一种新型复合滑模趋近律设计与分析

Design and analysis of a new compound sliding mode reaching law

针对传统幂次趋近律存在的抖振以及全局收敛缓慢的问题,提出一种新型复合滑模趋近律,该趋近律通过引入正切函数以及对传统幂次趋近律的改进,实现趋近律的快速收敛和无抖振特性.首先,引入正切函数,在初始状态已知的情况下使系统更快地收敛;其次,通过设计的趋近律改进传统幂次趋近律中含符号函数乘积项容易引起的抖振;然后,理论证明新型复合趋近律能够快速收敛且无抖振,并推导出趋近速率及稳态误差界;最后,以直线磁悬浮同步电动机磁悬浮系统为例,与双幂次趋近律和多幂次趋近律仿真对比,进一步验证新型复合趋近律能够明显缩短系统的动态过程并消除抖振,且存在模型不确定性及外加干扰作用下,系统仍能迅速地收敛到平衡点附近的领域内.

In order to solve the problem of chattering and slow global convergence of the traditional power law, a new compound sliding mode law is proposed, which introduces a tangent function and improves the traditional power law,thus the fast convergence and chattering-free characteristics of the reaching law are realized. Firstly, a tangent function is introduced, which can make the system converge faster when the initial state is known, the reaching law is designed to improve the chattering caused by the product term of the symbolic function in the traditional power reaching law. Then,the convergence rate and steady-state error bounds of the new compound reaching law are derived. Finally, taking the magnetic levitation system of a linear magnetic levitation synchronous motor as an example, the simulation results show that the new compound reaching law can obviously shorten the dynamic process of the system and eliminate chattering,and in the presence of model uncertainty and external disturbance, the system can converge rapidly to the region near the equilibrium point.