SCIENCE CHINA Information Sciences, Volume 64 , Issue 5 : 152208(2021) https://doi.org/10.1007/s11432-020-3109-x

Modeling and adaptive control for a spatial flexible spacecraft with unknown actuator failures

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  • ReceivedJul 10, 2020
  • AcceptedSep 1, 2020
  • PublishedApr 8, 2021



This work was supported by National Natural Science Foundation of China (Grant No. 62073030), Interdisciplinary Research Project for Young Teachers of USTB (Grant No. FRF-IDRY-19-024), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019A1515110728), Postdoctor Research Foundation of Shunde Graduate School of University of Science and Technology Beijing (Grant No. 2020BH002), and Beijing Top Discipline for Artificial Intelligent Science and Engineering, University of Science and Technology Beijing.


[1] Di Gennaro S. Output stabilization of flexible spacecraft with active vibration suppression. IEEE Trans Aerosp Electron Syst, 2003, 39: 747-759 CrossRef ADS Google Scholar

[2] Hu Q, Ma G. Variable structure control and active vibration suppression of flexible spacecraft during attitude maneuver. Aerospace Sci Tech, 2005, 9: 307-317 CrossRef Google Scholar

[3] Hu Q. Adaptive output feedback sliding-mode manoeuvring and vibration control of flexible spacecraft with input saturation. IET Control Theor Appl, 2008, 2: 467-478 CrossRef Google Scholar

[4] Liu H, Guo L, Zhang Y. An anti-disturbance PD control scheme for attitude control and stabilization of flexible spacecrafts. NOnlinear Dyn, 2012, 67: 2081-2088 CrossRef Google Scholar

[5] Chen T, Wen H, Wei Z. Distributed attitude tracking for multiple flexible spacecraft described by partial differential equations. Acta Astronaut, 2019, 159: 637-645 CrossRef ADS Google Scholar

[6] He W, Ge S S. Dynamic modeling and vibration control of a flexible satellite. IEEE Trans Aerosp Electron Syst, 2015, 51: 1422-1431 CrossRef ADS Google Scholar

[7] Ji N, Liu J. Vibration control for a flexible satellite with input constraint based on Nussbaum function via backstepping method. Aerospace Sci Tech, 2018, 77: 563-572 CrossRef Google Scholar

[8] Feng S, Wu H N. Hybrid Robust Boundary and Fuzzy Control for Disturbance Attenuation of Nonlinear Coupled ODE-Beam Systems With Application to a Flexible Spacecraft. IEEE Trans Fuzzy Syst, 2017, 25: 1293-1305 CrossRef Google Scholar

[9] Liu Y, Fu Y, He W. Modeling and Observer-Based Vibration Control of a Flexible Spacecraft With External Disturbances. IEEE Trans Ind Electron, 2019, 66: 8648-8658 CrossRef Google Scholar

[10] Wang J W, Liu Y Q, Sun C Y. Observer-based dynamic local piecewise control of a linear parabolic PDE using non-collocated local piecewise observation. 20 CrossRef Google Scholar

[11] Wang J, Krstic M. Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs. IEEE Trans Automat Contr, 2019, 64: 4653-4660 CrossRef Google Scholar

[12] He W, Meng T, He X. Iterative Learning Control for a Flapping Wing Micro Aerial Vehicle Under Distributed Disturbances.. IEEE Trans Cybern, 2019, 49: 1524-1535 CrossRef PubMed Google Scholar

[13] Zhao Z, He X, Ren Z. Boundary Adaptive Robust Control of a Flexible Riser System With Input Nonlinearities. IEEE Trans Syst Man Cybern Syst, 2019, 49: 1971-1980 CrossRef Google Scholar

[14] Zhao Z, Ahn C K, Li H X. Dead Zone Compensation and Adaptive Vibration Control of Uncertain Spatial Flexible Riser Systems. IEEE/ASME Trans Mechatron, 2020, 25: 1398-1408 CrossRef Google Scholar

[15] Ren Y, Chen M, Liu J. Bilateral coordinate boundary adaptive control for a helicopter lifting system with backlash-like hysteresis. Sci China Inf Sci, 2020, 63: 119203 CrossRef Google Scholar

[16] Zhao Z, Ahn C K, Li H X. Boundary Antidisturbance Control of a Spatially Nonlinear Flexible String System. IEEE Trans Ind Electron, 2020, 67: 4846-4856 CrossRef Google Scholar

[17] Liu Z, Zhao Z, Ahn C K. Boundary Constrained Control of Flexible String Systems Subject to Disturbances. IEEE Trans Circuits Syst II, 2020, 67: 112-116 CrossRef Google Scholar

[18] He W, Ge S S, Huang D. Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint. IEEE/ASME Trans Mechatron, 2015, 20: 1886-1897 CrossRef Google Scholar

[19] Do K D, Pan J. Boundary control of three-dimensional inextensible marine risers. J Sound Vib, 2009, 327: 299-321 CrossRef ADS Google Scholar

[20] Do K D, Lucey A D. Stochastic stabilization of slender beams in space: Modeling and boundary control. Automatica, 2018, 91: 279-293 CrossRef Google Scholar

[21] Tao G, Chen S, Joshi S M. An adaptive actuator failure compensation controller using output feedback. IEEE Trans Automat Contr, 2002, 47: 506-511 CrossRef Google Scholar

[22] Wang W, Wen C. Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica, 2010, 46: 2082-2091 CrossRef Google Scholar

[23] Cai J, Wen C, Su H. Robust Adaptive Failure Compensation of Hysteretic Actuators for a Class of Uncertain Nonlinear Systems. IEEE Trans Automat Contr, 2013, 58: 2388-2394 CrossRef Google Scholar

[24] Wang W, Wen C. Adaptive compensation for infinite number of actuator failures or faults. Automatica, 2011, 47: 2197-2210 CrossRef Google Scholar

[25] Wang C, Wen C, Lin Y. Adaptive Actuator Failure Compensation for a Class of Nonlinear Systems With Unknown Control Direction. IEEE Trans Automat Contr, 2017, 62: 385-392 CrossRef Google Scholar

[26] Lin H, Zhao B, Liu D. Data-based fault tolerant control for affine nonlinear systems through particle swarm optimized neural networks. IEEE/CAA J Autom Sin, 2020, 7: 954-964 CrossRef Google Scholar

[27] Xiao B, Hu Q, Shi P. Attitude Stabilization of Spacecrafts Under Actuator Saturation and Partial Loss of Control Effectiveness. IEEE Trans Contr Syst Technol, 2013, 21: 2251-2263 CrossRef Google Scholar

[28] Zhang A, Hu Q, Zhang Y. Observer-Based Attitude Control for Satellite Under Actuator Fault. J Guidance Control Dyn, 2015, 38: 806-811 CrossRef ADS Google Scholar

[29] Ma Y, Jiang B, Tao G. Uncertainty decomposition-based fault-tolerant adaptive control of flexible spacecraft. IEEE Trans Aerosp Electron Syst, 2015, 51: 1053-1068 CrossRef ADS Google Scholar

[30] Sun G, Xu S, Li Z. Finite-Time Fuzzy Sampled-Data Control for Nonlinear Flexible Spacecraft With Stochastic Actuator Failures. IEEE Trans Ind Electron, 2017, 64: 3851-3861 CrossRef Google Scholar

[31] Hu Q, Xiao B. Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness. NOnlinear Dyn, 2011, 64: 13-23 CrossRef Google Scholar

[32] Liu Z, Liu J, He W. Robust adaptive fault tolerant control for a linear cascaded ODE-beam system. Automatica, 2018, 98: 42-50 CrossRef Google Scholar

[33] Xing X, Liu J. PDE modelling and vibration control of overhead crane bridge with unknown control directions and parametric uncertainties. 13 CrossRef Google Scholar

[34] Krstic M, Smyshlyaev A. Adaptive control of PDEs. Annu Rev Control, 2008, 32: 149-160 CrossRef Google Scholar

[35] Krstic M, Smyshlyaev A. Adaptive Boundary Control for Unstable Parabolic PDEs-Part I: Lyapunov Design. IEEE Trans Automat Contr, 2008, 53: 1575-1591 CrossRef Google Scholar

[36] Roman C, Bresch-Pietri D, Prieur C. Robustness to In-Domain Viscous Damping of a Collocated Boundary Adaptive Feedback Law for an Antidamped Boundary Wave PDE. IEEE Trans Automat Contr, 2019, 64: 3284-3299 CrossRef Google Scholar

[37] Anfinsen H, Aamo O M. Automatica, 2018, 87: 69-82 CrossRef Google Scholar

[38] Wang J, Tang S X, Krstic M. Adaptive output-feedback control of torsional vibration in off-shore rotary oil drilling systems. Automatica, 2020, 111: 108640 CrossRef Google Scholar

[39] Wang J, Tang S X, Pi Y. Exponential regulation of the anti-collocatedly disturbed cage in a wave PDE-modeled ascending cable elevator. Automatica, 2018, 95: 122-136 CrossRef Google Scholar

[40] De Queiroz M S, Dawson D M, Nagarkatti S P, et al. Lyapunov-based Control Of Mechanical Systems. New York: Springer Science + Business Media, 2012. Google Scholar

[41] Bialy B J, Chakraborty I, Cekic S C. Adaptive boundary control of store induced oscillations in a flexible aircraft wing. Automatica, 2016, 70: 230-238 CrossRef Google Scholar

[42] Wang C, Wen C, Lin Y. Decentralized adaptive backstepping control for a class of interconnected nonlinear systems with unknown actuator failures. J Franklin Institute, 2015, 352: 835-850 CrossRef Google Scholar

[43] Ji N, Liu J. Adaptive actuator fault-tolerant control for a three-dimensional Euler-Bernoulli beam with output constraints and uncertain end load. J Franklin Institute, 2019, 356: 3869-3898 CrossRef Google Scholar

[44] RAHN C D. Mechatronic control of distributed noise and vibration. Berlin Heidelberg: Springer-Verlag, 2001. Google Scholar

[45] Xiao B, Hu Q, Zhang Y. Fault-Tolerant Attitude Control for Flexible Spacecraft Without Angular Velocity Magnitude Measurement. J Guidance Control Dyn, 2011, 34: 1556-1561 CrossRef ADS Google Scholar

[46] Xie G, Shangguan A, Fei R. Motion trajectory prediction based on a CNN-LSTM sequential model. Sci China Inf Sci, 2020, 63: 212207 CrossRef Google Scholar

[47] Liu L, Liu Y J, Li D. Barrier Lyapunov Function-Based Adaptive Fuzzy FTC for Switched Systems and Its Applications to Resistance-Inductance-Capacitance Circuit System.. IEEE Trans Cybern, 2020, 50: 3491-3502 CrossRef PubMed Google Scholar

[48] Zhou T, Chen M, Yang C. Data fusion using Bayesian theory and reinforcement learning method. Sci China Inf Sci, 2020, 63: 170209 CrossRef Google Scholar

[49] Yu X, He W, Li Y. Adaptive NN impedance control for an SEA-driven robot. Sci China Inf Sci, 2020, 63: 159207 CrossRef Google Scholar

  • Table 1  

    Table 1Adaptive fault tolerant control scheme for a 3D flexible spacecraft

    Plant Description
    Equations of motion Governing equations (14) and (15) and boundary conditions (16)
    Assumptions Assumptions assum1assum3
    Defined new variables $~l_{i}=\inf~_{t~\geq~0}~\sum_{j=1}^{m_{i}}\left|\varrho_{i,~j}\right|~\sigma_{i,~j}(t),~~~p_{i}=\frac{1}{l_{i}},~~~g_{i}=\sup~_{t~\geq~0}\left\|\delta_{i}(t)\right\|$
    Control input $\tau_{i}=\sum_{j=1}^{m_{i}}~\varrho_{i,j}~u_{i,~j}=\sum_{j=1}^{m_{i}}~\varrho_{i,j}~\sigma_{i,~j}(t)~v_{i,~j}(t)+\sum_{j=1}^{m_{i}}~\varrho_{i,j}~\overline{u}_{i,~j}(t)$
    Auxiliary signals $\zeta_i(t)$ satisfying $\int_{0}^{+\infty}~\zeta_{i}(t)~{\rm~d}~t<+\infty$
    Designed control scheme $v_{i,~j}(t)=-\operatorname{sign}\left(\varrho_{i,j}\right)~\overline{v}_{i},~\overline{v}_{i}=\frac{\omega_{i}~\hat{p}_{i}^{2}~\overline{\alpha}_{i}^{2}}{\sqrt{\omega_{i}^{2}~\hat{p}_{i}^{2}~\overline{\alpha}_{i}^{2}+\zeta_{i}^{2}(t)}}$
    Parameter update laws $\dot{\hat{p}}_{i}=\gamma_{p_{i}}~\omega_{i}~\overline{\alpha}_{i}, \dot{\hat{g}}_{i}=\gamma_{g_i}~\omega_{i}~\xi_{i}, \dot{\hat{d}}_{i}=\gamma_{d_i}~\omega_{i}~$
    Design parameters $c_i$ ($i$=1,2,3), $\alpha$, $\delta_1$ and $\delta_2$ satisfying (56) and (57)
  • Table 2  

    Table 2Parameters of a 3D flexible spacecraft

    Parameter Description Value
    $L$ The length of the panel 18.8 ft
    $E{I_y}$ The flexural rigidity of the panel in $O~Y_b$ axis 3550.8 lb$\cdot\textrm{ft}^2$
    $E{I_z}$ The flexural rigidity of the panel in $O~Z_b$ axis 3550.8 lb$\cdot\textrm{ft}^2$
    $I_{s1}$ The inertia tensor of the rigid satellite in $O~X_o$ axis 645 slug$\cdot\textrm{ft}^2$
    $I_{s2}$ The inertia tensor of the rigid satellite in $O~Y_o$ axis 100 slug$\cdot\textrm{ft}^2$
    $I_{s3}$ The inertia tensor of the rigid satellite in $O~Z_o$ axis 669 slug$\cdot\textrm{ft}^2$
    $\rho$ The mass density of the panel 2.86e-2 slug/ft
    $\gamma_b$ Panel damping 0.01 N$\cdot$s/ft

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