Robust fault accommodation strategy of the reentry vehicle: a disturbance estimate-triggered approach

Abstract

This study proposes a novel fault accommodation scheme for the strong coupled attitude system of the hypersonic reentry vehicle (HRV) with both actuator drift and loss of efficiency. A general coupling/fault/uncertainty effect-triggered control concept is first introduced for the HRV attitude tracking system to improve its robustness and dynamic performance, which can be derived easily via Lyapunov stability. The design of such a control approach is based on an improved adaptive disturbance observer (ADO) to estimate the lumped uncertainties and actuator faults. The proposed scheme can achieve graceful degradation in tracking performance for the fault-tolerant control system by eliminating the detrimental uncertainty and actuator fault while keeping the beneficial uncertainty and actuator fault. A detailed design procedure has been presented with consideration of the implementation problem. Simulation results obtained on the HRV have demonstrated the effectiveness of the approach proposed.

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Abbreviations

m :

Mass, slugs

Ma :

Mach number

V :

Velocity, ft/s

H :

Altitude, ft

\(\theta \) :

Flight-path angle, rad

\(\psi _v\) :

Azimuth angle

\(\alpha \) :

Angle of attack, rad

\(\beta \) :

Sideslip angle, rad

\(\gamma _v\) :

Bank angle, rad

\(\omega _x\) :

Roll rate, rad/s

\(\omega _y\) :

Yaw rate, rad/s

\(\omega _z\) :

Pitch rate, rad/s

\(\delta _e\) :

Elevator deflection, rad

\(\delta _a\) :

Aileron deflection, rad

\(\delta _r\) :

Rudder deflection, rad

\(\delta _{bf}\) :

Body flap deflection, rad

\(C_D\) :

Drag coefficient

\(C_L\) :

Lift coefficient

\(I_{xx}\) :

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

\(M_x\) :

Rolling moment, lbf-ft

\(I_{yy}\) :

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

\(M_{y}\) :

Yawing moment, lbf-ft

\(I_{zz}\) :

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

\(M_z\) :

Pitching moment, lbf-ft

\(I_{xy,xz,yz}\) :

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

Y :

Side force, lbf

L :

Lift force, lbf

D :

Drag force, lbf

\(\rho \) :

Density of air, slugs \(ft^3\)

T :

Thrust, lbf

\(\mu \) :

Gravitational constant, \( 1.39 \times 10^{16} ft^3/s^2\)

\(S_{ref}\) :

Reference area, \(ft^2\)

\(\phi \) :

Latitude, rad

R :

The radius of the earth, ft

a :

Speed of sound, ft/s

\(\bar{c}\) :

Reference length, ft

References

  1. 1.

    Parker, J., Serrani, A., Yurkovich, S., Doman, D.: Control-oriented modeling of an air-breathing hypersonic vehicle. J. Guid. Control Dyn. 30(3), 856–869 (2007)

    Article  Google Scholar 

  2. 2.

    Xingling, S., Honglun, W.: Sliding mode based trajectory linearization control for hypersonic reentry vehicle via extended disturbance observer. ISA Trans. 53(6), 1771–1786 (2014)

    Article  Google Scholar 

  3. 3.

    Zhang, Y., Xian, B.: Continuous nonlinear asymptotic tracking control of an air-breathing hypersonic vehicle with flexible structural dynamics and external disturbances. Nonlinear Dyn. 83(1–2), 86–891 (2016)

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Guo, Z., Guo, J., Chang, J., Zhou, J.: Coupling effect-triggered control strategy for hypersonic flight vehicles with finite-time convergence. Nonlinear Dyn. 95(2), 1009–1025 (2019)

    Article  Google Scholar 

  5. 5.

    Hu, X., Xu, B., Si, X., Hu, C.: Nonlinear adaptive tracking control of non-minimum phase hypersonic flight vehicles with unknown input nonlinearity. Nonlinear Dyn. 90(2), 1151–1163 (2017)

    Article  Google Scholar 

  6. 6.

    An, H., Wu, Q., Xia, H., Wang, C.: Fast tracking control of air-breathing hypersonic vehicles with time-varying uncertain parameters. Nonlinear Dyn. 91(3), 1835–1852 (2018)

    Article  Google Scholar 

  7. 7.

    Gibson, T. E., Crespo, L. G., Annaswamy, A. M.: Adaptive control of hypersonic vehicles in the presence of modeling uncertainties. In: 2009 American Control Conference, St. Louis, MO, pp. 3178–3183 (2009)

  8. 8.

    Zhou, J., Chang, J., Guo, Z.: A fault-tolerant control scheme within adaptive disturbance observer for hypersonic vehicle. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 233(3), 1071–1088 (2019)

    Article  Google Scholar 

  9. 9.

    Fiorentini, L., Serrani, A., Bolender, M.A., Doman, D.B.: Robust nonlinear sequential loop closure control design for an air-breathing hypersonic vehicle model. In: 2008 American Control Conference, Seattle, WA, pp. 3458–3463 (2008)

  10. 10.

    Dorobantu, A., Murch, A.M., Balas, G.J.: H-Infinity robust control design for the NASA AirSTAR flight test vehicle. In: AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Nashville, Tennessee (2012)

  11. 11.

    Xu, B., Guo, Y., Yuan, Y., Fan, Y., Wang, D.: Fault-tolerant control using command-filtered adaptive back-stepping technique: application to hypersonic longitudinal flight dynamics. Int. J. Adapt. Control Signal Process. 30(4), 553–577 (2016)

    MathSciNet  Article  Google Scholar 

  12. 12.

    Su, X., Jiang, Y., Jia, Y.: Modeling and robust decoupling control for hypersonic scramjet vehicle. Artif. Life Robot. 18(1–2), 58–63 (2013)

    Article  Google Scholar 

  13. 13.

    Ginoya, D., Shendge, P.D., Phadke, S.B.: Sliding mode control for mismatched uncertain systems using an extended disturbance observer. IEEE Trans. Ind. Electron. 61(4), 1983–1992 (2014)

    Article  Google Scholar 

  14. 14.

    Gao, G., Wang, J.: Observer-based fault-tolerant control for an air-breathing hypersonic vehicle model. Nonlinear Dyn. 76(1), 409–430 (2014)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Chang, J., Cieslak, J., Davila, J., Zolghadri, A., Zhou, J.: Analysis and design of second-order sliding-mode algorithms for quadrotor roll and pitch estimation. ISA Trans. 71(Part 2), 495–512 (2017)

    Article  Google Scholar 

  16. 16.

    Chang, J., Cieslak, J., Davila, J., Zhou, J., Zolghadri, A., Guo, Z.: A two-step approach for an enhanced quadrotor attitude estimation via IMU data. IEEE Trans. Control Syst. Technol. 26(3), 1140–1148 (2018)

    Article  Google Scholar 

  17. 17.

    Davila, J.: Exact tracking using backstepping control design and high-order sliding modes. IEEE Trans. Autom. Control 58(8), 2077–2081 (2013)

    MathSciNet  Article  Google Scholar 

  18. 18.

    Guo, Z., Chang, J., Guo, J., Zhou, J.: Adaptive twisting sliding mode algorithm for hypersonic reentry vehicle attitude control based on finite-time observer. ISA Trans. 77, 20–29 (2018)

    Article  Google Scholar 

  19. 19.

    Dong, W., Farrell, J.A., Polycarpou, M.M., Djapic, V., Sharma, M.: Command filtered adaptive backstepping. IEEE Trans. Control Syst. Technol. 20(3), 566–580 (2012)

    Article  Google Scholar 

  20. 20.

    Weiland, C., Longo, J., Gülhan, A., Decker, K.: Aerothermodynamics for reusable launch systems. Aerosp. Sci. Technol. 8(2), 101–110 (2004)

    Article  Google Scholar 

  21. 21.

    Tian, B., Fan, W., Zong, Q., Wang, J., Wang, F.: Nonlinear robust control for reusable launch vehicles in reentry phase based on time-varying high order sliding mode. J. Frankl. Inst. 350(7), 1787–1807 (2013)

    MathSciNet  Article  Google Scholar 

  22. 22.

    Dhadekar, D.D., Patre, B.M.: UDE-based decoupled full-order sliding mode control for a class of uncertain nonlinear MIMO systems. Nonlinear Dyn. 88(1), 263–276 (2017)

    Article  Google Scholar 

  23. 23.

    Dickeson, J., Rodriguez, A., Sridharan, S., Benavides, J., Soloway, D.: Decentralized control of an airbreathing scramjet-powered hypersonic vehicle. In: AIAA Guidance, Navigation, and Control Conference, p. 6281 (2009)

  24. 24.

    Wang, Q., Stengel, R.F.: Robust nonlinear control of a hypersonic aircraft. J. Guid. control Dyn. 23(4), 577–585 (2000)

    Article  Google Scholar 

  25. 25.

    Su, X., Jia, Y.: Self-scheduled robust decoupling control with H\(\infty \) performance of hypersonic vehicles. Syst. Control Lett. 70, 38–48 (2014)

    MathSciNet  Article  Google Scholar 

  26. 26.

    Guo, Z., Zhou, J., Guo, J., Cieslak, J., Chang, J.: Coupling-characterization-based robust attitude control scheme for hypersonic vehicles. IEEE Trans. Ind. Electron. 64(8), 6350–6361 (2017)

    Article  Google Scholar 

  27. 27.

    Guo, Z., Guo, J., Zhou, J.: Adaptive attitude tracking control for hypersonic reentry vehicles via sliding mode-based coupling effect-triggered approach. Aerosp. Sci. Technol. 78, 228–240 (2018)

    Article  Google Scholar 

  28. 28.

    Tian, B., Fan, W., Su, R., et al.: Real-time trajectory and attitude coordination control for reusable launch vehicle in reentry phase. IEEE Trans. Ind. Electron. 62(3), 1639–1650 (2014)

    Article  Google Scholar 

  29. 29.

    Tian, B., Yin, L., Wang, H.: Finite-time reentry attitude control based on adaptive multivariable disturbance compensation. IEEE Trans. Ind. Electron. 62(9), 5889–5898 (2015)

    Article  Google Scholar 

  30. 30.

    Chen, W., Ge, S.S., Wu, J., Gong, M.: Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy knowna priori. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 1842–1854 (2015)

    MathSciNet  Article  Google Scholar 

  31. 31.

    Alwi, H., Edwards, C.: An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction. Automatica 49(2), 642–651 (2013)

    MathSciNet  Article  Google Scholar 

  32. 32.

    Edwards, C., Lombaerts, T., Smaili, H.: Fault tolerant flight control: a benchmark challenge. Lect. Notes Control Inf. Sci. 399, 1–560 (2010)

    Google Scholar 

  33. 33.

    Hamayun, M.T., Edwards, C., Alwi, H.: An augmentation scheme for fault tolerant control using integral sliding modes. Fault Tolerant Control Schemes Using Integral Sliding Modes, pp. 103–121. Springer, Cham (2016)

    Google Scholar 

  34. 34.

    Jiang, J., Yu, X.: Fault-tolerant control systems: a comparative study between active and passive approaches. Ann. Rev. Control 36(1), 60–72 (2012)

    MathSciNet  Article  Google Scholar 

  35. 35.

    Fonod, R., Henry, D., Charbonnel, C., et al.: Robust FDI for fault-tolerant thrust allocation with application to spacecraft rendezvous. Control Eng. Pract. 42, 12–27 (2015)

    Article  Google Scholar 

  36. 36.

    Hall, C.E., Shtessel, Y.B.: Sliding mode disturbance observer-based control for a reusable launch vehicle. J. Guid. Control Dyn. 29(6), 1315–1328 (2006)

    Article  Google Scholar 

  37. 37.

    Kale, M.M., Chipperfield, A.J.: Stabilized MPC formulations for robust reconfigurable flight control. Control Eng. Pract. 13(6), 771–788 (2005)

    Article  Google Scholar 

  38. 38.

    Zhiqiang, G., Antsaklis, P.J.: Stability of the pseudo-inverse method for reconfigurable control systems. Int. J. Control 53(3), 717–729 (1991)

    MathSciNet  Article  Google Scholar 

  39. 39.

    Alwi, Halim: Edwards, Christopher: fault tolerant control using sliding modes with on-line control allocation. Automatica 44(7), 1859–1866 (2008)

    MathSciNet  Article  Google Scholar 

  40. 40.

    Falcoz, Alexandre, Henry, D., Zolghadri, A.: Robust fault diagnosis for atmospheric reentry vehicles: a case study. IEEE Trans. Syst. Man Cybern Part A Syst. Hum. 40(5), 886–899 (2010)

    Article  Google Scholar 

  41. 41.

    Brière, D., Pascal T.: AIRBUS A320/A330/A340 electrical flight controls-A family of fault-tolerant systems. In: FTCS-23 The Twenty-Third International Symposium on Fault-Tolerant Computing, IEEE (1993)

Download references

Acknowledgements

This study was supported by National Natural Science Foundation of China (Grant Number 61803308, 62003252).

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Correspondence to Zongyi Guo.

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Appendix

Appendix

Proof of the disturbance observer in Eq. (32)

Proof

Subtracting (9) from (35) yields the error system as

$$\begin{aligned} \left\{ \begin{array} {l} \dot{e}_i = -\sqrt{2L_{i}}(t)|e_i|^{1/2} \mathrm {sign}(e_i) + \tilde{d}_i\\ \dot{\tilde{d}}_i = -4L_i(t) \mathrm {sign}(e_i) - \dot{\zeta }_i\\ \end{array} \right. \end{aligned}$$
(56)

where \(\tilde{d}_i = \hat{\zeta }_i - \zeta _i\). Consider the following Lyapunov function candidate for the error system (56)

$$\begin{aligned} V(t) = \frac{1}{L_i^{2/3}(t)}\xi ^T P(t) \xi \end{aligned}$$
(57)

where

$$\begin{aligned} P(t) = \frac{1}{2}\begin{bmatrix} 18L_i(t) &{} \quad - \sqrt{2L_{i}}(t)\\ -\sqrt{2L_{i}}(t)&{} \quad 2 \end{bmatrix}, \xi = \begin{bmatrix} |e_i|^{1/2} \mathrm {sign}(e_i) \\ \tilde{d}_i \end{bmatrix} \end{aligned}$$
(58)

The derivative of \(\xi \) results in

$$\begin{aligned} \begin{aligned} \dot{\xi }&= \begin{bmatrix} \frac{1}{ 2|e_i|^{1/2}} \left( - \sqrt{2L_{i}(t)}|e_i|^{1/2} \mathrm {sign}(e_i) + \tilde{d}_i \right) \\ -4L_i(t) \mathrm {sign}(e_i)- \dot{\zeta }_i \end{bmatrix} \\&= - \frac{1}{ 2|e|^{1/2}} A_1(t) \xi + A_2(t) \end{aligned} \end{aligned}$$
(59)

where \(A_1 = \begin{bmatrix} \sqrt{2L_{i}(t)} &{} -1 \\ 8L_i(t) &{} 0\end{bmatrix}\) and \(A_2 = \begin{bmatrix} 0 \\ -\dot{\zeta }_i \end{bmatrix}\). Taking the derivative of V yields

$$\begin{aligned} \dot{V}&= -\frac{L_0}{2} \xi ^T \underbrace{ \begin{bmatrix} 9L_i^{-3/2}(t) &{} \quad -\sqrt{2} L_i^{-2}(t) \nonumber \\ -\sqrt{2} L_i^{-2}(t) &{} \quad 3L_i^{-5/2} (t) \end{bmatrix} }_{Q_1(t)} \xi \nonumber \\&+ \frac{\xi ^T P(t)A_2(t)}{L_i^{3/2}(t)} \nonumber \\&- \frac{1}{2L_i^{3/2}(t) |e_i|^{1/2}}{\xi }^T \underbrace{\left( A_1(t)^T P(t) + P(t)A_1(t)\right) }_{Q_2(t)} \xi \nonumber \\&=-\frac{1}{2}L_0\xi ^TQ_1(t)\xi -\frac{1}{2L_i^{3/2}(t) |e_i|^{1/2}} \xi ^T Q_2(t) \xi \nonumber \\&+ \frac{\xi ^T P(t)A_2(t)}{L_i^{3/2}(t)} \nonumber \\&\le -\frac{1}{2}L_0\xi ^TQ_1(t)\xi -\frac{1}{2L_i^{3/2}(t) |e_i|^{1/2}} \xi ^T \tilde{Q}(t) \xi \nonumber \\&\le - \underbrace{\frac{1}{2}L_0\frac{\lambda _{\mathrm{min}}(Q_1)}{ \lambda _{\mathrm{max}}(P)}}_{\eta _1} V \nonumber \\&- \underbrace{ \frac{1}{\sqrt{2} L_i(t)} \frac{\sqrt{\lambda _{\mathrm{min}}(P)} \lambda _{\mathrm{min}}(\tilde{Q})}{ \lambda _{\mathrm{max}}(P)}}_{\eta _2} V^{1/2} \end{aligned}$$
(60)

where

$$\begin{aligned}&\tilde{Q}(t) \nonumber \\&\quad = \sqrt{2L_{i}(t)} \begin{bmatrix} 10 L_i(t) - 2\Delta _i -\frac{2\Delta _i^2}{\sqrt{2L_{i}(t) }}&{} \quad -\sqrt{2L_{i}(t)} \\ -\sqrt{2L_{i}(t)} &{} \quad 2-\frac{2}{\sqrt{2L_{i}(t)}} \end{bmatrix} \end{aligned}$$
(61)

Since \(\dot{L}_i = L_0>0\), it is easily found that \(\tilde{Q}(t)\) will be positive in finite time. After that, we have \(\dot{V}+ \eta _1 V + \eta _2 V^{1/2} \le 0\). In view of Lemma 2 in [29], the vector \(\xi \rightarrow 0\) in finite time. Obviously, the identity \(\xi \equiv 0\) implies \(e_i \equiv 0\) and \(\tilde{d}_i \equiv 0\). Thus, the estimates of disturbances are available in finite time.

This completes the proof.

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Chang, J., Guo, Z., Cieslak, J. et al. Robust fault accommodation strategy of the reentry vehicle: a disturbance estimate-triggered approach. Nonlinear Dyn 103, 2605–2625 (2021). https://doi.org/10.1007/s11071-021-06237-1

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Keywords

  • Fault tolerant control
  • Adaptive disturbance observer
  • Coupling/fault/uncertainty effect
  • Reentry vehicle