矩阵二阶系统的鲁棒极点配置

Robust Pole Assignment in Matrix Second-order Linear Systems

直接在矩阵二阶框架下,利用特征结构配置参数化方法,研究矩阵二阶线性系统的鲁棒极点配置问题.将两种测量闭环特征值灵敏度方法有机地结合起来,给出一个新的优化性能指标,此指标的优化过程完全依赖于特征结构配置中的设计自由度.为进一步提高闭环系统的鲁棒稳定性,闭环极点也作为设计自由度的一部分参与优化.数值例子分析结果表明了该方法的有效性.

Robust pole assignment of matrix second-order linear systems is investigated directly in the matrix second order framework via a complete parametric eigenstructure assignment approach. Based on the combination of the two measurement approaches for closed-loop eigenvalue sensitivities, an optimized performance index is proposed. Due to the advantages of the eigenstructure assignment result, the optimized procedures of the performance index are totally dependent on design degrees of freedom provided in eigenstructure assignment. Also the closed-loop eigenvalues may be easily taken as a part of the design parameters and optimized within certain desired fields on the complex plane to improve robustness. Finally, an example of mass-spring system shows the effect of the proposed approach.