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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 robust pole assignment design problem for second-order linear systems with vibrations is studied. Based on the degree of freedom provided by the parameter solution of the matrix equation, a parametric expression of all state feedback control laws for the second order linear closed-loop system with the desired pole is given. The parametric expression of feedback control law is used to parameterize the error index which is used to measure the robustness of the system. Therefore, the robust pole assignment problem is transformed into the minimization of the error index. The robust pole placement design algorithm for solving this second-order linear system with vibration is given. The algorithm does not include the “return” process, which is convenient for engineering application. Numerical examples and simulation results show that the algorithm is simple and effective.