基于非线性函数提出了一种新型离散非线性指数趋近律,实现切换项系数随系统运动点到切换面的距离由大到小非线性变化,使系统运动点到达过程由快到慢的变速控制;设计了基于离散非线性指数趋近律的控制器,研究了几种离散趋近律存在的差异和问题,通过与几种离散趋近律在到达时间和抖振幅度的比较,证明非线性指数趋近律不仅缩短了到达时间,加快了趋近过程,间接增强了系统鲁棒性,而且进一步降低了系统抖振,改善了控制品质。

A novel discrete-time nonlinear exponential reaching law with a nonlinear function was proposed. The switching coefficients decreased nonlinearly as the distance between system mobile point and switching surface becoming closer step by step. The controller based on discrete-time nonlinear exponential reaching law was designed, and the differences and problems of some exponential reaching laws were analyzed. The comparison with some other discrete-time reaching laws shows that the reaching time of discrete-time nonlinear exponential reaching law has been reduced, the system robustness has been improved indirectly, the chattering has been reduced, and the dynamic quality of the control system has been enhanced significantly.