二阶滑模变结构控制系统的滑模到达条件

Reaching condition of sliding mode in second-order sliding mode variable structure control systems

为了削弱经典滑模变结构控制系统的抖振、简化二阶滑模变结构控制器的计算过程,提出了一个二阶滑模变结构控制系统的滑模到达条件.运用李雅普诺夫稳定性理论和常微分方程理论,得到了控制系统在该到达条件下的两个结果:系统相轨迹能实现在有限时间内收敛于滑动模态,控制系统具有较好的鲁棒性.最后通过该到达条件设计了系统的变结构控制器.仿真结果表明该到达条件能有效抑制系统抖振,并且具有良好的鲁棒性.

In order to suppress the system chattering exist in the classical sliding variable structure control and simplify the computational process of second-order sliding variable structure controller, a reaching condition of second-order sliding variable structure control was proposed. When the control system was under the reaching condition, two results were got by applying the ordinary differential e- quations theory and Lyapunov stability theory： the one is the system phase trajectory can converge to the sliding mode in finite time; the other is the control system has excellent robustness. Finally, a system variable structure controller was designed with the reaching condition. Simulation results show that the reaching condition with excellent robustness can suppress the system chattering effectively.