一类非线性系统的滑模振动主动控制

Active Sliding Mode Control of Vibration in a Class of Nonlinear System

基于滑模控制理论 ,研究了一类外激励作用下多自由度非线性系统的振动主动控制问题。利用滑模可达条件建立了滑模控制律。为解决外激励不可测所带来的控制律的不确定性问题 ,本文利用已知的外激励的上界这一参数消除了控制律的不确定性。利用 H∞最优控制论设计了切换函数。数值仿真结果表明 ,本文给出的控制方法能明显减小振动的幅值。特别是在外激励满足所谓的匹配条件下 。

Based on the theory of sliding mode control, active control of vibration in a class of nonlinear system with multi degrees of freedom under disturbance forces is studied. Sliding control law is derived from reaching conditions of sliding mode. The estimated upper bounds on magnitude of disturbance forces are adopted to eliminate uncertainties of control law due to unmeasurable disturbance forces. Sliding surface is designed by H ∞ optimal control theory. Simulational results show that vibration amplitudes of the controlled and uncontrolled degrees of freedom can be greatly reduced by using the proposed control strategy, especially in the case that disturbance forces meet the matching condition.