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

Original Paper
  • 18 Downloads

Abstract

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.

Keywords

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

List of symbols

\(\alpha \)

Angle of attack, rad

\(\bar{c}\)

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

\(c_\mathrm{e}\)

Constant, 0.0292

\(C_{\mathrm{D}}\)

Drag coefficient

\(C_{\mathrm{L}}\)

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

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

Moment coefficient due to pitch rate

\(C_{\mathrm{T}}\)

Thrust coefficient

D

Drag, lbf

h

Altitude, ft

\(h_\mathrm{d}\)

Reference altitude, ft

\(I_{\mathrm{yy}}\)

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

L

Lift, lbf

m

Mass, slug

\(M_{\mathrm{yy}}\)

Pitching moment, lbf-ft

q

Pitch rate, rad/s

r

Radial distance from Earth’s center, ft

\(R_\mathrm{e}\)

Earth radius, ft

S

Reference aerodynamic area, ft\(^2\)

T

Thrust, lbf

V

Velocity, ft/s

\(V_\mathrm{d}\)

Reference velocity, ft/s

Abbreviations

HFV

Hypersonic flight vehicle

FTC

Fault-tolerant control

SMC

Sliding-mode control

SMO

Sliding-mode observer

FLS

Fuzzy logic system

NN

Neural networks

Notes

Acknowledgements

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.

References

  1. 1.
    Xu, B., Shi, Z.K.: An overview on flight dynamics and control approaches for hypersonic vehicles. Sci. China Inf. Sci. 58(7), 1–19 (2015)MathSciNetGoogle Scholar
  2. 2.
    Shen, Q., Shi, P., Jiang, B.: Fault Diagnosis and Fault-Tolerant Control Based on Adaptive Control Approach. Springer International Publishing, New York (2017)CrossRefMATHGoogle Scholar
  3. 3.
    Shen, Q., Jiang, B., Cocquempot, V.: Fault-tolerant control for TCS fuzzy systems with application to near-space hypersonic vehicle with actuator faults. IEEE Trans. Fuzzy Syst. 20(4), 652–665 (2011)CrossRefGoogle Scholar
  4. 4.
    Gao, Z., Jiang, B., Gong, H., Xu, Y.: Fault-tolerant sliding mode control design for near space vehicle based on T-S fuzzy model. In: Fourth International Conference on Innovative Computing, Information and Control, pp. 211–214 (2009)Google Scholar
  5. 5.
    Hu, X.X., Wu, L.G., Hu, C.H., Gao, H.J.: Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle. J. Frankl. Inst. Eng. Appl. Math. 349(2), 559–577 (2012)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Wang, J., Wu, Y., Dong, X.: Recursive terminal sliding mode control for hypersonic flight vehicle with sliding mode disturbance observer. Nonlinear Dyn. 81(3), 1489–1510 (2015)CrossRefMATHGoogle Scholar
  7. 7.
    Zhou, L., Yin, L.: Dynamic surface control based on neural network for an air-breathing hypersonic vehicle. Optim. Control Appl. Methods 36(6), 774–793 (2016)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Wang, N., Wu, H.N., Guo, L.: Coupling-observer-based nonlinear control for flexible air-breathing hypersonic vehicles. Nonlinear Dyn. 78(3), 2141–2159 (2014)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hou, D., Wang, Q., Dong, C.: Output feedback dynamic surface controller design for airbreathing hypersonic flight vehicle. IEEE/CAA J. Autom. Sin. 2(2), 186–197 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Sun, H., Li, S., Sun, C.: Robust adaptive integral-sliding-mode fault-tolerant control for airbreathing hypersonic vehicles. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 226(10), 1344–1355 (2012)CrossRefGoogle Scholar
  11. 11.
    Rehman, O.U., Petersen, I.R., Fidan, B.: Robust nonlinear control design of a hypersonic flight vehicle using minimax linear quadratic Gaussian control. In: Decision and Control. IEEE, pp 6219–6224 (2010)Google Scholar
  12. 12.
    Kendoul, F., Yu, Z., Nonami, K.: Guidance and nonlinear control system for autonomous flight of minirotorcraft unmanned aerial vehicles. J. Field Robot. 27(3), 311–334 (2010)Google Scholar
  13. 13.
    Hu, Y., Sun, F., Liu, H.: Neural network-based robust control for hypersonic flight vehicle with uncertainty modelling. Int. J. Modell. Identif. Control 11(1/2), 87–98 (2010)CrossRefGoogle Scholar
  14. 14.
    Yang, F., Yuan, R., Yi, J.: Direct adaptive type-2 fuzzy neural network control for a generic hypersonic flight vehicle. Soft. Comput. 17(11), 2053–2064 (2013)CrossRefMATHGoogle Scholar
  15. 15.
    Guan, P., Xue, L., Liu, X.H., et al.: The adaptive fuzzy sliding mode control of hypersonic vehicle. In: 10th World Congress on Intelligent Control and Automation, Beijing, China, pp 51–56 (2012)Google Scholar
  16. 16.
    Xu, B.: Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity. Nonlinear Dyn. 80(3), 1509–1520 (2015)Google Scholar
  17. 17.
    He, J., Qi, R., Jiang, B., Qian, J.: Adaptive output feedback fault-tolerant control design for hypersonic flight vehicles. J. Franklin Inst. 352(5), 1811–1835 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang, S.X., Zhang, Y., Jin, Y.Q.: Neural control of hypersonic flight dynamics with actuator fault and constraint. Sci. China Inf. Sci. 58(7), 70206–070206 (2015)MathSciNetGoogle Scholar
  19. 19.
    Xu, Y., Jiang, B., Tao, G.: Fault tolerant control for a class of nonlinear systems with application to near space vehicle. Circuits Syst. Signal Process. 30(3), 655–672 (2011)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Wang, J.S., Yang, G.H.: Data-driven output-feedback fault-tolerant compensation control for digital pid control systems with unknown dynamics. IEEE Trans. Ind. Electron. 63(11), 7029–7039 (2016)CrossRefGoogle Scholar
  21. 21.
    Xu, B., Zhang, Q., Pan, Y.: Neural network based dynamic surface control of hypersonic flight dynamics using small-gain theorem. Neurocomputing 173(P3), 690–699 (2016)CrossRefGoogle Scholar
  22. 22.
    Yu, X., Liu, Z., Zhang, Y.: Fault-tolerant flight control design with finite-time adaptation under actuator stuck failures. IEEE Trans. Control Syst. Technol. PP 99, 1–10 (2016)Google Scholar
  23. 23.
    Yu, X., Zhang, Y., Liu, Z.: Fault-tolerant flight control design with explicit consideration of reconfiguration transients. J. Guid. Control Dyn. 39(3), 556–563 (2016)CrossRefGoogle Scholar
  24. 24.
    Laghrouche, S., Liu, J., Ahmed, F.S.: Adaptive second-order sliding mode observer-based fault reconstruction for pem fuel cell air-feed system. IEEE Trans. Control Syst. Technol. 23(3), 1098–1109 (2015)CrossRefGoogle Scholar
  25. 25.
    Edwards, C., Patton, R.J., Spurgeon, S.K.: Sliding mode observers for fault detection and isolation. Automatica 36(4), 541–553 (2000)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Tong, S.C., Li, Y.M., Feng, G.: Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans. Syst. Man Cybern. Part B. 41(4), 1124–1135 (2011)CrossRefGoogle Scholar
  27. 27.
    Marrison, C.I., Stengel, R.F.: Design of Robust Control System for a Hypersonic Aircraft. J. Guid. Control Dyn. 21(1), 58C62 (1998)CrossRefMATHGoogle Scholar
  28. 28.
    Wang, Q., Stengel, R.F.: Robust nonlinear control of a hypersonic aircraft. J. Guid. Control Dyn. 23(4), 577C585 (2000)CrossRefGoogle Scholar
  29. 29.
    Chen, F., Wang, Z., Tao, G., et al.: Robust adaptive fault-tolerant control for hypersonic flight vehicles with multiple faults[J]. J. Aerosp. Eng. 28(4), 04014111 (2015)CrossRefGoogle Scholar
  30. 30.
    Ji, Y., Zhou, H., Zong, Q.: Adaptive active fault-tolerant control of generic hypersonic flight vehicles[J]. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 229(2), 130–138 (2014)CrossRefGoogle Scholar

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

Personalised recommendations