参数不确定系统鲁棒镇定控制器设计的鲁棒可靠性方法

Robust reliability method for stabilizing controller design of systems with uncertain parameters

用区间变量描述系统参数的不确定性,从可靠性角度研究不确定系统的稳定鲁棒性设计问题。基于二次稳定性准则,提出了参数不确定系统鲁棒镇定控制器设计的鲁棒可靠性新方法。依据该法设计的控制系统可满足稳定性意义上的鲁棒可靠性要求,并给出保证系统稳定性所要求的基本参数的最大鲁棒界限。所给公式完全基于线性矩阵不等式(LMI)方法,求解方便。适用于不确定参数的摄动范围准确已知和未知等情况。对实际算例的设计和模拟结果与现有结果的比较研究表明了在传统的控制器设计中,保守性的增加并不意味着可靠性的增加。从而也说明了所提方法是实用、有效和可行的。

Uncertain parameters of control system are represented by interval variables, the issue of robust stabilization of uncertain systems are studied from the new viewpoint of reliability. A new robust reliability method for stabilizing controller design of uncertain systems is presented based on quadratic stability criterion. A controller designed by the proposed method could satisfy requirement for robust reliability in the sense of quadratic stability, and the maximum robustness bounds of the basic uncertain parameters could be provided. The presented formulations are within the framework of linear matrix inequality （LMI）, and are convenient to implement. The proposed method is suitable for both the cases that the bounds of uncertain parameters are known and unknown. It is shown by numerical simulations and comparison with available results of a numerical example that the increasing of conservatism in controller design by traditional methods does not means the increasing of reliability. The effectiveness and feasibility of the presented method is also demonstrated by the example.