机械系统的快速有限时间跟踪控制及其在航天器交会中的应用（英文）
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摘要
针对一类具有匹配干扰的二阶机械系统,本文研究了快速有限时间跟踪控制问题.结合有限时间反步法和非奇异快速终端滑模,本文提出了一种新的快速有限时间控制律,并给出了控制器参数所需满足的充分条件以保证系统的快速有限时间稳定性.进一步地,在一定情形下,所设计的快速有限时间控制律能够退化为经典的反步法、有限时间控制律和非奇异快速终端滑模控制律.最终,将所设计的控制律应用于航天器交会系统,数值仿真结果验证了所提方法的有效性.
This paper investigates the fast finite-time tracking control problem for a class of second-order mechanical system with matched disturbance. By employing the finite-time backstepping design approach and nonsingular fast terminal sliding mode(NFTSM) concept, a new form of fast finite-time control(FFTC) approach is proposed and the sufficient conditions of the controller parameters are given, which can guarantee the fast finite-time stability(FFTS). Furthermore,the FFTC law can be reduced to the classical backstepping control(BSC) law, finite-time control(FTC) law and NFTSM control(NFTSMC) law in the particular situations, which validates the completeness of the work. The simulation results of the application to spacecraft rendezvous system have demonstrated the effectiveness of the proposed approach.
This paper investigates the fast finite-time tracking control problem for a class of second-order mechanical system with matched disturbance. By employing the finite-time backstepping design approach and nonsingular fast terminal sliding mode(NFTSM) concept, a new form of fast finite-time control(FFTC) approach is proposed and the sufficient conditions of the controller parameters are given, which can guarantee the fast finite-time stability(FFTS). Furthermore,the FFTC law can be reduced to the classical backstepping control(BSC) law, finite-time control(FTC) law and NFTSM control(NFTSMC) law in the particular situations, which validates the completeness of the work. The simulation results of the application to spacecraft rendezvous system have demonstrated the effectiveness of the proposed approach.
引文
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[19]XU B.Composite learning finite-time control with application to quadrotors.IEEE Transactions on Systems,Man,and Cybernetics Systems,2017:1-10.
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[25]YANG J,DING Z T.Global output regulation for a class of lower triangular nonlinear systems:a feedback domination approach.Automatica,2017,76:65-69.
[26]SUN Z Y,XUE L R,ZHANG K M.A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system.Automatica,2015,58:60-66.
[27]GAO F Z,YUAN F S.Adaptive finite-time stabilization for a class of uncertain high order nonholonomic systems.ISA Transactions,2015,54:75-82.
[28]SUN Z Y,YUN M M,LI T.A new approach to fast global finite-time stabilization of high-order nonlinear system.Automatica,2017,81:455-463.
[29]ZHANG F,DUAN G R.Robust adaptive integrated translation and rotation control of a rigid spacecraft with control saturation and actuator misalignment.Acta Astronautica,2013,86(3):167-187.
[30]HU Q L,LI B,QI J T.Disturbance observer based finite-time attitude control for rigid spacecraft under input saturation.Aerospace Science and Technology,2014,39:13-21.
[31]FEHSE W.Automated Rendezvous and Docking of Spacecraft.New York,USA:Cambridge University Press,2003.
[2]WANG Q,XUE A K.Robust control for spacecraft rendezvous system with actuator unsymmetrical saturation:a gain scheduling approach.International Journal of Control,2018,91(6):1241-1250.
[3]GUO Yong,SONG Shenmin,LI Xuehui.Attitude and orbit coupled control for non-cooperative rendezvous and docking.Control Theory&Applications,2016,33(5):638-644.(郭永,宋申民,李学辉.非合作交会对接的姿态和轨道耦合控制.控制理论与应用,2016,33(5):638-644.)
[4]YU S H,YU X H,SHIRINZADEH B,et al.Continuous finite-time control for robotic manipulators with terminal sliding mode.Automatica,2005,41(11):1957-1964.
[5]WANG S,WANG W H,XIONG S F.Impact angle constrained threedimensional integrated guidance and control for STT missile in the presence of input saturation.ISA Transactions,2016,64:151-160.
[6]KHALIL H K.Nonlinear Systems.3rd ed.Upper Saddle River,USA:Prentice-Hall,2002.
[7]KRSTI′C M,KOKOTOVI′C P V,KANELLAKOPOULOS I.Nonlinear and Adaptive Control Design.New York,USA:John Wiley,1995.
[8]SWAROOP D,HEDRICK J K,YIP P P,et al.Dynamic surface control for a class of nonlinear systems.IEEE Transactions on Automatic Control,2008,45(10):1893-1899.
[9]GAO W B,HUNG J C.Variable structure control of nonlinear systems:a new approach.IEEE Transactions on Industrial Eletronics,1993,40(1):45-55.
[10]YANG Xiaoqian,LI Jian,DONG Yi.A novel non-singular fast terminal sliding mode control of nonlinear systems with uncertain disturbances.Control Theory&Applications,2016,33(6):772-778.(杨晓骞,李健,董毅.非线性不确定系统的非奇异快速终端滑模控制.控制理论与应用,2016,33(6):772-778.)
[11]WANG D,HUANG J.Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strictfeedback form.IEEE Transactions on Neural Networks,2005,16(1):195-202.
[12]BHAT S P,BERNSTEIN D S.Continuous finite-time stabilization of the translational and rotational double integrators.IEEE Transactions on Automatic Control,1998,43(5):678-682.
[13]MORENO J A.A linear framework for the robust stability analysis of a generalized super-twisting algorithm.Proceedings of the 6th International Conference on Electrical Engineering,Computing Science and Automatic Control.New York:IEEE,2009:12-17.
[14]LEVANT A.Homogeneity approach to high-order sliding mode design.Automatica,2005,41(5):823-830.
[15]WU Y Q,YU X H,MAN Z H.Terminal sliding mode control design for uncertain dynamic systems.Systems&Control Letters,1998,34(5):281-287.
[16]FENG Y,YU X H,MAN Z H.Non-singular terminal sliding mode control of rigid manipulators.Automatica,2002,38(12):2159-2167.
[17]YU S H,DU J L,YU X H,et al.A novel recursive terminal sliding mode with finite-time convergence.Proceedings of the 17th World Congress,the International Federation of Automatic Control.Amsterdam:Elsevier,2008:5945-5949.
[18]YANG L,YANG J Y.Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems.International Journal of Robust Nonlinear Control,2011,25(15):1865-1879.
[19]XU B.Composite learning finite-time control with application to quadrotors.IEEE Transactions on Systems,Man,and Cybernetics Systems,2017:1-10.
[20]QIAN C J,LIN W A continuous feedback approach to global strong stabilization of nonlinear systems.IEEE Transactions on Automatic Control,2001,46(7):1061-1079.
[21]HUANG X,LIN W,YANG B.Global finite-time stabilization of a class of uncertain nonlinear systems.Automatica,2005,41(5):881-888.
[22]CHENG Y Y,DU H B,HE Y G,et al.Finite-time tracking control for a class of high-order nonlinear systems and its applications.Nonlinear Dynamics,2014,2(76):1133-1140.
[23]HOU M Z,ZhANG Z K,DENG Z Q,et al.Global robust finite-time stabilisation of unknown pure-feedback systems with input dead-zone non-linearity.IET Control Theory and Applications,2016,10(2):234-243.
[24]ZHANG Z K,DUAN G R,HOU M Z.Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity.Journal of Franklin Institute,2017,354(10):4073-4101.
[25]YANG J,DING Z T.Global output regulation for a class of lower triangular nonlinear systems:a feedback domination approach.Automatica,2017,76:65-69.
[26]SUN Z Y,XUE L R,ZHANG K M.A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system.Automatica,2015,58:60-66.
[27]GAO F Z,YUAN F S.Adaptive finite-time stabilization for a class of uncertain high order nonholonomic systems.ISA Transactions,2015,54:75-82.
[28]SUN Z Y,YUN M M,LI T.A new approach to fast global finite-time stabilization of high-order nonlinear system.Automatica,2017,81:455-463.
[29]ZHANG F,DUAN G R.Robust adaptive integrated translation and rotation control of a rigid spacecraft with control saturation and actuator misalignment.Acta Astronautica,2013,86(3):167-187.
[30]HU Q L,LI B,QI J T.Disturbance observer based finite-time attitude control for rigid spacecraft under input saturation.Aerospace Science and Technology,2014,39:13-21.
[31]FEHSE W.Automated Rendezvous and Docking of Spacecraft.New York,USA:Cambridge University Press,2003.