振动二阶线性系统的鲁棒极点配置设计及其仿真分析

Design of Robust Pole Assignment in Vibrating Second-order Linear Systems and Its Simulation Analysis

研究了振动二阶线性系统的鲁棒极点配置设计问题。基于矩阵方程参数化解提供的自由度,给出了能使闭环振动二阶线性系统具有希望极点的所有状态反馈控制律的参数化表达式。利用状太反馈控制律的参数化表达式,将衡量系统鲁棒性的误差指标参数化,从而鲁棒极点配置问题就转化为误差指标的最小化问题。给出了求解该振动二阶线性系统的鲁棒极点配置设计算法,该算法不包含"返回"过程,故便于工程应用。数值算例及其仿真结果表明该算法的简单及有效性。

The design problem of robust pole assignment in a class of vibrating second-order linear systems was investigated. Based on the degrees offered by the parametric solutions of a matrix equation, the parametric expressions of all the state feedback control laws were proposed. By utilizing the parametric expressions of the state feedback control laws, the error performance of measuring the system＇s robustness was parameterized. Thus the design problem of robust pole assignment was changed into a problem of minimizing the error index. An algorithm to solve the problem of robust pole assignment in vibrating second-order linear systems was proposed, which does not include the ＂going back＂ course and is convenient to use in engineering. An illustrative example and its simulation results show the simpliness and effectiveness of the proposed algorithm.