基于LQR理论的电磁轴承控制系统鲁棒稳定性分析

Robust Stability Analysis of the Active Magnetic Bearings Control System Based on the LQR Theory

线性最优控制理论中采用的数学模型与实际物理模型总存在一定的差异,据此设计的控制参数不一定能满足实际系统稳定性的需要。针对这一问题,提出了一种分析线性最优控制系统鲁棒稳定界限的方法,并将其应用在基于LQR理论的电磁轴承控制系统的鲁棒稳定性分析中。结果表明:电磁轴承控制系统对模型矩阵摄动的鲁棒性在参数α确定时仅与加权矩阵Q、R的相对大小有关;选择较小的参数α和相对于加权矩阵R较大的Q阵、传感器采取外侧安装方式有利于提高电磁轴承控制系统对模型矩阵摄动的鲁棒性。此结论为主动电磁轴承控制器的设计和结构的设计提供了一定的理论依据。

In this paper,it was proposed that a method of analyzing the robustness of the linear quadratic state optimal control system with the view of solving the problem that the control parameters don＇t meet the necessity of the practical system stability because the mathematical model adoped in the design of LQR system is different from the practical system. And this method was applied in the analysis of robust stability bound of the magnetic bearings control system based on the LQR theory . The results show that the model perturbation robustness of the magnetic bearings control system is only relative to the comparative value of the weight matrix Q and R with the parameter a confirmed. It can enhance the matrix perturbation robustness of system with the small parameter a ,the weight matrix Q larger than R and the outer-located sensors. The analytical results provided the theory foundation for the controller design and structure of active magnetic bearings.