基于自适应趋近律的滑模控制方法
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摘要
为了提高系统的动态性能和稳态精度,在幂次趋近律和变速趋近律基础上提出一种自适应趋近律.当系统状态变量距离滑模面较远时,幂次项起主要作用,保证趋近速度足够大;当系统状态变量距离滑模面较近时,变速项起主要作用,随系统状态变量自适应调节滑模面参数,直至系统状态轨迹运行到稳定点.趋近律具有二阶滑模特性,可在有限时间内到达滑模面.当系统出现有界外部干扰时,系统状态及其导数可快速收敛到平衡点附近的邻域内.仿真结果表明:提出的自适应趋近律能够有效提高系统动态性能和稳态精度,增强系统鲁棒性.
A adaptive reaching law was proposed on the basis of exponential reaching law and variable speed reaching law,in order to improve dynamic quality and robustness of the system.When system state variable was far away from sliding mode surface,the exponential term played a major role,ensuring that the approach speed was high enough.When system state variable was closer to sliding mode surface,variable speed term played a major role.Sliding mode surface parameters were adjusted adaptively with system state variables until system state trajectory ran to the stable point. The reaching law had the characteristic of second-order sliding mode,which could reach the sliding surface in a limited time.When there was bounded external interference in the system,system state and its derivative could quickly converge to the neighborhood near the equilibrium point. Simulation results show that the proposed adaptive reaching law can effectively improve dynamic performance,steady-state accuracy and enhance robustness of the system.
A adaptive reaching law was proposed on the basis of exponential reaching law and variable speed reaching law,in order to improve dynamic quality and robustness of the system.When system state variable was far away from sliding mode surface,the exponential term played a major role,ensuring that the approach speed was high enough.When system state variable was closer to sliding mode surface,variable speed term played a major role.Sliding mode surface parameters were adjusted adaptively with system state variables until system state trajectory ran to the stable point. The reaching law had the characteristic of second-order sliding mode,which could reach the sliding surface in a limited time.When there was bounded external interference in the system,system state and its derivative could quickly converge to the neighborhood near the equilibrium point. Simulation results show that the proposed adaptive reaching law can effectively improve dynamic performance,steady-state accuracy and enhance robustness of the system.
引文
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[2] FRANCK P,EMMANUEL M,ALAIN G,et al.Robust output feedback sampling control based on second-order sliding mode[J].Automatica,2010,46(6):1096-1100.
[3] LIAN R J.Adaptive self-organizing fuzzy sliding-mode radial basis-function neural-network controller for robotic systems[J].IEEE Transactions on Industrial Electronics,2014,61(3):1493-1503.
[4] SLOTINE J J E,LI W.Applied nonlinear control[M].New York:Prentice-Hall Englewood Cliffs,1991.
[5] LEVANT A.Universal single-input-single-output(SISO)sliding-mode controllers with finite-time convergence[J].IEEE Trans on Automatic Control,2001,46(9):1447-1451.
[6] LAGHROUCHE S,PLESTAN F,GLUMINEAU A.Higher order sliding mode control based on integral sliding mode[J].Automatica,2007,43(3):531-537.
[7] DEFOORT M,FLOQUET T,KOKOSY A,et al.A novel higher order sliding mode control scheme[J].Systems&Control Letters,2009,58(2):102-108.
[8] SIRARAMIREZ H.On the dynamic sliding mode control of nonlinear systems[J].Int J of Control,1993,57(5):1039-1061.
[9] YU S,YU X,SHIRINZADEH B,et al.Continuous finite time control for robotic manipulators with terminal sliding mode[J].Automatica,2015,41(11):1957-1964.
[10] BANDYOPADHYAY B,FULWANI D,PARK Y J.A robust algorithm against actuator saturation using integral sliding mode and composite nonlinear feedback[C]//Proceedings of the 17th IFAC World Congress.Seoul:IFAC,2008:14174-14179.
[11]梅红,王勇.快速收敛的机器人滑模变结构控制[J].信息与控制,2009,38(5):552-557.
[12]张合新,范金锁,孟飞,等.一种新型滑模控制双幂次趋近律[J].控制与决策,2009,38(5):289-293.
[13]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社,1996.
[14]宋立忠,温虹,姚琼翠.离散变结构控制系统的变速趋近律[J].海军工程学院学报,1999(3):16-21.
[15] MARKS G M,SHTESSEL Y B,GRATT H.Effects of high order sliding mode guidance and observers on hitto-kill Interceptions[C]//Proc of AIAA Guidance,Navigation,and Control Conf and Exhibit.San Francisco:IEEE,2005:5960-5967.