二阶动力学系统模型的跟踪设计

考虑了基于分散状态反馈控制律的二阶动力学系统输出渐近跟踪设计,该控制律包括被控对象状态和参考模型状态两部分。给出了问题解的存在条件:两个矩阵方程,其中一个为二阶Sylvester矩阵方程。给出了所有控制器增益阵的完全参数化表达式。归纳出了二阶动力学系统模型参考输出跟踪控制律的设计算法。该算法直接基于原系统的参数矩阵,无须对系统增广或变换,仅涉及自由参数的选取和一些简单的代数运算,便于工程应用。仿真结果说明所给出的算法是有效的。

Tracking second-order dynamical systems

Output asymptotical tracking of a class of second-order dynamical systems based on decentralized state feedback control law is considered.The control law includes two parts,the controlled system state and the reference model state.First,the conditions for the existence of the solutions to the problem are given,which are two matrix equations,and one of them is second-order Sylvester matrix equation.Then complete parametric form of all controller gains is given.The algorithm for the model reference output tracking is concluded.This parametric method utilizes directly the original system data,so the method is simple and offers more convenience in control system designs.Simulations show the effectiveness of the proposed algorithm.