Nonlinear Dynamics

, Volume 92, Issue 3, pp 1299–1315 | Cite as

Nonlinear fuzzy fault-tolerant control of hypersonic flight vehicle with parametric uncertainty and actuator fault

  • Juan Niu
  • Fuyang Chen
  • Gang Tao
Original Paper


This study presents a nonlinear fuzzy fault-tolerant control (FTC) and a fault observer for longitudinal dynamics of hypersonic flight vehicle (HFV) with parameter uncertainty and actuator gain loss fault via sliding-mode and backstepping theory. An affine nonlinear dynamic model of HFV with parameter uncertainty and actuator fault is established based on feedback linearization technology. A nominal sliding-mode control is developed to track the command of altitude and velocity. Unknown nonlinear functions in the controller are approximated by fuzzy logic system through updating the weight parameters online. In view of the occurrence of actuator fault, a backstepping sliding-mode observer is constructed to estimate the fault. A nonlinear fuzzy FTC is then designed with the estimate fault obtained from the observer to address the problem of actuator fault and parameter uncertainty. The stability of the controller is analyzed utilizing Lyapunov theory. Numerical simulation results demonstrate the validity and robustness of the proposed controller and observer.


Fault-tolerant control Sliding mode Hypersonic flight vehicle Fault estimation Fuzzy logic system 

List of symbols

\(\alpha \)

Angle of attack, rad


Reference length, 80 ft

\(\beta _{\mathrm{Tc}}\)

Desirable throttle setting, \(\%/100\)

\(\beta _{\mathrm{T}}\)

Throttle setting, \(\%/100\)

\(\delta _{\mathrm{e}}\)

Elevator deflection, rad

\(\gamma \)

Flight-path angle, rad

\(\mu \)

Gravitational constant, ft \(^3\)/s\(^2\)

\(\omega _{\mathrm{n}}\)

Frequency of engine system, rad/s

\(\rho \)

Density of air, slug/ft\(^3\)

\(\xi _\mathrm{n}\)

Damping of engine system


Constant, 0.0292


Drag coefficient


Lift coefficient

\(C_{\mathrm{M}}(\alpha )\)

Moment coefficient due to angle of attack

\(C_{\mathrm{M}}(\delta _{\mathrm{e}})\)

Moment coefficient due to elevator deflection


Moment coefficient due to pitch rate


Thrust coefficient


Drag, lbf


Altitude, ft


Reference altitude, ft


Moment of inertia, slug-ft\(^2\)


Lift, lbf


Mass, slug


Pitching moment, lbf-ft


Pitch rate, rad/s


Radial distance from Earth’s center, ft


Earth radius, ft


Reference aerodynamic area, ft\(^2\)


Thrust, lbf


Velocity, ft/s


Reference velocity, ft/s



Hypersonic flight vehicle


Fault-tolerant control


Sliding-mode control


Sliding-mode observer


Fuzzy logic system


Neural networks



The project was supported by the National Natural Science Foundation of China (61533009, 61473146), a project funded by the Priority Academic Programme Development of Jiangsu Higher Education Institutions.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Department of Electrical and Computer EngineeringUniversity of VirginiaCharlottesvilleUSA

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