振动二阶线性系统的鲁棒特征结构配置设计及其仿真

Robust eigenstructure assignment design in vibration second-order linear systems and its simulation

考虑了振动二阶线性系统的鲁棒特征结构配置设计问题。基于振动矩阵方程的参数化解,提出了振动二阶线性系统的状态反馈特征结构配置设计参数化方法。该参数化方法给出了状态反馈控制律的参数化表达式,其所含参数向量为控制系统设计提供了全部自由度。利用该参数化法提供的自由度,给出了振动二阶线性系统鲁棒特征结构配置问题的优化求解方法,其中优化的是衡量系统鲁棒性的灵敏度指标。数值算例及其仿真结果表明,所提振动二阶线性系统的状态反馈特征结构配置算法和鲁棒特征结构配置算法简单且有效,便于工程应用。

The design problem of robust eigenstructure assignment in a class of vibration second-order linear systems is investigated. Based on the parametric solutions to the vibration matrix equation, a parametric method of state feedback eigenstructure assignment in the vibration second-order linear system is presented. The pro- posed parametric method gives the parametric expression for all the state feedback control law, whose parameter vectors offer all the design degrees of freedom. Based on the degrees of freedom offered by the parametric meth- od, an optimization method to solve the robust eigenstructure assignment in the vibration second-order linear systems is pointed out, in which the sensitivity performances to measure the system＇s robustness are optimized. An illustrative example and its simulation results show the algorithms of state feedback eigenstructure assignment and robust eigenstructure assignment in vibration second-order linear systems are simple and effective, thus they are convenient to use in engineering.