基于LMI技术的船舶舵减摇鲁棒控制器设计

LMI-based robust controller design of rudder roll damping for ships

针对船舶舵减摇的鲁棒H∞控制问题,研究了一种基于线性矩阵不等式(LMI)技术的鲁棒H∞控制器构建方法。不同于已有的研究成果,假定船舶舵减摇系统模型中存在线性分式不确定摄动,即鲁棒控制问题。在特定的条件下,线性分式不确定摄动可以转化为范数有界的不确定摄动,因此,假定系统模型中存在线性分式不确定摄动具备更强的通用性。结合H∞控制理论和Lyapunov稳定性理论进行系统的稳定性分析,通过LMI技术描述船舶舵减摇的鲁棒H∞控制器的存在条件,该条件可被Matlab软件专用工具箱求解。最后结论,通过Simulink仿真实验证明了文章所研究的求解方法是有效的。

A robust H∞controller was designed with linear matrix inequality( LMI). Under certain conditions,the linear fractional uncertainties can be converted into the norm-bounded uncertainties;therefore,it is more universal to suppose that there are linear fractional uncertainties in the system model. The authors analyzed the stability of the system with H∞theory and Lyapunov function and explored the existing conditions of H∞controller for rudder roll damping for ships with LMI. The robust H∞controller can be obtained with Matlab software LMI toolbox. The simulation results of Simulink show that the method is effective.