轧辊偏心的H_∞输出反馈鲁棒重复控制

H-infinity robust repetitive control with output feedback for roll eccentricity compensation

针对轧辊偏心问题,用线性矩阵不等式(LMI)方法设计了用于轧辊偏心补偿控制的H∞输出反馈鲁棒重复控制器,首先引入动态输出反馈来保证闭环系统的鲁棒稳定性,把重复控制器设计问题转化为H∞动态反馈控制器的设计问题,采用变量替换法将非线性矩阵不等式转化为线性矩阵不等式并对其求解进而得到控制器参数.另外在采用上述控制器保证系统鲁棒稳定性的同时,通过在重复控制器中引入一个前向系数进一步改善和提高系统的动态性能与稳态控制精度.理论证明与仿真研究表明当系统对象参数存在摄动时,这种控制器仍能有效地补偿轧辊偏心对产品质量的影响.

An H-infinity robust repetitive controller with output feedback for the roll eccentricity compensation is designed by using the linear matrix inequality（LMI） method. We employ the dynamic output feedback controller to robustly stabilize the closed-loop system, and treat the controller design problem as an H-infinity output feedback design problem. The nonlinear matrix inequality is transformed to linear matrix inequalities with variable substitution method, and the controller parameters are obtained by solving these linear matrix inequalities. Moreover, we introduce a feedforward gain into the repetitive controller to improve the dynamic performance and the static control accuracy, while ensuring the stability for the closed-loop system. Theoretical analyses and simulation studies show that the performance of the system satisfies the requirements, even though there are parameter perturbations in the controlled objects.