely responsive across a wide range of airspeeds.
At slow speeds, such as near level flight stall, the wing twisting remains effective at commanding a turn and recovering from turbulent disturbances. At higher speeds, the roll response is also effective, although the magnitude of the roll rate increases. Modeling of the control characteristics suggests that the roll response is largely linear over the airspeed range. The morphing is effective at providing small, high-rate control inputs needed to maintain a specific attitude or flight path. In such cases, the vehicle responds quickly to the initial command and recovers to unaccelerated flight as the command is returned to neutral.
The wing twisting also provides positive control characteristics at large amplitude deflections. Maximum roll command, which twists the wings anti-symmetrically 25
o o 10 , generates a roll rate in excess of 1000 s within 0 2 seconds. Neutralizing the morphing stops the roll in approximately the same time. During continuous rolls, the vehicle incurs relatively little yaw coupling. Yaw rate divergence from wing twisting is approximately an order of magnitude lower than the corresponding roll rate. At high roll rates, for instance, several complete rolls can be completed without an appreciable change in heading or pitch attitude. Basic flying tasks such as turns and bank angle correction are facilitated with mor- phing as compared to rudder-only control. The need for corrective control input during the maneuver is decreased because of the decreased coupling. Turns commanded solely through morphing are improved, where minimal rudder corrections are needed to main- tain coordination throughout the turn. The turn performance is especially improved in windy and gusty conditions, where the need to independently control bank angle and heading angle is increased.
5.4 Linear Modeling of Lateral Dynamics
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. The data acquisition system begins recording as soon as the motor is powered. 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 26 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. Specif- ically, the rates and accelerations 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 rich 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 and the resulting aircraft responses are shown in Figure 5–4.
15 150 150
10 100 100
50 50 5
0 0 0 −50 −50 −5 −100 −100 Rudder Command Roll Rate (deg/sec) −10 Yaw Rate (deg/sec) −150 −150
−15 −200 −200 0 1 2 3 4 5 6 0 1 2 3 4 5 0 1 2 3 4 5 Time(sec) Time(sec) Time(sec)
Figure 5–4: Doublet command to rudder (left), roll rate response (middle), and yaw rate response (right)
The roll rate and yaw rate measured in response to this command are shown in Figure 5–4. The roll rate is sufficiently large and indicates the rudder is able to provide lateral-directional authority; however, the yaw rate is clearly larger than desired. Actually, the yaw rate is similar 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 evidenced in the magnitude and phase relationship of the response measurements. Doublets, such as the pulse sequence shown in Figure 5–5, are also commanded to the morphing servo. The roll rate and yaw rate in Figure 5–5 are measured in response to the doublet. These measurements indicate the roll rate is considerably higher than the yaw rate. 27
8 150 150 6 100 100 4 50 50 2 0 0 0 −50 −50 −2 −100 −100 −4 Roll Rate (deg/sec) Yaw Rate (deg/sec) Morphing Command −6 −150 −150
−8 −200 −200 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Time(sec) Time(sec) Time(sec)
Figure 5–5: Doublet command to wing twist morphing (left), roll rate response (mid- dle), and yaw rate response (right)
Thus, the morphing is clearly an attractive approach for roll control because of the nearly-pure roll motion measured in response to morphing commands. The data from open-loop flights is then used to approximate a linear time-domain model using an ARX approximation [24]. This model is generated by computing optimal coefficients to match properties observed in the data. The assumption of linearity is reasonable since the maneuvers are small doublets around a trim condition. Also, the twisting command is anti-symmetric about the centerline of the aircraft.
The resulting model, having poles at -4.95 and -0.1194, is used to simulate responses of the aircraft. The simulated values of roll and yaw rates are shown in Figure 5–5 as dashed lines. The simulated responses show good correlation with the actual data. The model is thus considered a reasonable representation of the aircraft. The existence of such a model is important for future design of autopilot controllers but it is also valuable for interpreting the morphing. Essentially, the ability to identify a linear model with poles relating to the roll convergence and spiral convergence modes indicate the aircraft with morphing acts like an aircraft with ailerons.
5.5 Spin Characteristics of Wing Twist Morphing
Figure 5–6 shows the command and rotation rates during a conventional spin.
This maneuver is initiated from level flight by commanding positive elevator to increase the pitch rate and angle of attack. Right rudder command is then applied to 28 generate a yawing moment as the aircraft approaches stall. In this case, the yaw causes an asymmetric stall and starts the spin rotation. The aircraft response is relatively constant throughout the maneuver, although the roll rate tends to build up as the flight path changes from level to vertical. The autorotation continues as long as the positive elevator and rudder commands are held. Once the commands are neutralized, the rotation slows and comes to a stop with little or no opposite rudder input. Positive elevator is used to recover the aircraft to level flight at 363 seconds. Although this type of spin has been experienced several times, the entry pro- cedures tend to be difficult to reproduce. Specifically, applying rudder command at a low angle of attack (too early) prevents a stall from developing and results in a high-speed spiral dive. Both wind tunnel and CFD analysis have shown that the thin-undercambered airfoils used on the vehicle have delayed stall response. This delay affords such vehicles increased resistance to stall-spin departure, at least for positive loadings. The effect of morphing on positive (upright) spins is to accelerate the onset of the spin and to assist in the recovery process. This effect is most pronounced during cross-coupled controls, where the rudder direction is opposite to that of the morphing.
In such a case, the high angle of attack at the inside wing tip is further increased by the morphing actuation, leading to a subsequent stall-spin. Releasing the morphing command effectively reduces the wing angle of attack and produces nearly immediate recovery from an upright, conventional spin.
40
30 50 20
10 0 0
−10 −50 Command (deg) −20 Response (deg/s) elevator roll rate −30 rudder −100 pitch rate morphing yaw rate −40 359 360 361 362 363 364 359 360 361 362 363 364 Time (s) Time (s) Figure 5–6: Pilot commands (left) and responses (right) during conventional spin 29
Conventional spins are also performed with negative (down) elevator actuation to produce a starkly different response. In particular, the spin modes observed are of considerably higher energy. The rotation rates of a negative spin compared with an upright spin tend to be between 2 to 6 times greater. Based on rudimentary analysis, the stall characteristics of a thin under-cambered wing at negative angles of attack are far more severe than the characteristics at high angles of attack. In flight, the airplane is observed to have a very immediate and violent response to large negative elevator commands. Such an input is believed to cause a negative stall quickly, where any asymmetry about the yaw axis then produces a large rate of rotation.
Figure 5–7 shows an identified negative spin mode initiated by a morphing command with elevator and rudder. At 401 seconds, the aircraft responds to the constant control deflection by building up rotation rates on all three axis. The entry into the maneuver is relatively gradual and only after one second of control inputs have the pitch, roll, and yaw rates become significant. This particular type of spin stabilizes independently of the initial pro-spin control deflections. At 402 seconds, the controls are released, while the aircraft continues to spin. The application of positive elevator (for recovery) shortly afterwards appears to maintain the spin for some time. It is only with corrective opposite rudder command that the aircraft arrests the rotation and recovers from the spin. It is difficult to draw solid conclusions from this spin sequence. However, the two distinct modes observed in Figure 5–7 are attributed to primary and secondary spin characteristics, where the latter is caused by a premature recovery attempt. Similar spins have been observed from both left and right directions. Alternatively, Figure 5–8 shows a considerably different spin behavior for similar control combinations. Although initiated by commands similar to the previous spins, this type of spin exhibits a cyclic or periodic motion. It is perhaps with the timing of the control inputs or entry flight conditions that a difference can be found. Whereas 30
40 elevator 30 rudder morphing 50 20
10 0 0
−10 −50 Command (deg) −20 Response (deg/s) roll rate −30 −100 pitch rate yaw rate −40 400 401 402 403 404 405 400 401 402 403 404 405 Time (s) Time (s) Figure 5–7: Pilot commands (left) and responses (right) during spin in Figure 5–7 the elevator input lagged behind the rudder and morphing inputs, the spin depicted by Figure 5–8 shows the elevator leading slightly. The precise effect this has on the spin is unknown. However, the resulting aircraft response is shown to be 6 times greater in magnitude than a conventional spin.
From level, trimmed flight, the aircraft is subjected to full left wing morphing, full left rudder, and full negative elevator command. The initial reaction of the aircraft is to pitch down at a constant rate and incur a left roll and yaw from the wing morphing and rudder deflections. Once the wing has reached the negative stall angle, presumably facilitated by the deflected wing, a rapid spin ensues, nearly doubling the roll and yaw rates and reducing pitch rate. This pattern is repeated four times throughout the spin while pilot commands are held constant. Each cycle is proceeded by a period of low momentum, followed by a sharp change in pitch rate along with peaks in both the roll and yaw rates. Throughout the spin, the mean pitch rate is near zero. Each cycle generates a large negative pitch rate followed by a large positive pitch rate. Mean roll and yaw rate responses are non-zero during the spin. The lateral rates remain negative, achieving small negative values only as the pitch rate reverses direction. While the dynamics of such a maneuver are not very well understood, it appears that the morphing of the wing plays a large roll in both inducing and recovering from the spin. For instance, similar spin entries performed without morphing are characterized by considerably lower rotation rates and a continuation of the spin after command inputs are neutralized. However, the recovery of this cyclic spin mode occurs 31 nearly immediately after the controls are neutralized. As seen at 176 in Figure 5–8, the aircraft is incurring maximum rotation rate when command is returned to neutral. The rotation rates continue to follow the characteristic spike pattern and finally converge to zero.
40 elevator roll rate 30 rudder pitch rate morphing 50 yaw rate 20
10 0 0
−10 −50 Command (deg) −20 Response (deg/s)
−30 −100
−40 171 172 173 174 175 176 177 171 172 173 174 175 176 177 Time (s) Time (s) Figure 5–8: Pilot commands (left) and responses (right) during cyclic spin
In flight, this immediate convergence has the effect of stopping the aircraft in mid-rotation. Unlike the other spin modes observed, the cyclic spin mode has no apparent recovery apart from neutralizing the controls. The aircraft will continue to the end of a given cycle, cease rotation, and simply return to steady, controlled flight. The nose-down recovery typical of other spin modes is contrasted with an immediate recovery to level flight.
The usefulness of the cyclic spin mode depicted in Fig. 5–8 is perhaps ques- tionable, although it may give rise to a different mode of maneuvering for morphing aircraft. For instance, the above maneuver may be useful for a controlled vertical dis- placement. On initiating the entry, the airspeed quickly decays and starts the aircraft on a relatively slow vertical flight path. During this portion of the maneuver, the aircraft incurs a series of high rate of rotations, each separated by a period of low momentum. As evidenced by the recovery from the maneuver, this period can be used to recover the aircraft into stable flight. While previous spin modes required corrective rudder and significant altitude losses for recovery, this cyclic spin mode stopped once the controls were neutralized. 32
Attitude and airspeed entry conditions into the spin trials have been observed to have some impact on the stabilized spin modes; however, accurate measurements of the entry conditions were not possible. The lack of pressure sensors on the airframe precluded the gathering of such data. Excitation of a particular spin mode depended on the pilot ability to position the aircraft properly based on control feel and vehicle observations. The spin entry maneuvers were also attempted for other control combinations. Specifically, cyclic spins were attempted without wing twisting by using negative elevator and rudder deflection. These trials resulted in a stabilized spin but with considerably lower rotation rates than the cyclic spin. Additionally, this mode did not exhibit the periodic behavior achieved through wing twisting during a spin. CHAPTER 6 MULTI-POINT WING SHAPING
6.1 Aircraft Design
The multi-point wing-shaping aircraft employs a simple strategy to exercise increased control over the wing in twist. Actuation of the wing is accomplished through four concentric rotating spars that are attached to a flexible, extensible wing skin. The basic idea of this form of morphing is to have some control of the lift distribution over the wingspan. Since each of the four rotating spars can be controlled independently, the wing surface can be commanded to a variety of complex shapes.
In this manner, the morphing can be useful for longitudinal control, longitudinal trim, minimum drag, maximum drag, or stall resilience in addition to commanding roll rate. From a design perspective, the vehicle geometry is similar to the 24 in wing- twisting aircraft, as seen in Figure 6–1. The wing planform and airfoil are identical in fact, although the wing structure and membrane differ somewhat to accommodate the morphing spars. The wings are mounted along the middle of the fuselage to facilitate the mounting of the morphing actuators and mechanisms. The lower wing position and reduced dihedral also help eliminate excessive roll-yaw coupling.
Figure 6–2 shows the wing undergoing morphing to the outboard (wingtip) spar tubes alone and to both wingtip and midboard spar tubes simultaneously. Deformation is visually apparent by examining light reflections off of the leading edge and the shape of the trailing edge. 6.2 Morphing Mechanism
Concentric tube spars act as both primary load-bearing members and as control linkages (torque-tubes). A large diameter tube is fixed to the fuselage and acts as a bearing support for the rotating spars. The root section of the wing surface is
33 34
Figure 6–1: Top, side, and front views of the 24 in span multiple-position wing shap- ing vehicle also attached to this tube, creating an immobile joint between the inboard wing and fuselage. Two smaller tubes, one within the other, are supported by the fixed tube. The smallest tube extends the full span, while the center tube extends to the 60% position. Each of the outboard and midboard spars is actuated in twist via servos mounted in the fuselage, shown in Figure 6–3. Each servo is then able to command the incidence angle of the corresponding wing section independently.
A flexible wing surface is attached to each of the three wing spar tubes. Attach- ment points near the spar joints are left unconstrained in pitch angle. This freedom allows the incidence to smoothly taper between the rigidly attached sections of the wing surface. This structure permits twist morphing of each controlled wing section 35
Figure 6–2: Wing shaping MAV showing neutral position (top left), wingtip morphing (top right), and full wing morphing (bottom)
Figure 6–3: Spar torque-tube morphing actuators. The 4 front servos rotate concentric spar sections, aft 2 control rudder and elevator
o o ¨ from 10 to 10 incidence angle. Each of the four wing sections are commanded independently, allowing for considerable differential or collective configurability.
6.3 Flight Performance
The aircraft has undergone basic performance and handling flight tests. Roll control is achieved by differentially actuating the wingtip spars. The handling qualities and maximum roll rate are similar to the 24 in wing twisting aircraft. Actuating the 36 entire wing differentially (i.e. using both wingtip and midboard sections), achieves roll rates and performance measures considerably higher. The morphing is also being considered for use in conjunction with other control surfaces. Basic flight tests of combining collective midboard wing deflection with elevator command have shown potential for improvement in pitch rate performance. Additionally, this morphing may be suited for quasi-statically reconfiguring the wing twist to optimize spanwise lift distribution in flight. Such techniques are currently used by sailplane and commercial jet pilots to alter the lift properties of the wing for cruise, steep descent, and maximum performance flight phases. CHAPTER 7 VARIABLE GULL-WING ANGLE MORPHING
7.1 Aircraft Design
The aircraft discussed thus far have been limited in concept to relatively simplistic twisting or bending of the aircraft structure. However, because of the nature of such mechanisms, control over the aircraft is limited to high-bandwidth stabilization, maneuvering control, or retrimming. The morphing shapes achieved by such methods are not suitable for the gross aerodynamic reconfiguration that is typically associated with morphing. A new morphing aircraft design is proposed that uses a jointed spar structure to achieve a biologically-inspired form of morphing in addition to the twist control used on previous aircraft. The design of the aircraft is identical to the multiple-position wing shaping aircraft in all components except for the jointed spar and actuator. The aircraft configuration, shown in Fig. 7–1, is traditional in the sense of a single lifting surface, horizontal and vertical stabilizers, and tractor propeller. Apart from the morphing mechanisms, the aircraft is equipped with elevator, rudder, and throttle control. The vehicle airframe is largely composite carbon-fiber and mylar plastic. The monocoque fuselage is made using carbon-fiber cloth wrapped over a male mold [12]. Once cured and extracted, the structure is strong enough to withstand wing and tail loads without additional supporting structure. The aircraft is considered small enough to be considered in the class of micro air vehicles, since the wingspan at full extension is 26 in. The tail surfaces consist of a mesh of unidirectional carbon fiber strips. The perimeter strips support the overall planform, while the interior strips build up the surface rigidity. Hinges for the control surfaces are embedded within the carbon structure during the layup process. Additionally, mylar plastic covering is used for
37 38
Figure 7–1: Top and side view of variable gull-wing aircraft skin material on the tail feathers and portions of the wing. The resulting structure adds minimal weight to the vehicle, yet is strong enough to withstand flight loads and the occasional crash.
7.2 Morphing Mechanism
The wing planform shape provides sufficient area to keep the fully-instrumented aircraft at a reasonable wing loading, yet is also high enough in aspect ratio to provide good aerodynamic performance. Morphing the wings changes the wing geometry in several parameters. Table 7–1 lists the basic geometry changes incurred during gull-wing morphing. Figure 7–2 shows a frontal view of the vehicle during three configurations resulting from gull-wing morphing.
Table 7–1: Wing geometry change over variable gull-wing morphing range
Parameter Min Max Wingspan 20 in 26 in Planform area 77.7 in2 101.4 in2 Inboard wing relative to fuselage -40o 40o Outboard wing relative to fuselage -40o 40o 39
Figure 7–2: Vehicle undergoing neutral (top), positive (center), and negative (bottom) gull-wing morphing
A hinged spar structure, based loosely on bird skeletal physiology [33], provides the degree of freedom needed for gull-wing morphing. Each spar side consists of two tubular spars with one hinge at the fuselage joint and another between the two spars. The angle of the inboard spar is controlled by a vertical linear actuator. A telescoping shaft connects the spar with the output arm of the actuator. The shaft allows the actuator to move over the entire range without mechanically binding the spar. The angle of the outboard spar is passively controlled via a mechanical linkage parallel to the inboard spar. This linkage connects the control arm on the outboard spar directly to the fuselage. During actuation, the linkage causes the inboard and outboard sections to deflect in opposite directions. The ratio of these relative deflections is adjusted by changing the moment arm on the fuselage control arm and/or the outboard spar control arm. An important feature of the system is its ability to withstand flight loads without active control or energy consumption. Figure 7–3 shows the left side of the hinged spar in a positive gull-wing position.
A flexible wingskin is attached to the jointed spar so that the spar comes under the point of maximum camber. This position approximately corresponds with the 40
Figure 7–3: Variable gull-wing spar structure and control linkage, linear actuator visi- ble inside fuselage at left point of minimum pitching moment, in addition to reducing the frontal area of the wing. The wing skin consists of chordwise carbon-fiber battens and a single spanwise leading-edge member. Each batten is free to deform within the limits of the wing skin extension and carbon-fiber flexibility. In flight, this compliance allows the airfoil sections to deform in response to buffeting or steady airloads. As a result, the wing passively deforms and reduces the effect of atmospheric perturbations such as gusts and wind shear on the vehicle’s flightpath.
Conventional elevator and rudder control surfaces are used for pitch and yaw control. These surfaces are hinged to the fixed stabilizing surfaces with strips of
Tyvek. Rotary actuators mounted in the fuselage control the surface deflection. Control actuation limits are +/- 30o of travel, with actuation rate limits of 400o s. Roll control is provided by articulating wing tips on the outboard spar section.
A rotary servo mounted to the wingskin actuates against the spar, causing the wing surface to rotate about the spar. The surface is attached to the outboard spar so that rotation about the spar is unrestrained, except by the actuator motion. However, since the wingskin is continuous along each side of the aircraft, the result is a twist deformation centered at the actuator and extending both inward toward the fuselage 41 and outward toward the wingtips. Figure 7–4 shows a close-up view of the wing twist mechanism, outboard spar, and actuator.
Figure 7–4: Underside view of left wing showing wing twist effector
Control of the gull-wing is accomplished using a linear lead-screw actuator driven by a rotary servo. Rotating the lead-screw causes the output arm to slide vertically within the fuselage. At the lowest position, the inboard spars are deflected 40o upward. The lead-screw provides control of the wing shape without having to withstand the lifting loads directly; however, the actuation rate of the morphing is quite slow in comparison to the other surfaces. This slow actuation is not problematic since the morphing is being investigated strictly as a quasi-static effector. Command and response data are measured in-flight using an on-board micro data acquisition system. The device supports 30 channels of analog sensor input and samples between 50Hz to 500Hz. The data presented here is measured at 100Hz. Several external sensors are interfaced to the data logging, including 3-axis rate gyros, linear accelerometers and control surface position sensors for the elevator, rudder, wingtwist, and gull-wing angle.
7.3 Flight Performance
The variable gull-wing morphing sufficiently changes the flight performance for the vehicle to operate in several distinct flight regimes. Morphing the wings controls 42 several aerodynamic and dynamic parameters, including lift to drag ratio, sideslip coupling, and roll stability. These factors in turn affect the handling qualities of the vehicle to make certain flight tasks easier to perform in a particular morphing configuration.
The change in flight performance is the primary incentive behind the morphing; however, this paper is strictly concerned with the change in handling qualities and dynamic characteristics that accompany the performance changes. A more detailed analysis of the performance benefit enabled by gull-wing morphing was previously published [1].
7.3.1 Gliding Performance
Power-off gliding performance is tested to identify the effect of the morphing configuration. Glide performance is an important measure of lift to drag ratio. In turn, lift to drag ratio is representative of the aircraft’s capability in range, endurance, maneuvering, airspeed range, and efficiency. Thus, by testing the glide performance, inferences can be made about much of the remainder of the flight envelope, which is often more difficult to test. Glide tests are performed by cutting off motor power and allowing the vehicle to stabilize in a constant airspeed dive. The shallowest, sustainable dive angle corresponds to the maximum lift to drag ratio for a specified configuration. The numerical value of the lift to drag ratio is exactly equal to the glide ratio, which is the horizontal distance traveled divided by the altitude lost during the dive. The glide ratio can be determined using airspeed and altitude measurements from on-board the aircraft or by estimating distances from the ground. In the unmorphed configuration (0o gull-wing angle), the vehicle attains an approximate maximum glide ratio of 11. This value is typical for aircraft of this size and shape. As the wing is morphed in the positive direction, the glide ratio become 43 progressively lower. At 15o gull-wing angle, the glide ratio is noticeably reduced, causing the aircraft to descend at a much steeper angle. At 30o, the lift to drag ratio becomes very low. Ground estimates for the glide ratio are between 1 and 2. The result is that the aircraft is capable of descending at a 45o angle without gaining airspeed. Furthermore, the high gull-wing angle adds considerable lateral-stability, allowing the vehicle to attain a steep, stabilized dive without control departure tendencies. Such a configuration could be beneficial in allowing the vehicle to descend safely without requiring much horizontal distance. Negative gull-wing morphing has a similar effect on glide ratio. At -20o gull-wing angle, the glide ratio is approximately 3. The effect of the morphing on a stabilized dive is similar to the positive morphing, except that the benefits of sideslip to roll stability is greatly reduced. In fact, control input required to maintain a constant airspeed and glide angle is higher than both neutral and positively morphed cases.
Actuating the gull-wing morphing during a glide test illustrates the impact on lift to drag performance. During a steep, stabilized dive at -30o morphing, the gull-wing angle was slowly increased to 0o. The resulting flight path, when viewed from the side, resembled an exponential decay. As the morphing became less negative, the glide ratio became progressively shallower. Pitch control was used during this maneuver to find a trim airspeed corresponding to the maximum glide performance. Thus, the gull-wing morphing is sufficiently effective to control the glide angle of the aircraft and can be used to change the glide angle throughout the descent. 7.3.2 Climb Performance
The effect of gull-wing angle on climb performance is similar in nature to the effect on glide angle. Maximum climb performance is attained at a neutral gull-wing angle. Morphing the aircraft either in the positive or negative direction reduces climb rate, although the effect is more pronounced for positive gull-wing angles. 44
7.3.3 Stall Characteristics
Stall flight testing is performed to determine the effect of the morphing on departure characteristics. In particular, it is used to determine conditions where a stabilizing controller may be required to prevent loss of control. Additionally, the stall characteristics are useful in assessing whether certain stall-spin modes may be useful as evasive or high-performance flight maneuvers.
Flight testing a vehicle for stall characteristics requires a pilot to fly at high altitudes and be well versed in recovery techniques [32]. The stalls are entered by reducing the airspeed and using the elevator to pitch above the critical angle of attack. Elevator pressure is applied slowly to help eliminate any dynamic effects that might influence stall entry. Stalls are allowed to fully develop by holding positive elevator pressure throughout the test. Recovery from the stall or ensuing spin is performed when the aircraft has clearly demonstrated a particular mode or when altitude loss has become substantial. Stalls performed at neutral morphing are relatively benign and resulted in moder- ate altitude loss during recovery. The wing planform has a tendency to stall abruptly, but then regains control quickly. Control is lost for only a brief period as the aircraft pitches down and reduces angle of attack. Stalls at positive gull-wing angles are more difficult to enter and result in a smaller altitude loss during recovery. At high angles of attack and large positive elevator pressure, the vehicle simply enters a dive and buffets slightly. When provoked to stall with aggressive elevator deflection, the stall break is of lower intensity than the previous configuration. Recovery from a stall at high positive gull-wing angle is more immediate. Part of this improved resilience comes from a significantly decreased tendency to depart into a spin. The high angle of the wings has a stabilizing effect and seems to favor a symmetric stall when at high angles of attack. 45
Negative morphing contributes to a much more aggressive stall mode than observed with the previous configurations. The stall recovery also requires a greater amount of altitude and control input. Stalls also have a greater tendency of escalating into a spin. The spins are generally non-terminal, although one stall test resulted in an unrecoverable spin that resulted in some vehicle damage. Although the testing performed is hardly exhaustive, the observed characteristics indicate that the positive gull-wing contributes to highly desirable stall and recovery characteristics. However, the testing did not reveal any spin modes that could be useful as flight maneuvers.
7.4 Lateral-Directional Dynamics
Morphing introduces considerable complexity to flight dynamics because of variable geometry of the airframe. The variable gull-wing aircraft in particular morphs the wings in a manner that has considerable effect on many of the stability and control derivatives that control the lateral-directional modes. Modeling of the lateral-directional dynamics is restricted to Dutch roll and roll convergence. Spiral mode identification was not possible, considering that the data sets in analysis were relatively short in duration. Proper identification of this mode would require long data sets with little or no pilot input. Such tests are difficult to accomplish using small remotely piloted vehicles.
7.4.1 Roll Convergence
The roll mode is one of the most fundamental descriptions of the aircraft lateral- directional motion. The mode essentially describes resistance to rolling, whether through a control surface deflection or a perturbation. Aircraft handling qualities and lateral controller designs are highly dependent on the roll mode.
The roll mode, or roll convergence, is largely a function of the Clp derivative, which describes the change in rolling moment as a function of roll rate. This derivative in turn is a function of the vehicle geometry. As the vehicle shape changes, as in the 46
case of a gull-wing morphing aircraft, the Clp parameter and the corresponding roll mode are expected to change. The change in roll mode with morphing deflection then becomes a basic assessment of the change in handling qualities incurred due to morphing.
Wing-twist pulses are used to perturb the vehicle from a trimmed flight condition. The response of the vehicle to these pulses is used to identify important stability and control characteristics, namely the roll mode and the wing twist effectiveness. Pulse maneuvers are performed at cruise airspeed from straight and level flight. The pulse is repeated for a variety of command magnitudes and morphing positions.
The pulse maneuvers are performed such that the aircraft’s perturbation from the entry trim condition is relatively small. Larger pulses may exceed the range of aircraft responses that can be adequately represented by a linear model; however, the small size of the vehicle requires that the maneuver be large enough to be clearly evident to the remote pilot. In practice, the control pulses are performed to 30 or 40o bank angle in each direction. A typical wingtwist control pulse is shown in Figure 7–5. Commanded wingtwist deflection is measured along with the roll and yaw rate response. The roll angle data shown is estimated from the roll rate. The estimate is assumed to be a reasonable representation over short time periods and small angles of attack. Although the estimate may be off in absolute magnitude due to calibration or estimation errors, the trends clearly show the relative bank angle response. The top two plots in Figure 7–5 show a close correspondence between command input and roll response. Such response is typical of aircraft with high aileron control power. The yaw rate incurred during the maneuver is closely in phase with the estimated bank angle. The roll mode is modeled by computing a transfer function between the roll command and the roll rate response [24], [19]. Secondary effects of the command such 47
10
0 (deg) Command −10 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 500
0 (deg/s) Roll Rate −500 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 200
0 (deg) Roll angle −200 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 500
0 (deg/s) Yaw Rate −500 241.6 241.8 242 242.2 242.4 242.6 242.8 243 243.2 243.4 Time (sec)
Figure 7–5: Wing-twist command and response from flight data as adverse yaw and pitch coupling are neglected due to relatively small disturbance magnitudes. Other yaw effects such as sideslip or bank angle induced yaw rate are also not considered in the model. A MATLAB Auto-Regressive with Exogenous Input (ARX) discrete-time model is used to represent the roll mode. The coefficients of the model are computed from least-squares fit to the command and response data. The discrete-time model is used in simulation to determine the accuracy of the computed model. A final transformation is made to represent the model as a continuous-time state-space formulation. The formulation of the model assumes first-order rigid-body dynamics. Although structural modes may very well be present, the model structure and filtering techniques assume that any response above 7 Hz is strictly noise and is therefore not considered in the model. The models are represented in the state-space nomenclature shown in Equations
7.1 and 7.2.
x ˙ Ax ¨ bu (7.1)
and
y cx ¨ du (7.2) 48
Where x is the state vector and y is the output. u is the control input and A,b,c,d are the state-space matrices. Of particular importance are A and b, which are consid- ered the system plant and control effectiveness matrices. Pole locations for the roll mode at several gull-wing positions are shown in
Figure 7–6. The plot shows the poles migrating to a less negative value as the wing is morphed in the positive or negative direction from neutral. This migration accounts for the decreased sensitivity to command input as the wing is morphed.
−10
−15
−20
−25
−30
−35 Open−Loop Pole (Real Axis)
−40
−45 −20 −10 0 10 20 30 Gull−wing angle (deg)
Figure 7–6: Pole migration with gull-wing morphing angle
The physical significance of the change in poles is the effect on the lateral- directional handling qualities throughout the morphing range. The most negative value, occurring at 0o morphing position, indicates that the vehicle quickly attains a steady-state roll value when subjected to a control input or disturbance. Increasing the gull-wing morphing in the positive direction increases the response time of the vehicle to similar inputs. At the most positive morphing position of 30o, the vehicle is considerably less responsive than at the neutral morphing position. Morphing the gull-wings in the negative direction produces a similar effect on the roll mode. The migration of the open-loop poles from neutral to -20o is similar to a 15o positive morphing from neutral. 49
The controllability of the simulated systems also undergoes a change with gull- wing morphing position. Figure 7–7 shows the change in the b-matrix values over the tested range of morphing. The qualitative shape of the plot appears as a mirror image of the pole locations. In particular, the neutral gull-wing position here is a maxima while the b-matrix value falls as the wing is deflected in either direction. The plotted values represent the control effectiveness of the twisting wingtips in producing a roll acceleration. The higher the b-matrix value, the higher the control power of the wingtips.
1400
1300
1200
1100
1000
900 B−matrix value 800
700
600
500 −20 −10 0 10 20 30 Gull−wing angle (deg)
Figure 7–7: B-matrix value for first-order roll mode systems
Physically, this is likely a result of a combined effect of the increased gull-wing angle, decreased wingspan, and angled control surfaces. The latter change occurs because of the normal direction of the wingtips deviates from perpendicular to the span as the wing is morphed. Thus, some component of the added lift from the wingtip twisting occurs in the spanwise direction and has no effect on the roll moment. The change in the roll moment produced by the wingtips varies approximately with the cosine of the deflection angle of the outboard wing section. Figures 7–8 through 7–11 show results of the simulation models compared to flight data. Measured and simulated roll rates are generally in close agreement for all the models. 50
10
5
0
−5 Wing−twist (deg)
−10 243.5 244 244.5 245 245.5 246
400
200
0
−200 Roll Rate (deg/s)
−400 243.5 244 244.5 245 245.5 246 Time (sec)
Figure 7–8: Wing-twist command (top) at 0o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom)
10
5
0
−5 Wing−twist (deg)
−10 271.5 272 272.5 273 273.5
400
200
0
−200 Roll Rate (deg/s)
−400 271.5 272 272.5 273 273.5 Time (sec)
Figure 7–9: Wing-twist command (top) at 15o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom)
7.4.2 Dutch Roll Mode
The Dutch roll mode is an dynamic involving coupling between roll, sideslip, and yaw [28]. Poor Dutch roll properties can cause difficulties in stabilization and control, causing poor flight path tracking [26]. Unlike the roll mode, the Dutch roll mode involves significant coupling between the lateral-direction states and often with the longitudinal states. The characteristics of the mode are highly dependent on wing geometry. The wing shape directly affects factors such as roll and yaw damping, sideslip cross-coupling, and inertial properties, 51
10
5
0
−5 Wing−twist (deg)
−10 332 332.5 333 333.5 334 334.5 335
400
200
0
−200
−400 Roll Rate (deg/s)
−600 332 332.5 333 333.5 334 334.5 335 Time (sec)
Figure 7–10: Wing-twist command (top) at 30o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom)
10
5
0
−5 Wing−twist (deg)
−10 422 422.5 423 423.5 424
400
200
0
−200 Roll Rate (deg/s)
−400 422 422.5 423 423.5 424 Time (sec)
Figure 7–11: Wing-twist command (top) at -20o gull-wing, measured roll rate (:) and simulated roll rate (-) (bottom) all of which in turn affect the Dutch roll characteristics. In terms of vehicle geometry, the mode is largely dependent on dihedral angle, wingspan, vertical area distribution, and vertical center of gravity. Rudder control pulse maneuvers are used to excite the Dutch roll mode of the vehicle at two different gull-wing positions. The pulses are a series of consecutive step inputs in opposite directions. Each pulse perturbs the vehicle from trimmed flight in sideslip, roll, and yaw. The resulting vehicle response is then largely an indication of the Dutch roll mode. Control pulses are performed at 0o and 15o gull-wing angles. 52
Command and response data from rudder control pulses at 0o and 15o gull-wing angle are shown in Figures 7–12 and 7–13, respectively. The most apparent difference between the two pulses is the two-fold increase in the roll response magnitude for the 15o gull-wing case. Roll coupling with rudder and/or sideslip has increased dramatically with positive gull-wing deflection. The response at this morphing position is dominated by roll. Recovery oscillations in both roll and yaw are smaller and damp out faster than the neutral morphing case.
300 25 300
20 200 250
15 200 100 10 150
100 5 0
50 0 Yaw rate (deg/s)
Rudder (deg) −100 0 −5 Roll rate (deg/s) −50 −200 −10 −100
−15 −150 −300 0 50 100 150 200 250 −20 −200 0 50 100 150 200 250 0 50 100 150 200 250
Figure 7–12: Rudder control pulse at 0o gull-wing angle with measured data (:) and simulated response (-)
30 600 400
20 300 400
200 10 200 100
0 0 0 Rudder (deg) Roll rate (deg/s) Yaw rate (deg/s) −100 −10 −200
−200
−20 −400 −300
−30 −600 −400 0 50 100 150 200 250 300 0 50 100 150 200 250 300 0 50 100 150 200 250 300
Figure 7–13: Rudder control pulse at 15o gull-wing angle with measured data (:) and simulated response (-)
The model formulation required that the system account for both the roll rate and yaw rate response to rudder deflection. With one input and two outputs, a different system identification method was needed than was used previously. Using the ARX ap- proach to modeling the Dutch roll dynamics resulted in a relatively poor fit compared with the roll mode modeling. 53
A 4th-order state-space model is used to identify the lateral dynamics from the rudder control pulse data. Attempting to model strictly the Dutch roll mode as a second-order system resulted in poor fit in both roll rate and yaw rate. Increasing the order of the system to 4 considerably improved the fit for both states. The resulting model has two pairs of complex conjugate poles, although classical Dutch roll modes for conventional aircraft have only a single pair. The identified Dutch roll dynamics for two morphing models are shown in the equations below. The dynamics are given in state-space format. The state-space matrices are shown for the 0o gull-wing system in Equation 7.3-
7.6 the first set of equations and for the 15o system in Equation 7.7-7.10.
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0 00728 0 07607 0 06432 0 001042 x1
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0 1299 0 04688 0 01308 0 05232 x2
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A (7.3)
0 06621 0 004354 0 02822 0 05985 x3
§ §
0 02396 0 08451 0 0712 0 05431 x4
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0 001507 0 0004478 0 001323 x1
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0 0003071 0 001497 0 0002368 x2
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b (7.4)
0 0003202 0 004137 0 007136 x3
§ §
0 001106 0 01099 0 003608 x4
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34 99 488 6 3 619 9 66 y1
§
c § (7.5)
869 176 5 22 61 2 435 y2
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0 0 9822 0 y1
§
d § (7.6) 0 0 2639 1 82 y2
54
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0 00963 0 07148 0 05012 0 002864 x1
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0 1124 0 04497 0 01106 0 03917 x2
¦ ¦
A (7.7)
0 07133 0 06225 0 03205 0 1023 x3
§ §
0 01097 0 01318 0 08323 0 02391 x4
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0 001524 0 0004311 0 0009517 x1
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0 0002664 0 0006908 8 541e 005 x2
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b (7.8)
0 0001861 0 001469 0 006974 x3
§ §
0 001101 0 006893 0 001574 x4
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46 5 1348 5 786 19 65 y1
§
c § (7.9)
901 222 3 18 36 1 216 y2
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0 1 556 0 y1
§
d § (7.10)
0 0 9075 1 335 y2
The pole migration shown in Figure 7–14 depicts a considerable change in the aircraft characteristics during morphing actuation. The two complex pairs shift toward the right-hand plane during positive gull-wing angle changes. This pole migration has the effect of decreasing both the average natural frequency and the damping of the modes. The particular modal properties are listed in Table 7–2 and Table 7–3. The two modes listed are not necessarily Dutch roll modes; rather, they represent the more general rudder pulse response dynamics. For this reason, the dynamics are represented by two complex conjugate poles as opposed to the single pair associated with most conventional aircraft. Table 7–2: Dutch roll modes for 0o gull-wing
- Natural frequency Damping Mode1 0.6276 Hz 0.3993 Mode2 0.7584 Hz 0.2359 55
0.15
0.1
0.05
0 degree 0 15 degree Imaginary axis −0.05
−0.1
−0.042 −0.04 −0.038 −0.036 −0.034 −0.032 −0.03 −0.028 −0.026 −0.024 −0.022 Real axis
Figure 7–14: Open-loop Dutch roll mode pole migration for two morphing positions Table 7–3: Dutch roll modes for 15o gull-wing
- Natural frequency Damping Mode1 0.5220 Hz 0.2847 Mode2 0.7879 Hz 0.2522
The eigenvectors associated with each morphing system are shown in Tables 7–4 and 7–5 for gull-wing cases 0o and 15o, respectively. The 15o case shows that the morphing causes increased coupling between the states, in addition to introducing considerable phase changes. Such changes are apparent by examining the rudder control pulse data from Figures 7–12 and 7–13, where the coupling of the rudder input to roll rate and yaw rate changes with morphing.
Table 7–4: Dutch roll mode eigenvectors for 0o gull-wing
State Magnitude Phase (deg) Mode1 x1 0.4769 74.4588o x2 0.7309 0o x3 0.0753 101.3212o x4 0.4824 96.7250o Mode2 x1 0.0323 71.4868o x2 0.4240 78.8885o x3 0.4948 83.0143o x4 0.7575 180.000o 56
Table 7–5: Dutch roll mode eigenvectors for 15o gull-wing
State Magnitude Phase (deg) Mode1 x1 0.4525 67.8550o x2 0.3209 146.2772o x3 0.7064 180.000o x4 0.4396 -96.0538o Mode2 x1 0.3758 -84.8100o x2 0.5526 50.4414o x3 0.4516 -83.7154o x4 0.5912 0.00000o
Figure 7–15 shows bode plots for the two morphing systems. The top two plots depict the magnitude and phase response from rudder input to roll rate while the bottom two plots show the responses from rudder input to yaw rate. The most notable change between the two occurs in the magnitude of the roll rate response. For the 15o case, the peak response has a larger amplitude and occurs at a lower frequency than the neutral case. This result is in agreement with the eigenvalues, which show a lower natural frequency for the 15o morphing position.
Bode Diagram
From: u1 50
0 To: y1
−50 360
180 To: y1
0
50
Magnitude (dB) ; Phase (deg) 0 To: y2
−50 180
0 To: y2
−180 −3 −2 −1 0 1 10 10 10 10 10
Frequency (rad/sec)
Figure 7–15: Frequency response diagram for 0o gull-wing (:) and 15o gull-wing (-)
7.5 Longitudinal Dynamics
Longitudinal system identification is performed on elevator pulse data to determine the short period pitch mode and the Phugoid mode. Two morphing conditions are 57 considered for this analysis, 0o gull-wing and 15o gull-wing. A transfer function is computed between the elevator deflection and pitch rate response data using an output-error model. Tables 7–6 and 7–7 shows the results of the modeling in terms of the frequency and damping of the longitudinal modes. For each of the longitudinal dynamic models, the system identification process also predicted a negative real pole near zero. Table 7–6: Longitudinal modes for 0o gull-wing
- Natural frequency Damping Phugoid Mode 0.2945 Hz 0.5422 Short Period Mode 19.75 Hz 0.0303
Table 7–7: Longitudinal modes for 15o gull-wing
- Natural frequency Damping Phugoid Mode 0.6131 Hz 0.3912 Short Period Mode 19.95 Hz 0.1445
The system poles show a distinct change in the longitudinal dynamics during morphing. Specifically, the short period damping ratio has increased dramatically. The natural frequency of the mode is predicted to remain constant over the 150 change in gull-wing angle. For the Phugoid Mode, the simulation predicted an increase in the natural frequency with a corresponding decrease in the damping. These results, especially in the short period mode, are in agreement with pilot feedback. Pitch control during high gull-wing morphing is highly damped and responds sluggishly to elevator deflection. However, the limited data set precludes rigorous evaluation of the predicted models. Additionally, the noise in the data during the elevator pulse sequence flight test seemed higher in magnitude than noise in other data sets. The noise level creates difficulties in differentiating physical dynamics with sensor noise or vibration. Figure 7–16 shows simulated pitch rate response to an elevator pulse sequence plotted against measured pitch rate. The pulse is performed with a gull-wing angle 58 of 0o. The simulated response is in good agreement with the general trends of the measured response, although has a poor fit of the high frequency content. As a result, the predicted models are useful only as basic descriptions of the actual dynamics. Figure 7–17 shows the measured and simulated responses for a 15o gull-wing configuration. Again, the simulation model exhibits discrepancies with the measured data at high frequency oscillations. The data from the elevator pulse sequences is plotted against simulation time steps, with each step equal to 1/100th of a second.
100 400 80 300 60 200 40
100 20
0 0
−20 −100 Pitch Rate (deg/s) Pitch Rate (deg/s) −40 −200 −60
−300 −80
−400 −100 1100 1150 1200 1250 1300 1350 1400 1450 1500 1100 1150 1200 1250 1300 1350 1400 1450 1500 Time (steps) Time (steps)
Figure 7–16: Elevator pulse command (left), measured (:) and simulated( -) pitch rate responses (right)
400 100
80 300 60 200 40 100 20
0 0
−20
−100 Pitch Rate (deg/s)
Elevator Command (deg) −40 −200 −60 −300 −80
−400 −100 950 1000 1050 1100 1150 1200 1250 1300 950 1000 1050 1100 1150 1200 1250 1300 Time (steps) Time (steps)
Figure 7–17: 15o gull-wing elevator pulse command (left), measured (:) and simulated( -) pitch rate responses (right) CHAPTER 8 FOLDING WING AND TAIL MORPHING
8.1 Aircraft Design
A quasi-static morphing has also been implemented on a tandem-wing micro air vehicle, Figure 8–1, to allow the aircraft to achieve two distinct mission requirements in a single flight. The aircraft is designed to achieve stable, controllable forward flight for climb, cruise, and loiter phases, then transition to reverse flight for a slow, vertical descent. A single control actuator is used to sweep both front and aft wings forward, in addition to collapsing and extending vertical stabilizer surfaces. Table 8–1 summarizes the important properties of the aircraft.
Figure 8–1: Top view of unswept (left) and swept (right) configurations
8.2 Morphing Mechanism
The aircraft incorporates a dual-wing sweep angle morphing to change the location of the aircraft center. The wings are designed to sweep far enough forward such that the neutral point becomes forward of the center of gravity. In this configuration (Figure 8–2), forward flight is destabilized and reverse flight is stabilized.
In order to improve reverse flight stability, the wing sweep incorporates a collaps- ing vertical stabilizer on the aft wing and an expanding stabilizer on the forward wing.
59 60
Table 8–1: Properties of the folding wing-tail aircraft in two configurations
Property Folding Wing-Tail (Airigami) Wing Span 12 in Wing Area (unswept) 60 in2 Wing Area (swept) 65 in2 Vertical Stab Area (unswept) 7.61 in2
Vertical Stab Area (swept) 3.44 in2
Wing Loading (unswept) 11.02 oz ft2 Powerplant DC motor - 4 in prop Total Weight 4.59 oz
Each stabilizer is initially built into the wing structure and allowed to fold along nylon hinges.
Figure 8–2: Side view of unswept (top) and swept (bottom) configurations
Reverse flight is achieved only in descents with a near vertical flightpath. As such, the thrust from the propeller serves as both a drag producer and as a stabilizing device. The primary purpose of the wings and vertical stabilizer during this descent profile is to prevent the vehicle from diverging from the vertical attitude. In this orientation, the thrust serves to directly counteract the weight of the aircraft and slow the sink rate. The current powerplant uses a DC electric motor with a 4:1 gear reduction to turn a 4 in plastic prop. The thrust to weight ratio of the aircraft is slightly less than one, allowing for a substantial reduction in the sink rate at full throttle. Alternative motor 61 options may be used to increase thrust to weight ratio to greater than one. In such a case, the thrust could be used to achieve a zero sink rate and hover the aircraft during the descent phase. Although the aircraft is designed primarily for vertical reverse flights, other descent modes such as a controlled flat spin or high-alpha, oscillatory falling leaf mode may be possible with the sweep morphing. 8.3 Flight Trials
Basic flight trials have been conducted with the folding wing-tail vehicle to determine the feasibility of the design for enhanced vehicle agility. Although the objectives of fully-stabilized reverse flight descents were not met, the vehicle concept shows promise with additional development. The vehicle exhibits good handling and control characteristics in the tandem- wing forward flight mode. The hinged elevons on the aft wing are used collectively to command pitch rate and differentially to command roll rate. Pitch and roll rate responses to elevon deflection is sufficient to control the vehicle in climbs, turns, dives, and level flight.
The vehicle is considerably easier to control using the hinged control surfaces on the aft wing than using the wing twisting on the fore wing. The exact reason for this disparity in control is unclear, as different combinations of effector-wing placement were not conducted.
Figure 8–3 shows the dynamic pitch up maneuver is used to transition the vehicle from conventional forward flight to reverse flight. This maneuver involves achieving cruise airspeed in level flight, then increasing the pitch angle and flight path to near 90o vertical. The folding wing-tail morphing is then actuated to shift the aerodynamic center and center of lateral area forward. Flight trials of this maneuver have resulted in only short periods of reverse flight before the vehicle diverges into a flat spin. Stabilizing the aircraft in reverse flight requires additional thrust in addition to increased sweep angle. 62
Figure 8–3: Envisioned dynamic pitch up maneuver for forward to reverse flight transi- tion CHAPTER 9 SUMMARY
9.1 Recommendations
Flight tests of the morphing vehicles shows that shape change actuators have a considerable effect on the vehicle flight dynamics. This is certainly not an unexpected result, given that vehicle dynamics are directly dependent upon geometry and con- figuration. The tests showed that both dynamic and quasi-static morphing strategies can have a highly desirable impact on both the flight performance and the control effectiveness. However, the quantification of these changes is somewhat arbitrary, con- sidering that no comparisons were made to established handling quality or performance metrics. An important part of the future research will be to contextualize the benefits of the morphing for a vehicle in a realistic mission scenario. Doing so will ultimately determine the benefit of morphing and will also help identify the practical effects of the changes to the vehicle dynamics. The models identified from the flight data are quite limited in usefulness. The simple models show interesting effects of the morphing, but still do not address the more important problem of maneuvers and actuations beyond simple perturbations.
For a more generalized morphing actuation, the effects of inertial and aerodynamic asymmetries will introduce considerable coupling and nonlinearity that can only be modeled using a much more complex approach. The development of such an approach is currently underway. Higher fidelity modeling approaches become increasingly important for stabi- lization and control. A better understanding of the actual dynamics will help develop appropriate control theory for morphing vehicles. Whether conventional linearized controllers are appropriate for morphing or not will be seen. Perhaps a better approach
63 64 is to design the controller with implicit knowledge of the morphing effect. These issues are being addressed from a theoretical and computational standpoint. Once satisfactory results are obtained from this effort, the focus will transition to implementing these controllers on flight vehicles and experimentally validating controller designs.
9.2 Conclusions
Simple strategies for morphing on small vehicles have been demonstrated in flight.
These strategies, although not optimal, have improved the performance of the vehicles in many cases and increased the size of the flight envelope through shape changes. The morphing has been used to demonstrate high-agility and aggressive maneuvering. Small sensors were used to record the vehicle responses during a variety of flight test conditions. Models of the vehicle generated from the flight data indicate that linear, symmetric assumptions are reasonably accurate in representing the dynamics for small morphing commands. Vehicle dynamics observed during large morphing commands, however, were highly non-linear. The quasi-static morphing demonstrated on the variable gull-wing aircraft suf-
ficiently changed the flight performance to allow the vehicle to operate in several different modes. Such performance changes are critically important to the realization of morphing in commercial and military flight systems. The vehicle was also used to demonstrate the extent of the change in dynamics and handling qualities that occurs as a result of the geometric change. The change in dynamics illustrates the need for flight controllers that adapt or change with morphing condition. Such controllers are currently under development using the results of the flight testing, in addition to wind tunnel and theoretical modeling approaches. REFERENCES [1] M. Abdulrahim “Flight Performance Characteristics of a Biologically-Inspired Morphing Aircraft” Presentation at 54th AIAA Regional Student Conference, Memphis, TN, April 2004. [2] M. Amprikidis and J.E. Cooper, “Development of Smart Spars for Active Aeroelastic Structures,” AIAA-2003-1799, 2003. [3] J. Blondeau, J. Richeson and D.J. Pines, “Design, Development and Testing of a Morphing Aspect Ratio Wing using an Inflatable Telescopic Spar,” AIAA-2003- 1718. [4] J. Bowman, B. Sanders and T. Weisshar, “Evaluating the Impact of Morphing Technologies on Aircraft Performance,” AIAA-2002-1631, 2002. [5] M.J. Brenner, Aeroservoelastic Modeling and Validation of a Thrust-Vectoring F/A-18 Aircraft, NASA-TP-3647, September 1996. [6] D. Cadogan, T. Smith, R. Lee and S. Scarborough, “Inflatable and Rigidizable Wing Components for Unmanned Aerial Vehicles,” AIAA-2003-1801, 2003.
[7] B.D. Caldwell, “FCS Design for Structural Coupling Stability,” The Aeronautical Journal, December 1996, pp. 507-519. [8] C.E.S. Cesnik and E.L. Brown, “Active Warping Control of a Joined-Wing Airplane Configuration,” AIAA-2003-1716, 2003. [9] J.B. Davidson, P. Chwalowski, and B.S. Lazos, “Flight Dynamic Simulation As- sessment of a Morphable Hyper-Elliptic Cambered Span Winged Configuration,” AIAA-2003-5301, August 2003. [10] M. Drela and H. Youngren XFOIL 6.94 User Guide MIT Aero & Astro, Aero- craft, Inc. http://raphael.mit.edu/xfoil/, Dec 2001 [11] B. Etkin Dynamics of Flight Stability and Control 2nd Edition John Wiley & Sons, New York, 1982. [12] S.M. Ettinger, M.C. Nechyba, P.G. Ifju, and M.R. Waszak, “Vision-Guided Flight Stability and Control for Micro Air Vehicles,” Proceedings of the IEEE International Conference on Intelligent Robots and Systems, October 2002, pp. 2134-2140, IEEE, Lausanne, Switzerland.
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[13] G.A. Fleming, S.M. Bartram, M.R. Waszak, and L.N. Jenkins, “Projection Moire Interferometry Measurements of Micro Air Vehicle Wings,” Proceedings of the SPIE International Symposium on Optical Science and Technology, Paper 448-16, August 2001. [14] H. Garcia, M. Abdulrahim, and R. Lind, “Roll Control for a Micro Air Vehicle using Active Wing Morphing,” AIAA-2003-5347, August 2003.
[15] J.M. Grasmeyer and M.T. Keennon, “Development of the Black Widow Micro Air Vehicle,” AIAA-2001-0127, 2001. [16] I.M. Gregory, “Dynamic Inversion to Control Large Flexible Transport Aircraft,” AIAA-98-4323, 1998. [17] P.G. Ifju, S. Ettinger, D.A. Jenkins and L. Martinez, “Composite Materials for Micro Air Vehicles” Presentation at Society for Advancement of Materials and Process Engineering Annual Conference, Long Beach, CA, May 2001. [18] P.G. Ifju, D.A. Jenkins, S.M. Ettinger, Y. Lian, W. Shyy, and M.R. Waszak, “Flexible-Wing Based Micro Air Vehicles,” AIAA-2002-0705, January 2002. [19] K.W. Iliff, “Aircraft Parameter Estimation,” NASA-TM-88281, 1987.
[20] C.O. Johnston, D.A. Neal, L.D. Wiggins, H.H. Robertshaw, W.H. Mason and D.J. Inman, “A Model to Compare the Flight Control Energy Requirements of Morphing and Conventionally Actuated Wings,” AIAA-2003-1716, 2003.
[21] S.M. Joshi and A.G. Kelkar, “Inner Loop Control of Supersonic Aircraft in the Presence of Aeroelastic Modes,” IEEE Transactions on Control Systems Technology, Vol. 6, No. 6, November 1998, pp. 730-739.
[22] Y. Lian and W. Shyy, “Three-Dimensional Fluid-Structure Interactions of a Membrane Wing for Micro Air Vehicle Applications,” AIAA-2003-1726, April 2003.
[23] E. Livne, “Integrated Aeroservoelastic Optimization: Status and Direction,” Journal of Aircraft, Vol. 36, No. 1, January-February 1999, pp. 122-145. [24] L. Ljung, System Identification, Prentice Hall, Englewood Cliffs, NJ, 1987.
[25] P. de Marmier and N. Wereley, “Morphing Wings of a Small Scale UAV Using Inflatable Actuators for Sweep Control,” AIAA-2003-1802. [26] R.C. Nelson Flight Stability and Automatic Control McGraw Hill, Boston, MA, 1998. [27] E.W. Pendleton, D. Bessette, P.B. Field, G.D. Miller, and K.E. Griffin, “Active Aeroelastic Wing Flight Research Program: Technical Program and Model Analytical Development,” Journal of Aircraft, Vol. 37, No. 4, 2000, pp. 554-561. 67
[28] W.F. Phillips Mechanics of Flight John Wiley & Sons, Hoboken, NJ, 2004. [29] B. Sanders, F.E. Eastep and E. Forster, “Aerodynamic and Aeroelastic Characteris- tics of Wings with Conformal Control Surfaces for Morphing Aircraft,” Journal of Aircraft, Vol. 40, No. 1, January-February 2003, pp. 94-99. [30] L.V. Schmidt Introduction to Aircraft Flight Dynamics American Institute of Aeronautics and Astronautics, Inc., Reston, VA, 1998. [31] M.J. Solter, L.G. Horta, and A.D. Panetta, “A Study of a Prototype Actuator Concept for Membrane Boundary Control,” AIAA-2003-1736, April 2003. [32] R.W. Stone, and B.E. Hultz, Summary of Spin and Recovery Characteristics of 12 Models of Flying-Wing and Unconventional-Type Airplanes, NACA-RM-L50L29, March 1951. [33] H. Tennekes The Simple Science of Flight: From Insects to Jumbo Jets The MIT Press, Cambridge, MA, 1997.
[34] S. Tung, and S. Witherspoon, “EAP Actuators for Controlling Space Inflatable Structures,” AIAA-2003-1741, April 2003. [35] D. Viieru, Y. Lian, W. Shyy and P. Ifju, “Investigation of Tip Vortex on Aerody- namic Performance of a Micro Air Vehicle,” AIAA-2003-3597, 2003. [36] M.R. Waszak, J.B. Davidson, and P.G. Ifju, “Simulation and Flight Control of an Aeroelastic Fixed Wing Micro Air Vehicle,” AIAA-2002-4875, August 2002.
[37] M.R. Waszak, L.N. Jenkins, and P.G. Ifju, “Stability and Control Properties of an Aeroelastic Fixed Wing Micro Air Vehicle,” AIAA-2001-4005, August 2001. [38] R.W. Wlezien, G.C. Horner, A.R. McGowan, S.L. Padula, M.A. Scott, R.J. Silcox, and J.O. Simpson, “The Aircraft Morphing Program,” AIAA-98-1927, April 1998. BIOGRAPHICAL SKETCH Like most people, Mujahid Abdulrahim was born. His childhood teemed with the many adventures typically associated with adolescent life, including placing metal objects into electrical sockets and making inappropriate faces at the monkeys in the zoo. Luckily, he soon outgrew such shenanigans and began focusing on his career. Professional hopes of being an inventor, repairshop owner, electrical engineer, and aerial photographer soon gave way to his one true passion – aeronautical engineering.
Mujahid firmly decided his life’s path by consulting a poster in his 8th grade algebra class. This poster listed many professions and the types of math required on the job. The only profession that had checkmarks from basic algebra all the way up to string theory was aeronautical engineering – and so a dream was born. Mujahid has been active in various academic and competitive pursuits over his
6-year career at the University of Florida. These include the International Micro Air Vehicle Competition, AIAA Regional/National Student Conferences, research paper competitions, mountain bike racing, SCCA autocross racing, IMAC R/C scale aerobatics, R/C Funfly competitions, R/C on-road racing, and of course lab chewing gum Olympics. Mujahid’s primary research interest is in morphing aircraft design and flight vehicle dynamics. He has pursued a variety of novel approaches to morphing and flight control throughout his master’s research. The work follows his extracurricular interest in racing and maximum performance vehicle control. Mujahid’s life started in the Calgary Women’s Hospital in room A32 on the third floor. His travels have taken him quite far away from that hospital bed, all the way to
68 69 remote villages in Syria to visit his relatives and show them how to perform donuts on a motorbike. Life has been good.