Document
Real-Time Adaptive Control Allocation applied to a High Performance Aircraft * † † John B. Davidson , Frederick J. Lallman , and W. Thomas Bundick NASA Langley Research Center Hampton, VA 23681 Abstract In particular, reconfigurable control approaches This paper presents the development and seek to take advantage of this control redundancy to application of one approach to the control of aircraft mitigate the deleterious effects of control effector with large numbers of control effectors. This failure or battle damage [Buffington 1998, Brinker approach, referred to as real-time adaptive control 1999, Tallant 1999]. A key element in these allocation, combines a nonlinear method for control approaches is reconfigurable control allocation.
allocation with actuator failure detection and isolation.
The reconfigurable control allocator [Lallman 1985, The control allocator maps moment (or angular Durham 1992, Buffington 1997, Enns 1998] maps acceleration) commands into physical control effector moment (or angular acceleration) commands into commands as functions of individual control physical control effector commands as a function of effectiveness and availability. The actuator failure individual control effectiveness and availability. This detection and isolation algorithm is a model-based paper presents the development of an integrated approach that uses models of the actuators to predict reconfigurable control allocation method which actuator behavior and an adaptive decision threshold combines a nonlinear method for control allocation to achieve acceptable false alarm/missed detection with actuator failure detection and isolation (FDI) rates. This integrated approach provides control (figure 2). This integrated approach provides control reconfiguration when an aircraft is subjected to reconfiguration when an aircraft is subjected to actuator actuator failure, thereby improving maneuverability failure, thereby improving maneuverability and and survivability of the degraded aircraft. This method survivability of the degraded aircraft. Desktop and real- is demonstrated on a next generation military aircraft time piloted simulation are used to demonstrate the (Lockheed-Martin Innovative Control Effector) performance of this integrated adaptive control simulation that has been modified to include a novel allocation approach.
nonlinear fluid flow control control effector based on passive porosity. Desktop and real-time piloted Real-Time Adaptive Control Allocation simulation results demonstrate the performance of this The adaptive control allocation is an integrated integrated adaptive control allocation approach.
approach that combines two main elements: a nonlinear Introduction control allocation approach and actuator failure detection and isolation. These elements are discussed Future aircraft are being proposed with many more in more detail in the following sections.
control effectors than the traditional elevator, aileron, and rudder. Innovative control effectors under study Control Allocation range from thrust vectoring to all-moving wing tips In general, the forces and moments generated by the and actuated forebody surfaces to more exotic control effectors are a function of vehicle flight effectors such as shape-change materials and fluid- condition and effector commands. In the case where, at flow devices (figure 1). For example, hundreds or even a given flight condition, the control effectiveness is thousands of micro fluid-flow devices could be relatively linear with effector command and there is distributed in arrays across the upper and lower minimal control coupling, the system can be considered surface of a wing to allow direct control of the wing’s as a linear control allocation problem. The linear boundary layer. Optimal use of this large number of control allocation problem can be stated as follows.
effectors will be challenging, but the potential control Given the system power and redundancy offers the flight controls m B = δ (1) d designer freedom to maximize mission performance where m = a q x1 desired moment (or angular and enhance survivability.
d acceleration) vector, B = the linear control effectiveness * matrix, and δ = a m x1 control vector; determine δ to Research Engineer † Senior Research Engineer yield a desired m . The dimension of δ is assumed to d No copyright is asserted in the United States under Title 17, be greater than the dimension of m and δ is d U.S. Code. The U.S. Government has a royalty-free license constrained by δ ≤ δ ≤ δ .
min max to exercise all rights under the copyright claimed herein for Governmental purposes.
TH 2001 5 SIAM Conference on Control & Its Applications Weighted Pseudo-Inverse. One solution to the include additional terms to capture first-order control linear allocation problem is given by a weighted interaction effects and control effectiveness as a pseudo-inverse. The weighted pseudo-inverse is a function of command magnitude. The extended form is computationally efficient, closed-form solution that given by accommodates redundant and/or zero effective controls and allows removing controls from the B B B m = + δ + δ δ δ (4)
2 x j i d å
solution by zeroing the weight associated with that ij 1: j m = control. The weighted pseudo-inverse solution is 1: i m = obtained by minimizing where δ = absolute value of the elements of control T T ( ) J W m B = δ δ + λ − δ (2) d 2 vector δ and δ = absolute value of jth control.
j where W is a diagonal positive definite weighting The first term in equation (4) is the linear control effectiveness matrix. The second term models control matrix. Taking partial derivatives of J with respect to moment due to deflection magnitude. The third term δ and λ , setting these equal to zero and solving for models the reduction (or increase) in the control δ yields effectiveness of the ith control due to the magnitude of 1 T T − + ( ) WB BWB m B m δ = = (3) deflection of the jth control. Equation (4) can be written d d in matrix form as A common approach is to choose the weighting T matrix W to be a diagonal matrix of control position m B B I B = δ + δ + ⊗ δ δ (5)
( )
2 q x d limits squared. This results in a solution that emphasizes highly effective controls while minimizing where ⊗ denotes the kronecker matrix product and deflections of controls with reduced effectiveness.
δ = absolute value of the elements of control vector δ .
Two possible approaches used when controls exceed a constraint are: 1) the individual controls can be clipped The solution is obtained by minimizing at the constraint or 2) the entire control vector can be T scaled such that no constraints are violated. The J W = δ δ (6) scaling approach results in a solution that preserves the direction (i.e. the balance between pitch, roll, and yaw subject to the constraint given by equation (5), δ is moments) of the desired moment. In general, a constrained by δ ≤ δ ≤ δ and W is a diagonal min max weighted pseudo-inverse solution does not result in a positive definite weighting matrix. Numerical solution that achieves the maximum attainable optimization methods are being used to determine a moment while preserving the direction of the desired control vector δ that minimizes the cost function J .
moment. This limitation is overcome by employing Current solution methods do not reliably run in real- the weighted pseudo-inverse in a cascaded (multi- time; therefore, the extended approach was not used in pass) approach [Bordignon 1995]. This results in a the piloted simulation evaluation.
non-linear solution.
Extended Control Allocation. A limitation of the control-weighted pseudo-inverse method is that it is Actuator Failure Detection and Isolation based on a model of control effectiveness which Failure Detection and Isolation (FDI) in dynamic assumes non-interacting controls with a relatively systems has been the subject of considerable work for linear control effectiveness versus control command many years [Frank 1990, Patton 1994]. While some (deflection) relationship. Future configurations being approaches employ neural networks, most of the proposed with large numbers of distributed control methods developed for FDI involve the use of a model effectors have the potential for increases in control of the system for which failures are being diagnosed, power, but may exhibit significant control interactions and such is the case with the present approach. In the and nonlinearities. Research is currently being current application, FDI is used to detect actuator conducted to develop control allocation methods failures.
which can be applied to these future configurations.
For this effort it was assumed that the only The goal of this effort is to develop methods that measurements available from the actuators are the include key control interaction effects and can be command input and the actuator output, or position. At solved in real-time on flight control computers of the first thought, it might seem that a failure of the actuator future.
could simply be detected by comparing the measured The approach taken here in is to extend the linear position with the command, and, if these are different, a model of control effectiveness given by equation (1) to TH 2001 5 SIAM Conference on Control & Its Applications failure has occurred. However, because of the This increase in residual was caused by a model dynamic response of the actuator, the output will differ inaccuracy in the actuator rate limit.
from the command during most transients, and thus The actuator model used in the FDI system is a false failures will be declared unless the threshold for discrete second-order model with position and rate failure declaration is set unacceptably high. This limits. The model output is subtracted from the problem is overcome in a model-based FDI approach measured actuator position to form the residual. To by using a model of the actuator in the FDI system to simulate model errors, values of the actuator parameters predict actuator behavior as in figure 3, and by were varied to determine their effects on the residuals.
comparing the model output with the measured It was found that amplitude of the residuals due to actuator position. If the model is perfect, the no- model error (no failures) was determined primarily by failure residual will be zero. Thus, a failure is errors in the position and rate limit models with errors declared when the residual is not zero. Nominal in the natural frequency and damping being secondary.
measurement errors are accommodated by using a To obtain a quantitative measure of the effect of input non-zero decision threshold for comparison with the amplitude on the amplitude of the no-failure residuals, a residual. However, if model errors are significant, Monte Carlo analysis was conducted using a stand- + residuals can be quite different from zero. In fact, they alone MATLAB/Simulink -based simulation of the can be so large that a constant threshold must be set so actuator and the FDI system (figure 7). Actuator high to minimize false alarms that the missed detection position and rate limits and measurement errors were rate is unacceptable. In this case, acceptable false randomly varied run-to-run as were the amplitudes of alarm/missed detection rates can often be achieved by the command inputs. The range of variation of the rate use of an adaptive decision threshold. If the actuator limit was chosen based on the rate limit versus hinge- and its model are linear, the residual caused by model moment model of the actuators in a current fighter error is a linear function of the input amplitude, and aircraft. Analysis of these results were used to the adaptive threshold can vary linearly with the determine the parameter values of the current adaptive- amplitude of the input. For actuators which are threshold actuator FDI design.
nonlinear due to limiting, generating an adaptive Implementation threshold as a function of a composite signal, which at each sample is the maximum of the real-time and The integrated Control Allocator is organized into delayed versions of the command provides much five main elements (see Figure 8): Command improved false alarm/missed detection performance.
Interconnect, Effector Aero Model, Control Mixer, In the current work the adaptive threshold was Control Distributor, and the Actuator FDI. These implemented in the following form elements are discussed in the following.
The Command Interconnect maps stability-axis ì max , a b + δ δ
( )
cmd dly rotational acceleration commands into desired body- ï axis moments and provides inertial coupling & & ï max , cu d + δ δ − δ ≤ δ
( ) ( )
lim cmd dly cmd ï compensation. The Effector Aero Model contains th = í linearized control effectiveness coefficients as a a b + δ ï lim function of flight condition. The control mixer contains ï & & max , cu d + δ δ − δ > δ
( ) ( ) the control allocation algorithm. Two algorithms are
lim cmd dly cmd ï î currently under study – a position limit weighted pseudo-inverse and the extended control allocation.
where u(•)=unit step function.
The Control Distributor maps control commands to the An example of the adaptive threshold behavior can individual control effectors.
be seen in figures 4 through 6. These data were Left and right one-sided controls are modeled as a generated in the stand-alone desktop simulation of an single control in the Aero Model and the Mixer and are actuator. Figure 4 shows the actuator position, and the mapped into left and right surface commands in the amount of surface activity that is typical of a Control Distributor. During nominal operation, the maneuvering high performance aircraft. Note that the allocator distributes the controls based upon the internal actuator failed at its current position at about 35.8 model of the individual control effectiveness as a seconds. Figure 5 is a plot of the adaptive threshold function of flight condition.
and the absolute value of the residual for this case and The control allocator accepts inputs from the shows the increased residual after the failure. Figure 6 Actuator Failure Detection element, which continually is a time-expanded version of figure 5 showing that monitors the health of the control surface actuators.
the no-failure residual near 15 seconds would have When informed by the FDI that an actuator failure has produced a false alarm had not the threshold adapted.
+ The Mathworks, Inc.
TH 2001 5 SIAM Conference on Control & Its Applications occurred, the allocator removes the failed control from The control law is designed to give conventional the set of available controls and redistributes the responses to three-axis pilot controls. Pitch rate, roll remaining controls to accommodate the failure. rate and sideslip angle commands are scheduled with the available control power in each axis.
Application to ICE Aircraft The longitudinal control law is a proportional-plus- This integrated allocation method has been integral arrangement with feed-forward that produces a implemented in a modified version of the Lockheed- pitch acceleration command for the control allocator.
Martin Innovative Control Effector (LM-ICE) Longitudinal control stick deflections command pitch simulation [Dorsett 1996]. The LM-ICE aircraft is a rate at low speed. The control law transitions to normal 65 degree swept delta-wing, tailless, single-engine, acceleration command at high speed. Feedback gains supersonic fighter. This configuration incorporates a were chosen following the guidance of MIL-STD- large number of redundant conventional and 1797A for short-period frequency and damping ratio.
innovative control effectors including elevons, pitch Attitude angles are used to compensate for gravity.
flaps, pitch and yaw thrust vectoring, all-moving wing Roll rate and the angle of sideslip are used to tips (AMT’s), spoiler-slot deflectors (SSD’s), and compensate for pitch rate sensor offsets that occur when outboard leading-edge flaps (OLEF’s) (figure 9).
the airplane rolls with sideslip.
This simulation has been modified to include a Lateral control stick deflections command stability- new control effector based on passive porosity [Hunter axis roll rate by means of a single feedback gain on roll 2001]. Passive Porosity (PassPort), as used in this rate error. Rudder pedal deflections command the angle study, is a control device that changes aerodynamic of sideslip by means of a proportional-plus-derivative forces on a vehicle wing by equalizing the pressure controller. Sideslip error feedback provides static gradient on the exterior surface. Actuation is directional stability. Stability-axis yaw rate combined accomplished by opening and closing a minimum with attitude angles and lateral acceleration to form a depth cavity (plenum) (figure 10a). The plenum is synthesized rate-of-change of sideslip that provides yaw designed with a porous surface conforming to the damping. Phase margins in both the longitudinal and wing shape. For this study, eight separate devices lateral-directional channels are enhanced by lead filters.
were installed on each wing (figure 10b). The Initial control system gains were obtained using controller actuates each device discretely to an “on” or frequency-domain design techniques on a set of “off ” position. No control interaction data is currently continuous models. The models range from Mach 0.225 available for the passive porosity, therefore it was to Mach 0.9 with altitudes ranging from sea level to assumed that the use of the passive porosity had no 40,000 feet. The control law was discretized and tested effect on the moments produced by the other controls.
for large-amplitude motions on a nonlinear desktop An example of one of the control interaction simulation. Additional refinements were made in effects exhibited by the ICE aircraft is shown in figure response to piloted simulation results.
11. Due to its location, deflection of the spoiler-slot The Effector Aero Model for the allocator contains deflector can significantly effect the forces and pitch, roll, and yaw moment effectiveness coefficients moments produced by the elevons and pitch flap, as for each control as a function of flight condition. The illustrated in the figure. This figure shows coefficients were calculated for controls at full positive aerodynamic pitch (11a) and roll (11b) moment and negative deflections using piece-wise linear fits of coefficients for the right elevon and spoiler-slot the ice database.
deflector as a function of angle-of-attack at a low An example is presented to demonstrate the speed flight condition. The plots show elevon performance of the extended allocation approach at a effectiveness for +/-30 degree elevon deflection with flight condition with significant control interactions.
the spoiler-slot deflector at 0 and 45 degrees. The The control effectiveness of the ICE aircraft at a low spoiler-slot deflector pitch and roll effectiveness is speed flight condition can be modeled using the also plotted for comparison with the elevon. At low extended approach by angles-of-attack, the elevon pitch and roll moments are m B B B = δ + δ + δ δ (7) significantly reduced (by approximately 60%) by 2 x ssd ssd deflection of the spoiler-slot deflector.
where All actuators are simulated as second-order T systems with rate and position limits except the δ = δ δ δ δ δ δ δ δ é ù le re amt ptv ytv pp pf ssd ë û passive porosity actuator. Dynamic data is currently not available for passive porosity. The actuator was and le = left elevon, re = right elevon, amt = all-moving chosen to be modeled by a position and rate-limited wing tip, ptv = pitch thrust vectoring, ytv = yaw thrust first-order system. Actuator dynamics and limits are given in Table 1.
TH 2001 5 SIAM Conference on Control & Its Applications vectoring, pp = passive porosity, pf = pitch flap, and gunsight tracking task using a pre-recorded ssd = spoiler-slot deflector. maneuvering target projected on the simulator dome.
The first term in equation (7) is the linear control The attack aircraft starts at an initial condition of effectiveness matrix. The second term models pitch Mach=0.6, altitude=11700 feet, in straight and level moment due to deflection of the all-moving wing tip flight. The target aircraft starts at the same initial and spoiler-slot deflector. The third term models the condition and 500 feet ahead of the attack aircraft. The reduction in the control effectiveness of the left target performs a series of roll reversals with conditions elevon, right elevon, and pitch flap due to deflection of varying between 300-500 knots-equivalent-airspeed, the spoiler-slot deflector. The control effectiveness 9500-12200 feet in altitude, and 1-7 g’s. Pilot tracking and coupling matrices are given in Table 2.
performance was measured by target cone angle ε , For comparison, the desired control-moment vector defined as the angle between the attacking aircraft’s x- m was allocated among the control effectors using a body axis and a vector from the attacker to the target.
d cascaded pseudo-inverse approach and using the (figure 15) [Foster 1998]. Pilot tracking time histories extended linear approach, where the desired moment are given in figure 16 for a left elevon failure at 15 sec vector (pitch moment, roll moment, yaw moment) is with FDI On (16a) and FDI Off (16b). Both sets of time histories are plotted against a baseline tracking case T 0 50000 100000 m =
[ ]
d with no failures. As can be seen in figure 16a, the FDI On with failure time histories compare very favorably The weighting matrix W was set to identity. The to the baseline both in terms of stick activity and target extended linear solution was determined using the cone angle. In this case the allocator, advised of the MATLAB constrained optimization routine failure by the FDI, compensates by redistributing the (CONSTR). The control deflections resulting from commands to the remaining functioning effectors. Pilot the two approaches are shown in figure 12. The comments for this case were: “slightly more oscillatory control moments achieved by applying these control (than baseline)”, “minor increase in workload”, “good deflection solutions to the nonlinear aero model are tracking”. Figure 16b shows FDI Off with failure time given in figure 13. As can be seen, by including histories compared to the baseline. In this case the control interaction effects the extended linear solution allocator is ignorant of the failure. Time histories show results in a better match to the desired moment.
more stick activity and significantly larger target cone angle. Pilot comments for this case were: “major increase in workload (after failure)”, “unable to track Desktop and Piloted Simulation Evaluation target”. The simulation results demonstrate that the Desktop and piloted simulations are currently integrated control allocator is able to reconfigure after being conducted to evaluate and refine the approach.
actuator failures to allow the tracking task to be The desktop simulation is implemented in completed.
+ MATLAB/Simulink . Piloted simulations are being conducted in NASA Langley’s Differential Maneuvering Simulator (DMS). The DMS is a fixed- Concluding Remarks base generic fighter simulator having wide-angle This paper has presented the development of a visual displays and is capable of simulating two real-time adaptive control allocation approach. The airplanes as they maneuver relative to each other.
integrated approach combines a nonlinear approach to For the piloted simulation evaluations, a control control allocation, with actuator failure detection and weighted pseudo inverse allocation approach was used isolation. This integrated approach provides control with the actuator FDI. The SSD and OLEF’s were not reconfiguration when subjected to actuator failure, used.
thereby improving the degraded aircraft’s The response of the actuator FDI system to an maneuverability and survivability. This paper also elevon failure at 10 seconds in one of the piloted addressed system implementation issues. The method simulation runs is plotted in figure 14. The FDI system has been demonstrated on a Lockheed-Martin detected the failure in 0.0625 seconds, and the control Innovative Control Effector simulation that has been allocator removed the surface from use on the next modified to include actuated passive porosity. Desktop computational cycle. This was typical of the FDI and real-time piloted simulation results demonstrate the performance in the piloted simulations.
performance of this integrated reconfigurable control Pilot-in-the-loop tracking tasks were conducted to allocation approach.
assess the performance of the integrated control In the next phase of this work a real-time parameter allocation approach. Test subjects performed a identification module, currently in development, will be integrated into the system. Also in development are a parity-space-based FDI module for detecting and + The Mathworks, Inc.
TH 2001 5 SIAM Conference on Control & Its Applications isolating failures in redundant flight control sensors, a Patton, R. J.: Robust Model-based Fault Diagnosis: The cascaded pseudo-inverse implementation of State of the Art. IFAC/INACS Symp. on Fault frequency-apportioned control allocation, and Detection, Supervision, and Safety for Technical incorporation of additional unconventional control Processes -SAFEPROCESS '94 , 1994.
effectors, such as fluidic thrust vectoring and synthetic Tallant, G.S.; Niestroy, M.A.; Eberhardt, R.L.; jets. Additional research is also required to develop Monaco, J.F.; and Ward, D.G.: Reconfigurable Systems improved modeling of control effector interactions and for Tailless Fighter Aircraft – Restore. AFRL-VA-WP- reliable and efficient solution methods to enable non- TR-1999-3078, 1999.
linear real-time control allocation.
Wood R. M. and Bauer S.X.: Advanced Aerodynamic References Control Effectors. SAE 1999-01-5619, 1999.
Aeronautical Systems Division, Air Force Systems Command, “Military Specification - Flying Qualities of Piloted Vehicles,” MIL-STD-1797A, January 1990.
Bordignon, K. and Durham, W.: Closed-Form Solutions to Constrained Control Allocation Problem.
J. of Guidance Control and Dynamics . Vol.18, No.5, 1995.
Brinker, J.S. and Wise, K.A.: Reconfigurable Systems for a Tailless Fighter Aircraft - Restore. AFRL-VA- WP-TR-1999-3067, 1999.
Buffington, J.: Tailless Aircraft Control Allocation.
AIAA-97-3605.
Buffington, J.; Chandler, P.; and Pachter, M.: Integration of On-line System Identification and Optimization-based Control Allocation. AIAA-98- 4487.
Dorsett, K. and Mehl, D.: Innovative Control Effectors (ICE). WL-TR-96-3043, January 1996.
Durham, W.: Constrained Control Allocation. AIAA- 92-4550.
Enns, D.: Control Allocation Approaches. AIAA-98- 4109.
Frank, P.M.: Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge-based Redundance - A Survey and Some New Results. Automatica , vol. 26, no. 3, 1990, pp. 459-474.
Foster J.V.; Ross, H.M.; Brown, P.W.; Rivers, R.A.; et al.: Piloted Simulation Study of High-Angle-of- Attack Roll-Maneuvering Criteria for Fighter Airplanes. NASA TP-1998-208727.
Graham, A., Kronecker Products and Matrix Calculus: with Application , John Wiley and Sons, New York, 1981.
Hunter, C.A.; Viken, S.A.; Wood, R.M.; and Bauer, S.X.S.: Advanced Aerodynamic Design of Passive Porosity Control effectors. AIAA 2001-0249.
Lallman, F.J.: Relative Control Effectiveness Technique with Application to Airplane Control Coordination. NASA TP-2416, 1985.
TH 2001 5 SIAM Conference on Control & Its Applications Real-Time Adaptive Control Allocation FDI Actuator Failure Measurements Detection / Isolation Pilot δ Nonlinear a cmd cmd Control Inputs Control Law Allocation ICE Feedback Measurements Figure 1. Future Aircraft with Distributed Array of Micro Figure 2. Real-Time Adaptive Control Fluid-Flow Control Effectors. Allocation.
Residual FDI Flag Command Actuator Compare +_ Threshold Model Generator Actuator position, deg.
-20 0 10 20 30 40 50 Time, sec.
Figure 3. Actuator Failure Detection and Isolation. Figure 4. Failed Actuator Position.
20 20 Threshold Threshold Residual Residual 10 10 Amplitude Amplitude 0 0 0 10 20 30 40 50 10 20 Time, sec. Time, sec.
Figure 5. FDI Threshold and Residual for Figure 6. Expanded View of Threshold Failed Actuator. and Residual.
TH 2001 5 SIAM Conference on Control & Its Applications Desired Body-Axis Stability-Axis Moments Inter- Acceleration thresh = 1 + 0.11*abs(u) → thresh = 1 + 0.11*abs(u) connect Commands B d cmd Aero Control Control matrix Flight Condition Model Mixer Distributor Max( | residual | ) Failure 2 Effector Flags Actuator Positions FDI 0 10 20 30 40 50 60 Max( | cmd amplitude | ) Figure 7. Monte Carlo Analysis for Adaptive- Figure 8. Integrated Adaptive Control Threshold FDI Design. Allocation Implementation.
Elevon AMT SSD • Advanced tailless, delta wing configuration Passive • Low radar signature, high agility Pitch Porosity Flap • Aero data for 0.3<M<2.16, -4.0< α <90.0, -30.0< β <30.0 • Simulation includes increments for steady rotations, Pitch & controls, control interactions, hinge moments Yaw TV • Innovative Control Effectors (ICE) Pitch and yaw Thrust-Vectoring (TV), elevons, pitch flaps, all-moving wing tips (AMT’s), spoiler-slot deflectors (SSD’s), differential leading edge flaps (DLEF’s) [Dorsett 1996] • Nominal configuration modified to include actively controlled passive porosity effectors Figure 9. Modified Lockheed-Martin Innovative Control Effector (ICE) Configuration.
(Aircraft Figure from Dorsett 1996.)
Boundary Layer Porous Outer Holes Skin δ δ δ δ v e p D < δ L t > 2D t h Plenum h > 2D 8 D Region p Solid Inner Surface Figure 10a. Schematic of Passive Porosity Effector. Figure 10b. Passive Porosity on ICE.
(Figure from Wood 1999.)
TH 2001 5 SIAM Conference on Control & Its Applications e l e v = + 3 0 , s s d = 0 elev=+30,ssd=0 e l e v = - 3 0 , s s d = 0 elev=+30,ssd=45 e l e v = - 3 0 , s s d = 4 5 elev=-30,ssd=0 e l e v = + 3 0 , s s d = 4 5 elev=-30,ssd=45 e l e v = 0 , s s d = 4 5 elev=0,ssd=45 roll moment coefficient pitch moment coefficient 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 angle of attack (deg) angle of attack (deg) Figure 11a. Pitch Moment Coefficient – Elevon and Figure 11b. Roll Moment Coefficient – Elevon and Spoiler-Slot Deflector. Spoiler-Slot Deflector.
Table 1. Effector Dynamics and Limits.
Effector Dynamics Position Limit Rate Limit (freq (r/s), damping) (deg) (deg/sec) Elevon (63.246 , 1.107) -30 / +30 150 AMT (63.246 , 1.107) 0 / 60 150 Pitch TV (39.189 , 1.001) -15 / +15 60 Yaw TV (39.142 , 1.001) -15 / +15 60 Passive Pososity* 80.0 0 / 8 40 Pitch Flap (63.246 , 1.107) -30 / +30 50 * First order model Table 2. Control Effectiveness and Coupling Matrices.
3368.4 3368.4 0 1089.8 0 0 2698.6 0 − − − − é ù ê ú 2268.1 2268.1 1531.9 0 0 6395.1 0 1929.7 B = − ê ú 95.7 95.7 443.6 0 1089.8 1162.7 0 1516.8 − − − ê ú ë û 0 0 1020.0 0 0 0 0 1548.3 é ù ê ú 0 0 0 0 0 0 0 0 B = ê ú 0 0 0 0 0 0 0 0 ê ú ë û 74.09 74.09 0 0 0 0 2.8 0 − é ù ê ú 49.8 49.8 0 0 0 0 0 0 B = x ssd ê ú 0 0 0 0 0 0 0.9 0 − ê ú ë û TH 2001 5 SIAM Conference on Control & Its Applications Cascaded PSI 40 Extended Lin Deflection (degs) -20 -40 lel rel amt ptv ytv pp pf ssd Figure 12. Control Deflections – Cascaded Pseudo-Inverse and Extended Linear Approaches.
x 10 Desired Achieved - Cascaded PSI Achieved - Extended Lin Moment ft-lb -2 Pitch Roll Yaw Figure 13. Desired and Achieved Control Moments – Cascaded Pseudo-Inverse and Extended Linear Approaches.
Command Position FDI Flag ε x Target 0 Amplitude Aircraft -5 Attack 9 10 11 Aircraft Time, sec.
Figure 14. Elevon Failure Detection in Figure 15. Target cone angle, ε .
Piloted Simulation.
(Figure from Foster 1998.)
TH 2001 5 SIAM Conference on Control & Its Applications FDI On – LE Failure No Failure Figure 16a -50 Theta, deg 0 5 10 15 20 25 30 35 40 45 50 -100 Phi, deg 0 5 10 15 20 25 30 35 40 45 50 Pitch Stk, in -5 0 5 10 15 20 25 30 35 40 45 50 Roll Stk, in -2 0 5 10 15 20 25 30 35 40 45 50 5 Cone Ang, deg 0 5 10 15 20 25 30 35 40 45 50 Time, sec FDI Off – LE Failure No Failure Figure 16b -50 Theta, deg 0 5 10 15 20 25 30 35 40 45 50 -100 Phi, deg 0 5 10 15 20 25 30 35 40 45 50 Pitch Stk, in -5 0 5 10 15 20 25 30 35 40 45 50 Roll -2 Stk, in 0 5 10 15 20 25 30 35 40 45 50 5 Cone Ang, deg 0 5 10 15 20 25 30 35 40 45 50 Time, sec Figure 16. Piloted Target Tracking Time Responses – Left Elevon Failure at 15 sec, FDI On (16a) and FDI Off (16b).
TH 2001 5 SIAM Conference on Control & Its Applications