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Observer-based fault-tolerant control for an air-breathing hypersonic vehicle model

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Abstract

This paper focuses on controller and observer design for the longitudinal model of an air-breathing hypersonic vehicle (AHV) subject to actuator faults and limited measurements of the states. The feedback linearization method is firstly employed for a modified AHV model with actuator faults, and dynamic effect caused by the actuator faults on the linearized model is analyzed. Based on full state information, an adaptive controller is designed using the Lyapunov method, which guarantees reference command tracking of the AHV under actuator faults. Next, to estimate the unmeasurable states used in the adaptive controller, a sliding observer is designed based on the sliding control method and the Filippov’s construction of the equivalent dynamics (FCED). Finally, the adaptive controller is combined with the sliding observer to generate the observer-based adaptive controller, which relies only on partial state information. Simulations demonstrate that the observer-based adaptive controller achieves desired tracking performance and good robustness in the presence of actuator faults.

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Abbreviations

C D :

Drag coefficient

\(C_{D}^{\alpha^{i}}\) :

ith-order coefficient of α contribution to C D  (1/radi)

\(C_{D}^{\delta_{e}^{i}}\) :

ith-order coefficient of δ e contribution to C D (1/radi)

\(C_{D}^{0}\) :

Constant term in C D

C L :

Lift coefficient

\(C_{L}^{{\alpha}}\) :

First-order coefficient of α contribution to C L (1/rad)

\(C_{L}^{{\delta_{e}}}\) :

First-order coefficient of δ e contribution to C L (1/rad)

\(C_{L}^{0}\) :

Constant term in C L

C M,α :

Contribution to moment due to angle of attack

\(C_{M,{\delta_{e}}}\) :

Control surface contribution to moment

\(C_{M,\alpha}^{{\alpha^{i}}}\) :

ith-order coefficient of α contribution to C M,α (1/radi)

\(C_{M,\alpha}^{0}\) :

Constant term in C M,α

\(C_{T}^{{\alpha^{i}}}\) :

ith-order coefficient of α contribution to C T (1/radi)

\(\bar{c}\) :

Mean aerodynamics chord (m)

c e :

Elevator coefficient in \(C_{M,{\delta_{e}}}\) (1/rad)

D :

Drag (N)

g :

Acceleration due to gravity (m/s2)

h :

Altitude (m)

h ref :

Reference command for altitude (m)

I :

Moment of inertia (kg m2)

L :

Lift (N)

M :

Pitching moment (N m)

m :

Vehicle mass (kg)

Q :

Pitch rate (rad/s)

S :

Reference area (m2)

T :

Thrust (N)

V :

Velocity (m/s)

V ref :

Reference command for velocity (m/s)

α :

Angle of attack (rad)

β i :

Fuel-to-air ratio contribution to \(C_{T}^{{\alpha^{i}}}\) (1/radi)

β′ i :

Constant term in \(C_{T}^{{\alpha^{i}}}\) (1/radi)

δ e :

Elevator deflection (rad)

ζ :

Damping ratio for the Φ dynamics

θ :

Pitch angle (rad)

\(\bar{\rho}\) :

Air density (kg/m3)

ρ 0 :

Parameter in the air density model (kg/m3)

Φ :

Fuel-to-air ratio

Φ c :

Commanded value of Φ

ω :

Natural frequency for the Φ dynamics

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61074026 and 90916003.

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  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, China

    Gang Gao & Jinzhi Wang

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  1. Gang Gao
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Correspondence to Jinzhi Wang.

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Gao, G., Wang, J. Observer-based fault-tolerant control for an air-breathing hypersonic vehicle model. Nonlinear Dyn 76, 409–430 (2014). https://doi.org/10.1007/s11071-013-1135-x

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