基于区间分析的参数不确定系统PID鲁棒控制器设计

针对区间对象PID鲁棒控制器设计问题，提出了一种基于广义Kharitonov定理和区间分析集逆算法的设计方法。该方法根据广义Kharitonov定理将区间对象的鲁棒稳定控制器综合问题转化为多个顶点对象同时稳定的控制器综合问题，根据劳斯判据得到与控制器参数相关的不等式组，采用基于区间分析的集逆算法求解该不等式组得到PID鲁棒控制器参数。数值算例表明所提出的设计方法可以以任意设定精确度逼近使得整个区间对象族稳定的PID控制器参数域，与传统图解法相比求得的结果是可靠的，同时该方法能够根据集逆算法解集情况准确判断假定的控制器是否可行。

Robust design of PID controller for interval plants based on interval analysis

The robust design of PID controller for interval plants is considered. A new approach is presen- ted which is based on the generalized Kharitonov theorem and the algorithm of set inversion via interval analysis. According to the generalized Kharitonov theorem, robust PID controller design problem for interval plants can be solved by stabilizing the corresponding extreme plants. Then the Roth tables are established and the problem is formulated as a set of inequalities, which are solved by the algorithm of set inversion via interval analysis. Numerical examples show that the proposed method can character the set of all values of the controller parameters that guarantees the robust stability with any supposed accuracy and its solution is reliable. Furthermore, it can find if the supposed controller is feasible or not.