Adaptive failure compensation for aircraft tracking control using engine differential based model
Summary (2 min read)
Introduction
- Actuator failures, adaptive compensation, aircraft flight control, engine differentials, tracking, also known as Keywords.
- Effective compensation of control component failures is crucial for aircraft flight safety.
- In [2], several multivariable adaptive control algorithms for flight control reconfiguration were presented with a failure characterized by a locked left horizontal tail surface.
- The problem was formulated as a nonlinear disturbance rejection problem in the presence of actuator failures and simulation results using an F-16 aircraft model were discussed.
- For the design of such control schemes, an aircraft model with independently adjustable engine thrusts is necessary.
II. ENGINE DIFFERENTIAL BASED MODEL
- As described in [8], a nonlinear aircraft dynamic model in body-axis coordinate system which incorporates engine differentials can be described by the force equations m(u̇+ qw − rv) = u, v and w are the bodyaxis components of the velocity of the center of mass.
- P, q and r are the body-axis components of the angular velocity of the aircraft.
- X , Y and Z are the body-axis aerodynamic forces about the center of mass.
- (II.13) represent the effect of engine thrust differentials, that is, if the left and right engine thrusts are equal, these matrices are zero.
- This engine differential based model in which the two engine thrusts and the ailerons are taken into account separately captures the essential dynamics of the aircraft in the engine differential mode, and is capable of coping with some actuator failures such as rudder failures or engine failure, which cannot be achieved without using engine differentials.
A. Problem Formulation
- An example of such actuator failures is when an aircraft control surface (such as the rudder or an aileron) is stuck at some unknown fixed position at an unknown time instant.
- The control objective is to design an adaptive state feedback control signal to be applied to the actuators in u, to ensure closed-loop signal boundedness, and asymptotic tracking: limt→∞(x(t)−xd(t)) = 0, where xd(t) is a desired state trajectory, in the presence of unknown actuator failures.
B. Adaptive Compensator Designs
- The failures are assumed to occur instantaneously, i.e., σi are piecewise constant functions of time.
- For asymptotic tracking, the authors first present a desired nominal design for the system (III.1) without any actuator failures.
- Assumption 3.1 also requires the knowledge of A and B. (This condition basically implies that the nominal LQ regulator used for generating the desired trajectory is designed to be robust to parameter uncertainties).
IV. APPLICATION TO FLIGHT CONTROL
- The authors demonstrate application of the adaptive failure compensation technique to a transport aircraft by presenting some simulation results for trajectory tracking in the presence of unknown rudder and aileron failures.
- The authors shall first describe the aircraft model used in simulation, and then present the simulation results.
A. Aircraft Model for Simulation Study
- For their simulation study, the authors use a transport aircraft model.
- The non-zero terms in A(3) and B(3) represent the engine thrust differential effect.
- The authors consider two types of constant actuator failures: rudder failure and aileron failure.
- It represents the rudder stuck in its position at instant tf , and cannot be moved.
B. Simulation Results
- The authors present the simulation results for the asymptotic tracking of xd(t) by x(t) to demonstrate the performance of the system with the adaptive failure compensation scheme described in Section 3.2.
- The initial value of the state vector is zero, i.e., the airplane is in steady wings-level flight.
- For their simulation study, the authors examine two cases: (I) system responses with adaptive failure compensation with failure (IV.2) and (II) system responses with adaptive failure compensation with aileron failure (IV.3).
- These design parameters were chosen by trial and error.
- This objective cannot be achieved with a fixed controller.
V. CONCLUDING REMARKS
- A dynamic model of aircraft with independently adjustable engine throttles and ailerons was considered for failure compensation in the presence of rudder or aileron failure.
- This model captures the key features of aircraft flight dynamics when in the engine differential mode and facilitates the development of an adaptive failure compensation approach to handle actuator failures using functioning actuators that can be of types different from the failed actuators.
- First, robustness of the adaptive scheme to model errors, and relaxation of the requirement of knowledge of the system matrices, need to be investigated.
- In addition, the effects of actuator nonlinearities including output and rate saturation, as well as actuator dynamics, need to be addressed.
ACKNOWLEDGMENTS
- This research was partially supported by NASA Langley Research Center under grant NCC-1-02006.
- The authors would like to thank the reviewers for their helpful comments.
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Cites background from "Adaptive failure compensation for a..."
...Current State of the Art: It is not possible to mention the many on-going efforts by industry and government projects to develop adaptive flight control systems.[10, 13, 15, 16, 35, 50-53] Although most of the industry development programs are proprietary, the Air Force VVIACS (Verification and Validation of Intelligent and Adaptive Control Systems)[54] and NASA IRAC (Intelligent Resilient Adaptive Control)[55] efforts represent multi-year programs with industry partners have been initiated to define methodologies and test procedures for adaptive flight control systems....
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References
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Additional excerpts
...In [2], several multivariable adaptive control algorithms for flight control reconfiguration were presented with a failure characterized by a locked left horizontal tail surface....
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333 citations
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"Adaptive failure compensation for a..." refers background in this paper
...where ti is the unknown failure time instant and ūi is the unknown constant failure value [11]....
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188 citations
Additional excerpts
...In [ 9 ], an algorithm for aircraft failure detection and compensation was presented, which incorporated multiple model adaptive estimation methods....
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182 citations
"Adaptive failure compensation for a..." refers methods in this paper
...In [2], several multivariable adaptive control algorithms for flight contr ol reconfiguration were presented with a failure characterize d by a locked left horizontal tail surface....
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Frequently Asked Questions (14)
Q2. What future works have the authors mentioned in the paper "Adaptive failure compensation for aircraft tracking control using engine differential based model" ?
Several important and challenging issues need to be addressed in future research.
Q3. What are the main issues that need to be addressed in future research?
In addition, the effects of actuator nonlinearities including output and rate saturation, as well as actuator dynamics, need to be addressed.
Q4. How can the authors obtain the linearized aircraft model with engine differentials?
By applying the linearization procedure around the equilibrium point of interest, the authors can obtain the linearized aircraft model with engine differentials.
Q5. What is the feedback control law for asymptotic state tracking?
As the new adaptive failure compensation scheme for asymptotic state tracking, the feedback control law isv(t) = K̂x(t) + κ̂rd(t) + θ̂, (III.9)where K̂ = [K̂1, K̂2, . . . , K̂m]
Q6. What is the simplest way to obtain the linearized aircraft model?
This engine differential based model in which the two engine thrusts and the ailerons are taken into account separately captures the essential dynamics of the aircraft in the engine differential mode, and is capable of coping with some actuator failures such as rudder failures or engine failure, which cannot be achieved without using engine differentials.
Q7. What is the meaning of state tracking for the aircraft dynamic model linearized at an equilibrium point?
0. 2The physical meaning of state tracking for the aircraft dynamic model linearized at an equilibrium point (xo, Uo) is that the operation of the aircraft follows a desired trajectory in a neighborhood of the equilibrium point.
Q8. What is the condition that implies that the nominal LQ regulator used for generating the desired trajectory?
(This condition basically implies that the nominal LQ regulator used for generating the desired trajectory is designed to be robust to parameter uncertainties).
Q9. what is the adaptive failure compensation scheme?
This adaptive actuator failure compensation scheme has the following desired properties:Theorem 3.1: The control law (III.9), updated from (III.10)–(III.12) and applied to the system (III.1) subject to the actuator failures (III.2) under Assumption 3.1, ensures that all closed-loop system signals are bounded and limt→∞(x(t) − xd(t)) = 0, for any failure pattern σ ∈ Σ with uncertain parameters.
Q10. What is the effect of engine thrust differentials?
T̄ ′′′δtl−T̄ ′′′δtr 0 0 0 0 0 0 (II.13) represent the effect of engine thrust differentials, that is, if the left and right engine thrusts are equal, these matrices are zero.
Q11. What is the corresponding set of actuator states?
There are 2m possible combinations of actuator states (each actuator is either normal or failed), and therefore 2m−1 possible failure patterns that constitute a set denoted by Σ̄.
Q12. What is the stabilzability and rank condition in Assumption 3.1?
The stabilizability and rank condition in Assumption 3.1 characterizes the system redundancy condition needed for actuator failure compensation.
Q13. What is the commutativity of the matrix trace operator?
T and the commutativity property of the matrix trace operator, i.e., Tr(XY ) = Tr(Y X), the following equalities hold:eTPB(I−σ)(K̂−Kσ)x(t) = ∑i6=i1,i2,...,ip(K̂i−Ki) TxeTPbi,eTPB
Q14. what is the force equationsm(u+qw rv)?
As described in [8], a nonlinear aircraft dynamic model in body-axis coordinate system which incorporates enginedifferentials can be described by the force equationsm(u̇+ qw − rv) = X −mg sin θ + (TL + TR) cos ǫ (II.1)m(v̇ + ru− pw) = Y +mg cos θ sinφ (II.2)m(ẇ+pv−qu) = Z+mg cos θ cosφ−(TL+TR) sin ǫ (II.3)and moment equationsIxṗ+Ixz ṙ+(Iz−Iy)qr+Ixzqp = L+l(TL−TR) sin ǫ (II.4)Iy q̇ + (Ix − Iz)pr + Ixz(r 2 − p2) = M (II.5)Iz ṙ + Ixz ṗ+ (Iy − Ix)qp− Ixzqr = N + l(TL − TR) cos ǫ (II.6) where m is the mass of the aircraft.