放卷张力系统H_∞鲁棒控制器的设计

H_∞ Robust Control Design for Unwinding Tension System

针对印刷机放卷系统对张力控制稳定性的要求,利用线性矩阵不等式(LMI)方法对放卷张力系统H∞鲁棒控制进行了分析研究和仿真验证.根据放卷系统的工作机理,建立了放卷张力系统的非线性数学模型,通过对系统不确定时变参数的分析,进一步对系统进行了线性化改造.在建立的放卷张力系统模型基础上,利用LMI方法进行了H∞鲁棒控制器的设计,并对控制器的抗干扰性能进行了仿真验证.仿真结果表明,利用LMI方法可以较容易地实现放卷张力系统的鲁棒控制.由于LMI控制器的设计具有不需要权函数和自动优化控制器参数,以及通过极点配置能够满足性能要求等特点,因此在参数时变和外部扰动情况下,可以保证放卷张力系统的渐进稳定性,并且可使系统性能得到优化.

An H∞controller based on linear matrix inequality（LMI） method is presented to strengthen the stability of the tension in unwinding section of printing press,and the controller is analyzed and verified by the simulation.A nonlinear model is established according to the unwinding system working principle,and a linear model is constructed by analyzing the uncertain and time-varying parameters.Then an H∞ controller is designed following the linear model with LMI.The robust disturbance rejection performance of the H∞controller is verified by the simulation,and the results show that the unwinding tension system can be controlled easily with LMI robust control concepts.LMI-based controller is endowed with advantages of requiring no weighting functions,optimizing the parameters of controller automatically and meeting transient requirements with pole placement constraints,and ensures the unwinding tension system to get asymptotically stable and the performance can be optimized according to the time-varying parameters and external disturbances.