一类非线性系统准滑模控制的稳态误差分析

针对一类具有未知控制增益的不确定非线性系统准滑模跟踪控制,通过分析跟踪误差和滑模变量之间的关系,利用有界输入有界输出稳定的思想,分别推导了采用Slotine形式的传统滑模面和传统积分滑模面时系统的稳态跟踪误差的界.将其与现有的几种方法进行比较,该方法求得的稳态跟踪误差界更精确.根据给定的稳态跟踪误差要求,可设计出适合抑制抖振的饱和函数.通过仿真算例验证了所提出方法的有效性.

Steady- state error analysis of quasi sliding mode control for a class of nonlinear systems

For the quasi sliding mode tracking control of a class of uncertain nonlinear systems with unknown control
gain, after analyzing the relationship between tracking error and sliding variable and using the idea of BIBO stability, the
boundedness of the steady-state error is derived when using Slotine form conventional sliding surface and conventional
integral sliding surface, respectively. Compared with known boundedness of steady-state error computed by using current
methods, the boundedness of steady-state error derived with the proposed method is more accuracy. Furthermore, by
specifying the tracking error that is required, an appropriate saturation function to eliminate chattering is designed.
Simulations results show the effectiveness of the proposed method.