基于Ackermann公式的滑模控制设计方法

A new sliding mode control design method based on the Ackermannformula

从滑模变结构控制的机理出发,设计了具有理想动态特性和较强鲁棒性的滑模控制器。该方法使用了Ackermann公式来设计滑模控制,从而可以使滑模控制的不连续超平面以简单的方式表达。在此基础上引入了Butterworth滤波器传递函数的极点作为系统的理想特征值,使闭环系统及滑模面达到了较理想的动态特性,并采用Sigmoid函数来取代开关函数更有效的抑制滑模控制的抖动;通过倒立摆控制的仿真实例验证了该方法的控制效果,且在系统参数不确定时,取得较快的收敛速度和较好的控制性能。所设计的控制器在系统动态过程中显示改进型Butterworth滤波器的动态特性,静态时在有限时间内到达期望的滑模面的邻域,整个系统具有较为理想的动态特性。

Based on the mechanism of sliding mode variable control, a controller which has the desired dynamic behavior and strong robustness has been designed. The discontinuity plane for sliding mode control may be found in an explicit form by means of the Ackermann formula. It is shown that the sliding mode has the desired dynamic behavior using the pole of a Butterworth filter and that Sigmoid functions can restrain chattering of the systems. This method was employed to control an inverted pendulum system and simulations are given for when the plant contains uncertain parameters. The method has better control performance than previous methods. The controller in the dynamic process shows the particularity of the improved Butterworth filter and can quickly achieve the desired sliding mode surface during the steady state. The systems have the desired dynamic characteristics.