Document
AIAA 2004-5114
Wind Tunnel Test of an RPV with
Shape-Change Control Effector and
Sensor Arrays
David L. Raney and Randolph H. Cabell
NASA Langley Research Center
Hampton, VA 23681
Adam R. Sloan
Stanford University
Stanford, CA 94305
William G. Barnwell and S. Todd Lion
North Carolina State University
Raleigh, NC 27695
Bret A. Hautamaki
University of Michigan
Ann Arbor, MI 48104
AIAA Guidance, Navigation & Control Conference
16-19 August 2004
Providence, Rhode Island
For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics, 1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.
AIAA 2004-5114 Wind Tunnel Test of an RPV with Shape-Change Control Effector and Sensor Arrays * ‡ † David L. Raney and Randolph H. Cabell Adam R. Sloan NASA Langley Research Center Stanford University Hampton, VA 23681 Stanford, CA 94305 † § § William G. Barnwell and S. Todd Lion Bret A. Hautamaki North Carolina State University University of Michigan Raleigh, NC 27695 Ann Arbor, MI 48104 ABSTRACT A variety of novel control effector concepts have recently emerged that may enable new approaches to flight control. In particular, the potential exists to shift the composition of the typical aircraft control effector suite from a small number of high authority, specialized devices (rudder, aileron, elevator, flaps), toward larger numbers of smaller, less specialized, distributed device arrays. The concept envi sions effector and sensor networks composed of relatively small high-bandwidth devices able to simultan eously perform a variety of control functions using feedback from disparate data sources. To investigate this concept, a remotely piloted flight vehicle has been equipped with an array of 24 trailing edge shape-change effectors and associated pressure measurements. The vehicle, called the Multifunctional Effector and Sensor Array (MESA) testbed, was recently tested in NASA Langley’s 12-ft Low Speed wind tunnel to characterize its stability properties, control authorities, and distributed pressure sensitivities for use in a dynamic simul ation prior to flight testing. Another objective was to implement and evaluate a scheme for actively controlling the spanwise pressure distribution using the shape-change array. This report describes the MESA testbed, design of the pressure distribution controller, and results of the wind tunnel test.
INTRODUCTION The presumed benefits of such a shift toward dis- tributed effector systems are speculative and come at Recent discoveries in material science and fluidics some cost, particularly in the form of increased system have been used to create a variety of novel effector complexity. In addition to the aforementioned distributed devices that may enable new approaches to aerospace control objectives, potential benefits include reduced fuel vehicle flight control. Potential exists to shift the compo - consumption, enhanced maneuverability, reconfigura- sition of future aircraft control effector suites from a bility, health monitoring, failure tolerance and mission relatively small number of high authority, specialized adaptability. Whether distributed systems will be able to devices (rudder, aileron, elevator, flaps), toward in- buy their way onto future flight vehicles is likely to creasingly larger numbers of smaller, less specialized, depend upon a great number of mission-specific factors distributed effector and sensor device arrays. Such and trade offs. But their development and demonstration effector arrays might operate in a decentralized fashion at the fundamental research level will expand the design on local data from a distributed pressure sensor or accel- space and present options that may enable new missions erometer network to perform highly distributed tasks and new capabilities, or enhance existing functions.
such as load alleviation, flutter suppression, separation control, or pressure regu lation, while simultaneously Although several research efforts at universities, performing more centralized stability augmentation and government labs and industry are underway to develop maneuver control tasks using feedback from a conven- and characterize novel effector devices including syn- tional inertial measurement unit and air data sensor suite.
thetic jets, shape-change blisters, and micro flaps, Future aerospace vehicles might use large networks of relatively few activities address the incorporation of sensor and effector devices in this capacity, thereby large groups of such devices into aerospace vehicle flight augmenting or replacing conventional control surfaces.
control systems. This research seeks to develop flight * Research scientist, Dynamics and Control Branch, Senior Member AIAA.
‡ Research scientist, Structural Acoustics Branch, Senior Member AIAA.
† Graduate Student, Mechanical and Aerospace Engineering Department, Member AIAA.
§ Undergraduate, Mechanical and Aerospace Engineering Department, Member AIAA.
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American Institute of Aeronautics and Astronautics AIAA 2004-5114 control concepts for aerospace vehicles that incorporate used ten distributed high-bandwidth ultrasonic motors to measurements from distributed sensor arrays and issue warp a seamless airfoil trailing edge into a variety of commands to large numbers of distributed effectors to continuous geometries with the potential to produce simultaneously perform multiple control functions. maneuver control moments. In this case, the distributed Control algorithms are developed and evaluated using a shape-change effector system provides the airfoil with computer simulation model and wind tunnel testing of a greater adaptability and functionality than could be small remotely piloted aircraft. achieved by a single large aileron effector occupying the same area.
BACKGROUND The present investigation focuses on the use of a Prior work by Park and Green focused on optimizing small remotely piloted vehicle as a testbed for the devel- the placement of distributed shape-change “bump opment of flight control algorithms using distributed effector” devices over the surface an advanced aircraft effector and sensor arrays. The testbed is equipped with a configuration for maneuver control purposes by applying total of 24 trailing edge shape-change effector devices automatic differentiation software to a potential flow 2 and associ ated pressure measurements. The flight analysis model. They applied these bump devices to vehicle, called the Multifunctional Effector and Sensor Lockheed Martin’s Innovative Control Effector (ICE) Array (MESA) testbed, was built by NC State University configuration in a conceptual design. A follow-on with support from NASA’s Aircraft Morphing Program.
investigation by Padula and Rogers examined the use of The vehicle has been tested in Langley’s 12-ft Low genetic algorithms for determining placement of the Speed Tunnel to characterize its basic stability proper- shape-change devices. These efforts yielded a suite of ties, control authorities, and distributed pressure surface bump control effectors for the ICE configuration.
responses to effector deflections for use in a dynamic A related investigation by Raney and Montgomery simulation model prior to flight testing . An add itional developed a flight dynamic simulation and control design objective of the wind tunnel test was to implement and for the vehicle using this bump effector suite. The study evaluate a scheme for regulating the spanwise pressure found that the effector suite offered promise for seamless distribution on the testbed using the distributed sensor aircraft flight control in a low-rate maneuver mode that and effector array. The ability of the system to achieve might be use ful for stealth purposes, but that the author- and regulate a range of commanded spanwise pressure ity of the surface bump devices was not sufficient to distributions in the presence of turbulence, flight condi- replace the conventional effector suite for this vehicle.
tion per turbations, and device failures was examined.
An unrelated investigation by Bieniawaski, Kroo, This report describes the MESA remotely piloted and Lee developed a testbed that used distri buted micro- vehicle (RPV), the design of the spanwise pressure trailing edge effectors (MiTEs) together with distributed 5,6 distribution controller for use with the model’s trailing accelerometers in a flutter suppression control system.
edge effector and sensor array, and the results of both Wind tunnel tests demonstrated successful flutter sup- phases of the wind-tunnel test, consisting of open-loop pression using a novel control design that was generated characterization of the flight vehicle and closed-loop by a “reinforcement learning” policy search technique.
evaluation of the pressure distribution control design.
The investigation demonstrated the potential benefits of control through the use of a large number of small, EXPERIMENTAL RPV MODEL mechanically simple, distributed effector devices, and The MESA RPV was created by modifying a flight developed a unique approach to control synthesis that vehicle that had been originally designed, constructed, was specifically tailored for distributed effector and and flight-tested by a team of aerospace engineering sensor arrays.
seniors at NC State University during the 2001-2002 A series of investigations that were funded under the term. The original vehicle, named Thunderstruck , was DARPA/AFRL/NASA/Northrop Grumman Smart Wing similar in planform and appearance to the NASA-Boeing Program have demonstrated the potential of distributed BWB design, although its two large vertical stabilizers actuation systems to create gap-less, hinge-less were a notable departure. The configuration is shown in continuous mold line control surfaces for adaptive wing Figure 1, along with a view of the final prototype during 7,8 designs. In particular, an investigation by Wang, et al its graduation flight. The vehicle used a symmetric addressed the design of distributed actuation sy stems to NACA 0015 airfoil and had a wingspan of 9.4 feet, root generate continuous shape-change deflections of the chord of 4.9 feet, and takeoff weight of 39 pounds. The trailing edge of an airfoil. A number of material and vehicle was designed to cruise at 80 miles per hour with actuation system concepts were examined, including a predicted stall speed of 30 miles per hour. An AMT shape-memory alloys (SMAs), piezo stacks, and Mercury Turbojet engine provided 14.82 pounds of ultrasonic motors. The pros and cons of each system available thrust. The aircraft was capable of carrying were examined and a final design was generated that five pounds of payload.
American Institute of Aeronautics and Astronautics AIAA 2004-5114 Figure 1. Isometric and planform views of Thunderstruck , with a photo of the vehicle during its graduation flight.
For the purposes of this investigation, Thunderstruck The placement and number of effector devices that was transformed into the MESA RPV testbed under a were incorporated into the MESA testbed was influenced cooperative agreement with NC State. New wings were by several factors. Due to accessibility issues within the designed and fabricated, each of which included a dis- existing aircraft fuselage, it was decided that the shape- tributed array of 12 shape-change trailing edge effector change array should be confined to the removable wing devices and 12 distributed pressure measurements. The sections. Wing thickness and chord limited the ou tboard design of the shape-change devices composing the placement of the devices. Refraining from extending the trailing edge array required several iterations. array into the outboard-most wing area also left space for a conventional aileron that could be used in conjunction Shape-Change Effector Array with the remaining conventional surfaces to trim and control the testbed during takeoff, landing, and other Initially, the hope was to create a completely non-research functions. Potential flow analysis gener ated seamless shape-change trailing edge array such as the linear aerodynamic force and moment estimates that one designed in [9], but the weight and complexity of the were used in flight dynamic simulation studies to iden- resulting design was not suitable for this flight vehicle.
tify an installation region that would provide control Instead, it was decided to create a discretized authorities comparable to the conventional effector suite.
approximation of a continuous mold line fully morphable These considerations lead to the final design decision to trailing edge array by dividing the wing trailing edge into include twelve devices on each wing. The modified wing twelve small hingeless shape-change control surfaces panels increased the RPV weight by 3 lb.
able to bend in the vertical plane. Each device consists of two thin spring steel skin sections that are split at the The MESA RPV is shown in Figure 3. In addition to trailing edge of the wing. The spring steel plates, having the shape-change effector suite, the conventional aileron, a thickness of 0.007”, are warped by a lightweight elevon and rudder control effectors are apparent in the hobby-class Hobbico CS-5 servomotor through a pull- figure. Shown in Figure 4 is a panel model of the vehicle pull wire linkage; the opposing surface restores the that was used in the potential flow analysis to generate actuated surface to its neutral position. Each effector preliminary estimates of stabil ity and control character- segment measures 1.5” wide x 4” long, and is capable of istics for the flight dynamic simulation model. The deflecting through a range of ± 15 degrees. This design potential flow results will be com pared with wind tunnel allowed the array to be constructed of light weight, measurements later in this report. Table 1 summa rizes inexpensive, commonly available and reliable supplies.
the flight vehicle characteristics. Further detail regarding Figure 2 shows a side view of the prototype effector design, fabrication, and pre liminary testing of the shape- design in the undeflected and fully deflected positions.
change effector array is provided in [10].
Rudder 12 Shape-Change Aileron Spring Steel Effector Devices Elevon Plates Linkage Wires Removable 12 Pressure Wing Section Measurements Servo Fuselage Motor Section Figure 2. Side view of shape-change effector prototype.
Figure 3. MESA RPV with modified wing panels.
American Institute of Aeronautics and Astronautics AIAA 2004-5114 Shape 2: Shape 1: linearly varying offset constant offset Shape 3: Shape 6: half sine-wave alternating +/– Figure 4. Potential flow panel model used to develop preliminary stability and control estimates.
Parameter ! Value Figure 5. Effector array segments deployed in trailing Takeoff Weight, lb 42 edge shapes 1, 2, 3 and 6.
Wing Area, ft 17.77 Span, ft 9.38 po tential flow prediction for the region of maximum Mean Chord, ft 2.86 pressure sensitivity to control surface deflection. Surface Vcruise, ft/s 117 pressure taps were positioned 4.05” upstream of the Vstall, ft/s 44 trailing edge of each effector segment, for a total of 24 Inertias, slug ft Ixx 0.0808 pressure taps, 12 per wing. The taps were equally spaced Iyy 1.6362 in the spanwise direction at intervals of 1.5” with the first Izz 2.3832 tap located 0.75” from the root chord of the removable Ixz 0.0900 wing section shown in Figure 3. The taps measured 0.040” in diameter and were connected to a Pressure Table 1 . MESA flight vehicle characteristics Systems Inc. Electronic Scanning Pressure (ESP) module through 0.040” diameter nylon tubing.
Effector Deployment Modes and Shapes The effector array could be operated in either open- The ESP module was placed inside the model to minimize the pressure measurement lag associated with loop or closed-loop command modes. The open-loop mode allowed commands to be generated using one of tubing length. The ESP had a range of ±10” H O, and was capable of electronically multiplexing up to 32 inde- three settings. The first setting permitted independ ent deflections of individual effector segments. The second pendent pressure measurements. The ESP was located inside a thermostatically controlled heater box within the setting permitted the selection of one of six static trailing edge shapes, in which each effector took part in approxi- model to eliminate the influence of temperature fluctuations on the pressure transducers. Measurements mating a portion of the shape. A total of six shapes were from the 24 pressure taps on the model were implemented consisting of a constant offset of the trail- electronically scanned and multiplexed by the ESP ing edge, a linearly sloped offset, half sine wave, whole sine wave, a 1.5-cycle sine wave, and finally an alter- module at a time interval of 1.5 ms, so the measurement at each tap was updated every 36 ms.
nating plus/minus deflection. Photos of the left wing of the model with effector segments deployed in trailing Control Interface edge shapes 1, 2, 3, and 6 are shown in Figure 5. The third open-loop setting permitted the array to be driven The distributed pressure measurement and effector dynamically with an arbitrary deflection time history.
array control interface was designed and implemented using dSpace™ hardware-in-the-loop computer compo- The closed-loop command mode drove the effector nents and software together with Matlab’s Simulink™ positions with a real-time hardware-in-the-loop feedback programming environment and Real-Time Workshop™ control system designed to achieve a commanded pres- code generation package. The real time control process sure distribution at the spanwise taps. The feedback was implemented with a step size of 0.75 ms.
control algorithm will be presented later in this report.
The experimental setup included the ability to Distributed Pressure Measurements control all moveable surfaces of the model remotely Pressure measurement taps were placed upstream of using the dSpace real-time interface. The dSpace system included a dedicated Power PC 750MHz processor, each effector to investigate the potential to control the 16–bit A-to-D and D-to-A boards, four digital I/O serial spanwise pressure distribution with the shape-change connections and a software interface designed to permit array. Locations of the taps were determined using a American Institute of Aeronautics and Astronautics AIAA 2004-5114 real-time hardware-in-the-loop execution of control FORCE AND MOMENT RESULTS algorithms. The dSpace system was located in the wind Force and moment data obtained from the test were tunnel control room. The system not only provided the compared with potential flow predictions that had been ability to control the model effectors with open-loop generated prior to the test. The potential flow analysis commands, but also to drive them with closed-loop 11 was performed using the PMARC code with the panel signals from the pressure distribution controller. To model shown in Figure 4. Potential flow predictions for achieve this capability it was necessary to implement the coefficient of lift and pitching moment vs. angle of data acquisition software that drove the ESP module attack are compared with wind tunnel data in Figure 7.
within the dSpace real-time control algorithm. Four Moments are referenced to the aircraft center of gravity BASIC-X™ servo serial boards were used to translate located 26 inches aft of the nose.
position commands from the dSpace system into pulse The gradual stall break shown in the upper plot of train signals for the effector servos. Each board could Figure 7 is typical of blended wing-body configurations.
drive up to eight servos. The boards were located within Linear aerodynamic predictions based on potential flow the model and were remotely commanded via the dSpace analysis assume inviscid, irrotational, unseparated flow, serial connections using RS232 protocol.
and so become increasingly unreliable as the vehicle FACILITY AND TEST CONDITIONS approaches stall. The vehicle trims in 80 mph cruise at approximately 4 degrees AOA, but trims on approach The model was tested in NASA Langley’s 12-ft Low and landing at approximately 9 to 10 degrees. The wind Speed Tunnel, operated by the Vehicle Dynamics Branch tunnel results indicate a serious reduction in static pitch of the Airborne Systems Competency. The 12-Foot Low- stability at or near the approach condition.
Speed Tunnel is an atmospheric pressure, open circuit tun nel enclosed in a 60-foot diameter sphere. The test Potential flow predictions for coefficients of yaw section is octagonal, having a width and height of 12 feet and roll vs. sideslip at the trim angle of attack of and a length of 15 feet with each octagonal side 4 degrees are shown in Figure 8. Both of these coef- measuring 5 feet. The maximum operating dynamic ficients exhibit stable trends with sideslip angle. The pressure is q = 7 psf (V =77 ft/sec at standard sea level), potential flow analysis appears to provide reasonable -1 for a Reynolds number of approximately 490,000 ft . predictions for the lateral/directional stability coefficients at the cruise condition, and these characteristics are very In this experiment, the model was tested over a similar at the landing condition.
range of angle of attack (AOA) from -2 to 20 degrees and sideslip from -6 to 6 degrees, and at dynamic 1.4 Wind Tunnel pressure of 5 psf, corresponding to tunnel speed of 1.2 CMARC 45 mph. The model’s nominal flight speed is 80 mph, and this testing was conducted at approximately half that speed due to limitations associated with heating of the 0.8 tunnel drive system. The model was mounted on a sting L 0.6 C that exited through the lower surface of the f uselage. The 0.4 mounting system included an internal 6-component strain gauge balance to provide force and moment data.
0.2 Figure 6 shows the aircraft mounted in the test section.
-2 0 2 4 6 8 10 12 14 16 18 20 -0.2 0.02 a (deg) a (deg) -2 0 2 4 6 8 10 12 14 16 18 20 -0.02 -0.04 m -0.06 C -0.08 -0.1 Wind Tunnel -0.12 CMARC -0.14 Figure 6. MESA RPV mounted in the NASA Langley Figure 7. Comparison of wind tunnel data with PMARC 12-Foot Wind Tunnel. predictions for lift (top) and pitching moment (bottom).
American Institute of Aeronautics and Astronautics AIAA 2004-5114 Control Authorities – Conventional Effectors Control Authorities – Individual Devices The conventional effectors were tested over their Control effector deflection sweeps were performed full range of motion in 2-degree increments at AOAs of for each of the 24 devices that composed the trailing 0, 4, 8, and 12 deg. Deflection limits for the elevon, edge shape-change effector array. Angle of attack and aileron, and rudder surfaces are ±20, ±15, and ±14 deg, control deflection increments were necessarily coarse to respectively. Positive deflections are defined as trailing limit the size of the test matrix. Each device was tested edge down for symmetric elevons, right trailing edge up over its full deflection range of –15 to +15 degrees in 5- for ailerons, and trailing edge right for rudders. degree increments at four angles of attack (0, 4, 8, and 12 degrees). Remote control of all effector settings through Control moment vs. surface deflection angle are the dSpace console in the tunnel control room permitted shown in Figure 9 for an AOA of 4 deg. Primary automation of the test procedure, which greatly improved authorities for pitch due to symmetric elevon, roll due to the ability to rapidly cover a large test matrix.
aileron, and yaw due to rudder are shown at the top of the figure. Secondary (adverse and proverse) moment Figure 10 shows the pitch, roll, and yaw authority effects are shown in the plot at the bottom. The plots for effector number six, as numbered from inboard to suggest that the conventional effector suite will provide outboard, on the right wing at an angle of attack of 4 adequate control authority. Pitch and roll moments due to degrees. The positive sense of deflection for all the rudder deflections are not negligible, and will be taken effector array devices is defined as trailing edge up. The into account in the flight control system design. These behavior is fairly linear and typical of that observed for data along with additional measurements that were all the trailing edge devices. Potential flow predictions of collected during the wind tunnel test have been used in a control moments produced by deflection of the dynamic simulation to verify that conventional effector individual devices were also developed, and these were suite will provide adequate control authority for typical over-predicted by roughly a factor of 2.
flight maneuvers. The conventional effectors will be Linear fits to the wind tunnel moment data were used during non-research portions of flight and as a used to generate control authority derivatives for each of backup to the shape-change effector array if needed.
0.015 0.006 Wind Tunnel CMARC 0.01 0.004 0.005 0.002 n C -25 -15 -5 5 15 25 -6 -4 -2 -1 0 1 2 4 6 -0.005 -0.002 -0.01 -0.004 Moment Coefficient Clda -0.015 Cmde Cndr -0.006 -0.02 b (deg) Control Deflection (deg) 0.004 0.008 Wind Tunnel 0.003 0.006 CMARC 0.002 0.004 0.001 0.002 l C -25 -15 -5 5 15 25 -6 -4 -2 -1 0 1 2 4 6 -0.001 -0.002 -0.002 -0.004 Moment Coefficient Cldr -0.003 Cmdr -0.006 Cnda -0.008 -0.004 Control Deflection (deg) b (deg) Figure 8. Comparison of wind tunnel data with PMARC Figure 9. Control moment vs. surface deflection for predictions for yawing moment (top) and rolling moment conventional elevon, aileron and rudder effectors, (bottom) vs. sideslip, AOA= 4 deg. AOA= 4 deg.
American Institute of Aeronautics and Astronautics AIAA 2004-5114 the 24 shape-change effectors. These are presented in Control Authorities – Trailing edge Array Shapes Figure 11, where the effector segments are numbered in Control moments were measured for the effector ascending order from inboard to outboard, with negative array devices deployed collectively to produce trailing numbers corresponding to the left wing array and edge shapes, as shown in Figure 5. The shapes could be positive corresponding to the right wing. Hence, effector applied to each wing individually or together in a sym- segment number –12 designates the outboard-most left metric or anti-symmetric fashion, and with varying scale wing effector, and +12 designates the outboard-most factor. A scale factor of 15 corresponded to full deflec- right wing effector.
tion of the shape, a condition in which one or more of the Deflection of a single effector device clearly individual devices had reached saturation. Figure 12 produces useful control moments, but the result is small shows a plot of effector deflection vs. segment number enough that groups of effectors will be required to for the six trailing edge shapes applied to the right wing generate sufficient moments for typical flight maneuvers. with a scale factor of +15. The shapes were tested using The individual devices were particularly ineffective at scale factors ranging from -15 to +15 in increments of 5.
generating yawing moment, as indicated by Figures 10 Figure 13 shows a plot of control moment vs. deflec- and 11. The low yaw authority of the individual effector tion scale factor for the six trailing edge shapes applied segments raises the question of deploying the array in to the right wing only. Not surprisingly, shape 1, which collective fashion intended to generate drag on one wing, simply sets all devices to a constant deflection, produces and thus yawing moment. Such a configuration was the largest pitch and roll moments. But if an objective is among the six predefined deployment shapes that were to mimic a continuous mold-line effector, then shape 3 evaluated during the next portion of the wind tunnel test.
appears to generate relatively large moments while satis- fying this requirement. Shapes 4 and 6 are capable of 0.0040 generating yaw moment while generating only minimal Cl Cm 0.0030 pitch and roll.
Cn Figures 11 and 13 represent differing approaches to 0.0020 characterizing the authority of the effector array, and 0.0010 their comparison raises important issues regarding 0.0000 methods of control allocation and mixing for effector -20 -10 0 10 20 arrays composed of large numbers of relatively low- -0.0010 authority devices. One issue is whether allocation should -0.0020 be based on individual device authorities, or rather upon Moment Coefficient (Right Wing Segment No.6) authorities of basis functions representing collective -0.0030 deployment configurations. Both approaches have pros -0.0040 and cons. As devices composing the array become Control Deflection (deg) smaller and more numerous, the dimension of the control matrix goes up while individual authority goes down, Figure 10. Control moment vs. surface deflection for increasing the potential for ill-conditioned matrices.
shape-change effector number 6 on the right wing, AOA= 4 deg.
Also, in some cases, the devices will only be effec- tive when deployed collectively in a particular combination, and this effect may be missed by an indi- 2.0E-04 Right Wing Left Wing vidual device-wise characterization. A good example is ) -1 1.5E-04 the generation of yawing moment. When the yawing moment of the crow mix configuration (shape 6) was 1.0E-04 predicted by using superposition of the individual 5.0E-05 linearized device authorities, the result was less than 60% of the measured authority for that configuration.
0.0E+00 Presumably, device interactions were important in this -5.0E-05 configuration, and these effects were not captured by the Cl /deg individual linearized authorities.
-1.0E-04 Cm /deg Control Authority (deg Cn /deg A basis function approach appears to provide a -1.5E-04 means of reducing the high dimensional low authority -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 challenge, but is also likely to lead to difficulty in de- Effector Segment No.
riving full authority from the array when a basis function Figure 11. Linearized control authorities for each shape- is commanded to saturation. Furthermore, how should change device in the trailing edge effector arrays such bases be identified? In the MESA experiment the American Institute of Aeronautics and Astronautics AIAA 2004-5114 0.02 Shape 1 Shape 2 0.015 Shape 1 Shape 3 Shape 4 0.01 , deg Shape 5 Shape 6 -5 d 0.005 -15 0 2 4 6 8 10 12 Shape 2 -0.005 Roll Moment -0.01 , deg -5 d -0.015 -15 -0.02 0 2 4 6 8 10 12 -20 -15 -10 -5 0 5 10 15 20 0.025 Deflection Scale Factor 0.02 Shape 3 0.015 -5 , deg d 0.01 -15 0.005 0 2 4 6 8 10 12 Shape 4 5 -0.005 Pitch Moment -0.01 , deg -5 d -0.015 -15 -0.02 0 2 4 6 8 10 12 -20 -15 -10 -5 0 5 10 15 20 0.003 Deflection Scale Factor 0.0025 Shape 5 , deg 0.002 -5 d 0.0015 -15 0 2 4 6 8 10 12 0.001 0.0005 Yawl Moment Shape 6 , deg -5 d -0.0005 -15 -0.001 0 2 4 6 8 10 12 -20 -15 -10 -5 0 5 10 15 20 Effector Segment No. Deflection Scale Factor Figure 13. Control moment vs. deflection scale factor Figure 12. Effector deflection vs. segment number for for the six trailing edge shapes applied to the right wing, the six trailing edge shapes applied to the right wing with AOA= 4 degrees.
a scale factor of +15.
crow mix configuration was selected for shape 6 as a PRESSURE MEASUREMENT AND CONTROL likely yaw generator based upon conjecture. But perhaps alternating in groups of two might have been even more Variations in the spanwise pressure distribution were effective. measured in response to deflections of the individual trailing edge effectors. The influence of an effector Hence, there is a need for methodologies to provide deflection was greatest at the closest pressure measure- thorough and efficient characterization of high dimen- ment, and diminished as distance to the measurement sional arrays. Whether experimentally or analytically location increased. This trend is clearly visible in the plot evaluated, the test matrix must explore combinations of of spanwise pressure measurements in response to device deflections to identify significant nonlinearity and deflections of +15 and -15 degrees for shape-change interactions, and the combinatorial possibilities increase effector segment number 4 on the right wing, shown in rapidly with the number of elements in the array. If the Figure 14. This plot provides an indication of the degree control effector suite of future flight vehicles is truly to which maximum deflection of a single device is able progressing toward large networks of distributed devices, to influence the spanwise pressure distribution.
issues such as allocation, efficient testing, and charac- Pressure measurements such as those shown in terization of high dimensional effector arrays will become increasingly significant. Potential solutions may Figure 14 were collected for each of the 24 shape-change effectors at settings of -15, -10, -5, 5,10, and 15 degrees arise from a blending of information technology concepts with flight control. Decentralized approaches may be for angles of attack of 0, 4, 8 and 12 degrees. The meas- urements were then used to generate pressure sensitivity envisioned that draw upon principles from collaborative robotics, network theory or cellular automata. matrices for the effector and sensor array using a least- American Institute of Aeronautics and Astronautics AIAA 2004-5114 squares fit to the pressure variation in response to control, mission-adaptive performance enhancement, effector deflection at each sensor location. This process health monitoring, distributed load alleviation, or dis- resulted in a separate 12x12 pressure sensitivity matrix tributed flutter suppression.
for the right and left wings at each angle of attack.
The ability to sense and modify the spanwise pres- The pressure sensitivity matrices tended to be diago- sure distribution acting on the wing would presumably nally dominant since each device influenced its own have application to distributed load alleviation and pressure measurement most strongly, with diminishing mission-adaptive performance enhancement functions by influence on adjacent measurements. A representative providing the capacity to tailor the spanwise lift distribu- sensitivity matrix for the right wing at 4 degrees angle of tion. Such tasks might be assigned a lower priority and attack is shown in Figure 15 as a colormap of the sensi- performed concurrently with the task of generating tivities. The pressure sensitivity matrices were used in moments for flight control purposes. To further examine the formulation of a feedback control system that was this possibility a pressure distribution control system that designed to achieve and regulate a commanded spanwise uses the effector and sensor array was developed. The pressure distribution at each of the 24 sensor locations. system uses a time domain implementation of the least 12,13 mean squares (LMS) algorithm to achieve and regu- Pressure Distribution Control Design late a commanded spanwise pressure distribution consisting of specified conditions at each of the 24 The MESA testbed was developed to explore the use of multifunctional effector and sensor arrays. A pressure measurement locations.
fundamental aspect of the research is to investigate For the controller synthesis, let the (n x 1) vector of control concepts that exploit the ability of these arrays to pressure coefficient variations be given by, simultaneously perform a variety of tasks such as flight C p = Hd (1) 0.15 +15 deg where d is the (n x 1) vector of effector displacements, -15 deg and H is the (n x n) sensitivity matrix relating effector 0.1 displacements to pressure variation. The error vector of differences between the measured and desired pressure 0.05 Cp coefficient vectors is denoted, D e = C p - C p (2) desired measured -0.05 where C p = C p in the case of zero measurement measured error (no external perturbations, no measurement noise).
-0.1 The nominal control objective is to minimize the error in 0 2 4 6 8 10 12 Eq. 2 subject to constraints on the maximum effector Pressure Sensor No.
displacement. This is achieved by minimizing the Figure 14. Pressure variations in response to deflections of objective function, J: effector segment 4 on the right wing, AOA = 4 deg.
T J = E e n e n subject to (3)
( ) ( )
{ }
c ( d ) < 0 , i = 1,…n i th where E {} is the expectation operator, and c is the i i convex constraint on the effector displacement vector, d .
† The control objective function may be rewritten to include the constraints as penalties: n T J = E e n e n + s c d  (4)
( ) ( ) { } ( ) [ ]
i { }
i z where s determines the relative importance of the constraints in the objective function. The constraint penalty term, [ c ( d )] in Eq. 4 is defined by, i z † Ï c d £ 0 D Cp/deg
( )
i c d = max c d , 0 = Ì (5)
( ) [ ] ( ) [ ]
i i z c d
( ) otherwise
i Ó The LMS algorithm is a stochastic gradient descent Figure 15. Colormap of pressure sensitivity matrix for procedure for solving a least squares problem, such as right wing effector and sensor array at 4 degrees AOA.
† American Institute of Aeronautics and Astronautics AIAA 2004-5114 th Eq. 4. At the k time step, new values for the displace- desired spanwise pressure distribution at the trailing edge ments are computed according to, sensor array. The relatively long rise time of the closed loop system shown in Figure 16 represents a trade-off ∂ J d ( k + 1 ) = d ( k ) - m (6) between speed of convergence and measurement noise ∂ d rejection. This trade is controlled by the adaptation rate where μ determines the rate of adaptation. The LMS parameter, m . For this experiment, the parameter was algorithm uses an instantaneous estimate of the gradient.
assigned a value of 1.0, resulting in a rise time of This estimate is given by: approximately 5 seconds, which is sufficient for a flap- † like cruise performance optimization function. Future Ê ˆ ∂ J ∂ c n T i experiments will vary the adaptation parameter to = 2 - H e + s c d (7)
 ( ) Á ˜
[ ]
i i z ∂ d ∂ d Ë ¯ investigate the potential for faster convergence.
The results suggest the potential to employ a similar th Let the i constraint be defined such that the absolute approach to command larger scale shape changes of a th value of the deflection of the i effector must be less continuously deformable aircraft structure, such as envi- † than a maximum deflection, d . Thus, max sioned by the Aircraft Morphing Program, to generate a desired global pressure distribution for mission-adaptive c = |d | - d (8) i i max performance optimization or distributed load alleviation purposes. Yet to be addressed is the prioritization and Therefore, blending of these functions with the multi-axis moment Ï sign d for i = j
∂ c ( )
generating functions required for stabilization and i i = Ì (9) maneuver control if the same multifunctional array is ∂ d 0 otherwise Ó j used for both purposes.
th With the preceding definitions, the update for the i effector displacement is, CONCLUDING REMARKS † This report has described a project that seeks to
d ( k + 1 ) = d ( k ) - m - H (:, i ¢ ) e ( k ) + s [ c ] sign ( d ) [ ] (10)
i i i z i investigate controls challenges associated with novel th where H(:,i)’ denotes the transponse of the i column of effector and sensor concepts within NASA’s Aircraft H . After initial simulations of the algorithm a further Morphing Program. In particular, the potential exists to constraint was added that enforced smoothness of the † shift the composition of an aircraft’s control effector effector deployment distribution by penalizing large suite from a small number of high authority, specialized displacements relative to adjacent effectors. The array devices (rudder, aileron, elevator, flaps), toward arrays was thus made to approximate a seamless continuously composed of larger numbers of smaller, less specialized, deformable shape-change trailing edge effector. The distributed effector and sensor devices able to update expression was implemented in C-code for real- simultaneously perform a variety of control functions time control of the model hardware during the wind using feedback from disparate data sources. To tunnel test. The shape change deflection angle limit, d max investigate this concept, a remotely piloted flight vehicle was set to 15 degrees. The parameters m and s were has been equipped with an array of 24 trailing edge assigned values of 1.0 and 0.1, respectively.
shape-change effectors and associated pressure meas- urements to create a representative testbed that embodies Pressure Distribution Control Test Results the fundamental controls challenges.
The controller was evaluated during the closed-loop 0.15 Commanded portion of the wind tunnel test. A series of pressure 0.1 distribution commands was created based on known 0.05 achievable distributions that had been measured during the previous portion of the test. Figure 16 shows an D C p example time history of the commanded and measured -0.05 p pressure coefficients at a single pressure tap as the C controller attempted to track a series of step commands. -0.1 Figure 17 shows a time history colormap of commanded -0.15 Measured pressure coefficients (top) and measured pressure -0.2 coefficients (bottom) at all 24 sensor locations from the run shown in Figure 16. Figure 18 shows a 3-d plot of -0.25 0 10 20 30 40 50 60 Time (sec) control effector deflections from the same time history.
Time, sec Figure 16. Time history of commanded and measured The LMS controller is clearly effective in com- manding the shape changes required to achieve the pressures at a single sensor location, AOA= 4 degrees.
American Institute of Aeronautics and Astronautics AIAA 2004-5114 approach offers promise for application to larger scale continuously deformable shape-change configurations D C p such as those envisioned in the Morphing Program.
Sensor Challenges associated with control characterization and No.
allocation for high dimensional effector arrays were noted and have yet to be addressed. Prioritization and blending of flight control and pres sure regulation functions are also topics requiring additional research.
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American Institute of Aeronautics and Astronautics