张国山，李现磊
AuthorsHTML:张国山，李现磊
AuthorsListE:Zhang Guoshan，Li Xianlei
AuthorsHTMLE:Zhang Guoshan，Li Xianlei
Unit:天津大学电气自动化与信息工程学院
Unit_EngLish:School of Electrical and Information Engineering，Tianjin University，Tianjin 300072，China
Abstract_Chinese:针对传统趋近律存在的抖振问题，以及全局收敛速度较为缓慢的情况，本文通过对以往的多种幂次趋近律和指数趋近律进行对比分析，提出了一种新型幂次趋近律．该趋近律在以往幂次趋近律的基础上通过函数改进和新型函数的引入，实现了系统的快速收敛和无抖振．首先，新型幂次趋近律通过改进变指数项，在避免了系统收敛到滑模面时变指数项存在的抖振问题的同时，保留了变指数项在系统远离滑模面时优于比例项和幂次项的快速收敛性．其次，新型幂次趋近律引入了正切函数，在初始状态可知的条件下通过调节正切函数参数能够实现系统更快速的收敛性．本文通过理论证明了新型幂次趋近律能够实现系统快速收敛到滑模面且无抖振，并提出了趋近律中的参数设定方法，保证了系统在有界扰动条件下能够实现有限时间内快速地收敛到期望稳态精度．最后，通过对多种趋近律进行对比仿真验证了该趋近律的有效性，并通过系统在有界扰动下的仿真验证了参数设定方法的正确性，航天器姿态机动控制仿真进一步验证了新型幂次趋近律和参数设定方法的有效性和正确性．
Abstract_English:To address the chattering problem and slow global convergence speed of the traditional reaching law，this study compared and analyzed the previous power law and exponential reaching law and proposed a new power reaching law，which achieved chatter-free fast global convergence of the system through the improvement of functions and introduction of new functions on the basis of the previous power reaching law. First，by improving a variable exponential term，the new power reaching law avoided the chattering problem of the exponential term when the system converged to the sliding surface，and retained the fast global convergence of the variable exponential term over the proportional and power terms when the system was far from the sliding surface. Second，the new power reaching law introduced a tangent function，which could achieve fast global convergence of the system by adjusting the tangent function parameters under the condition that the initial state is known. This study proved through the theory that the new power reaching law enables the system to quickly converge to the sliding surface without chattering and proposed the parameter setting method for the reaching law to ensure that the system can quickly converge to the desired steady-state accuracy within a finite time in case of bounded disturbance in the system. Finally，the effectiveness of the reaching law is verified by comparing simulations of multiple reaching laws. The correctness of the parameter setting method is verified by conducting simulations of the system under bounded disturbance. The spacecraft attitude control simulation further verified the validity and correctness of the new power reaching law and parameter setting method.
Keyword_Chinese:滑模控制；正切函数；幂次趋近律；全局快速收敛
Keywords_English:sliding mode control；tangent function；power reaching law；global fast convergence

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