滑模控制快速分段幂次趋近律设计与分析
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摘要
针对滑模变结构控制中出现的抖振问题,提出了一种分段幂次趋近律。该趋近律采用分段函数方式设计,具有较快的收敛速率、较多的调节参数,并且针对不同阶段的趋近律分开设计互不影响。理论证明了该趋近律达到滑模面时无抖振、固定时间收敛,详细推导出了收敛时间的表达式。在系统存在不确定性和外界干扰时能收敛于干扰稳定界,求出了干扰稳定界范围,给出了各参数对收敛速率和干扰稳定界的影响程度。以小卫星姿态机动控制为例,通过对比仿真实验,证明了所提趋近律的优越性。
A piecewise power reaching law of sliding mode control is proposed to solve the chattering problem.The reaching law is designed by piecewise function.It has a faster convergence speed and more adjustment parameters,and the reaching law of different stages does not interfere with each other.It is proved that the system has no chattering phenomenon and can converge in fixed-time,and the convergence time is derived in detail.In the presence of uncertainties and external disturbances,the system can converge to the disturbance stability boundary,and the range is given.The influence of parameters on the reaching speed and disturbance stability boundary is given.The proposed reaching law is applied in the attitude control system of small satellite.Simulation results show the superiority of the proposed reaching law.
A piecewise power reaching law of sliding mode control is proposed to solve the chattering problem.The reaching law is designed by piecewise function.It has a faster convergence speed and more adjustment parameters,and the reaching law of different stages does not interfere with each other.It is proved that the system has no chattering phenomenon and can converge in fixed-time,and the convergence time is derived in detail.In the presence of uncertainties and external disturbances,the system can converge to the disturbance stability boundary,and the range is given.The influence of parameters on the reaching speed and disturbance stability boundary is given.The proposed reaching law is applied in the attitude control system of small satellite.Simulation results show the superiority of the proposed reaching law.
引文
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[24]廖瑛,杨雅君,王勇.滑模控制的新型双幂次组合函数趋近律[J].国防科技大学学报,2017,39(3):105-110.LIAO Y,YANG Y J,WANG Y.Novel double power combination function reaching law for sliding mode control[J].Journal of National University of Defense Technology,2017,39(3):105-110.
[25]蒲明,蒋涛,付克昌.输入受限约束下的无抖振有限时间稳定趋近律设计[J].控制与决策,2018,33(1):135-142.PU M,JIANG T,FU K C.Finite time stable chattering-free reaching law design with bounded input[J].Control and Decision,2018,33(1):135-142.
[26]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社,1996:241-254.GAO W B.Theory and design method for variable sliding mode control[M].Beijing:Science Press,1996:241-254.
[2]LI H,SHI P,YAO D.Adaptive sliding mode control of Markov jump nonlinear systems with actuator faults[J].IEEE Trans.on Automatic Control,2017,62(4):1933-1939.
[3]BAEK J,JIN M,HAN S.A new adaptive sliding-mode control scheme for application to robot manipulators[J].IEEETrans.on Industrial Electronics,2016,63(6):3628-3637.
[4]CUI R,CHEN L,YANG C,et al.Extended state observerbased integral sliding mode control for an underwater robot with unknown disturbances and uncertain nonlinearities[J].IEEETrans.on Industrial Electronics,2017,64(8):6785-6795.
[5]VAIDYANATHAN S,AZAR A T.Hybrid synchronization of identical chaotic systems using sliding mode control and an application to vaidyanathan chaotic systems[J].IEEE Trans.on Medical Imaging,2015,17(1):549-569.
[6]GUAN P,LIU X J,LIU J Z.Adaptive fuzzy sliding mode control for flexible satellite[J].Engineering Applications of Artificial Intelligence,2005,18(4):451-459.
[7]HUANG X,ZHANG C,LU H,et al.Adaptive reaching law based sliding mode control for electromagnetic formation flight with input saturation[J].Journal of the Franklin Institute,2016,353(11):2398-2417.
[8]QIAN R,LUO M,SUN P.Improved nonlinear sliding mode control based on load disturbance observer for permanent magnet synchronous motor servo system[J].Advances in Mechanical Engineering,2016,8(4):1-12.
[9]KOMMURI S K,RATH J J,VELUVOLU K C.Sliding mode based observer-controller structure for fault-resilient control in DC servomotors[J].IEEE Trans.on Industrial Electronics,2018,65(1):918-929.
[10]CHAKRABARTY S,BANDYOPADHYAY B.A generalized reaching law for discrete time sliding mode control.[J].Automatica,2015,52(C):83-86.
[11]CHAKRABARTY S,BANDYOPADHYAY B.A generalized reaching law with different convergence rates[J].Automatica,2016,63(C):34-37.
[12]LIU X,SHAN Z,LI Y.Dynamic boundary layer based neural network quasi-sliding mode control for soft touching down on asteroid[J].Advances in Space Research,2017,59(8):2173-2185.
[13]NI J,LIU L,LIU C,et al.Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system[J].IEEE Trans.on Circuits&Systems II Express Briefs,2017,64(2):151-155.
[14]YANG H,BAI X,BAOYIN H.Finite-time control for asteroid hovering and landing via terminal sliding-mode guidance[J].Acta Astronautica,2017,132(C):78-89.
[15]SUN L,ZHENG Z.Finite-time sliding mode trajectory tracking control of uncertain mechanical systems[J].Asian Journal of Control,2017,19(1):399-404.
[16]YAN W,HOU S,FANG Y,et al.Robust adaptive nonsingular terminal sliding mode control of MEMS gyroscope using fuzzy-neural-network compensator[J].International Journal of Machine Learning&Cybernetics,2017,8(4):1-13.
[17]MOHAMMADI A R,SHABBOUEI HAGH Y,PALM R.Robust control by adaptive non-singular terminal sliding mode[J].Engineering Applications of Artificial Intelligence,2017,59(C):205-217.
[18]ZHANG Y,YAO Z,YAO Z,et al.An analysis of the stability and chattering reduction of high-order sliding mode tracking control for a hypersonic vehicle[J].Information Sciences,2016,348(C):25-48.
[19]OLIVEIRA J,OLIVEIRA P M,BOAVENTURA-CUNHAJ,et al.Chaos-based grey wolf optimizer for higher order sliding mode position control of a robotic manipulator[J].Nonlinear Dynamics,2017,90(2):1-10.
[20]PANATHULA C B,ROSALES A,SHTESSEL Y B,et al.Closing gaps for aircraft attitude higher order sliding mode control certification via practical stability margins identification[J].IEEE Trans.on Control Systems Technology,2018,26(3):2020-2034.
[21]YU S H,YU X H,SHIRINZADEH B,et al.Continuous finitetime control for robotic manipulators with terminal sliding mode[J].Automatica,2005,41(11):1957-1964.
[22]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,2013,28(2):289-293.ZHANG H X,FAN J S,MENG F,et al.A new double power reaching law for sliding mode control[J].Control and Decision,2013,28(2):289-293.
[23]张瑶,马广富,郭延宁,等.一种多幂次滑模趋近律设计与分析[J].自动化学报,2016,42(3):466-472.ZHANG Y,MA G F,GUO Y N,et al.A multipower reaching law of sliding mode control design and analysis[J].Acta Automatica Sinica,2016,42(3):466-472.
[24]廖瑛,杨雅君,王勇.滑模控制的新型双幂次组合函数趋近律[J].国防科技大学学报,2017,39(3):105-110.LIAO Y,YANG Y J,WANG Y.Novel double power combination function reaching law for sliding mode control[J].Journal of National University of Defense Technology,2017,39(3):105-110.
[25]蒲明,蒋涛,付克昌.输入受限约束下的无抖振有限时间稳定趋近律设计[J].控制与决策,2018,33(1):135-142.PU M,JIANG T,FU K C.Finite time stable chattering-free reaching law design with bounded input[J].Control and Decision,2018,33(1):135-142.
[26]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社,1996:241-254.GAO W B.Theory and design method for variable sliding mode control[M].Beijing:Science Press,1996:241-254.