矩阵二阶线性系统的鲁棒渐近跟踪

Robust Asymptotic Tracking in Matrix Second-order Linear System

直接在矩阵二阶线性系统的框架下,研究结构参数不确定性二阶系统的鲁棒渐近跟踪问题.该问题可以分成两部分,即鲁棒反馈镇定器和前馈跟踪补偿器的设计问题.首先,利用特征结构配置和模型参考跟踪理论,在矩阵二阶系统的框架下给出了鲁棒反馈镇定器和前馈跟踪补偿器的参数化设计方法.建立了闭环极点关于开环系统矩阵参数摄动灵敏度的参数化表达式,并在此基础上给出了一个简单、有效的算法,通过该算法利用系统中所有自由度来优化所得控制器.最后,航天器交会仿真实验验证了算法的有效性.

Robust asymptotic tracking problem of second-order system with structural parameter uncertainties is investigated directly in the matrix second-order linear system framework. It is shown that the problem can be decomposed into two parts, that is, the design problems of robust feedback stabilizing and feed-forward tracking compensation controller. Based on eigenstructure assignment approach and the model reference tracking theory, a parametric design approach for ro- bust feedback stabilizing and feed-forward tracking compensation controllers is proposed in the matrix second order system framework, and insightful parameterizations of the closed loop eigenvalues sensitivities to the perturbed elements in the open loop system matrices are obtained. Based on the above methods, a simple and effective algorithm is then proposed. All the design degrees of freedom are used to optimize the controller through the algorithm. Its effectiveness is verified by an spacecraft rendezvous example.