基于LMI方法的电液舵机动刚度H_∞控制器分析与设计

Analysis and design of a stiffness H_∞ controller of electro-hydraulic rudder based on the LMI method

舵机刚度特性决定着航行器对舵面位置的"把控"能力,航行器运动时随着舵面负载扰动频率的变化,刚度特性也是不断变化的,如果某一频率点上刚度达到最小值,引起了舵面剧烈抖动,整个航行器的运行安全将无法保证。所以舵机控制器设计过程中需要大量的仿真计算,从开始设计阶段找到提高舵机刚度特性的方法;建立电液舵机的系统模型,仿真得到系统刚度特性,基于LMI方法设计了H_∞控制器,通过求解含约束条件的LMI优化问题使设计的控制器能够较大程度上的提高系统动刚度。仿真结果表明:控制器能提高了系统抗扰动能力,系统的刚度在一定扰动频率范围内不变,扰动通道增益减小;在系统参数发生波动的情况下依然能保持较好的抗扰动能力,鲁棒性较强,结合实际项目验证了设计控制器的有效性。

The stiffness of a steering gear determines the control ability of the aircraft to the position of the rudder.When the aircraft is moving,with the change of the load disturbance frequency of the rudder,the stiffness characteristics are also changing.If the stiffness of a frequency point is minimum,the rudder surface is drastically jitter,and the safety of the entire vehicle will not be guaranteed.Therefore,a large number of simulation calculations are needed during the design of a steering gear controller,and the method of reducing the disturbance should be found at the beginning of the design phase.In this paper,the system model of an electro-hydraulic rudder was set up first,and the stiffness characteristics of the system were obtained by simulation.Then the H∞controller was designed based on the Linear Matrix Inequality method,by solving the LMI optimization problem with constraint conditions.The designed controller can improve the dynamic stiffness of the system to a great extent.Finally,the simulation results show that the controller can improve the anti disturbance ability of the system.The stiffness of the system is constant in a certain range of disturbance frequency,and the control gain of the disturbance channel is reduced.When the system parameters fluctuate,the system can still keep good anti-disturbance ability and strong robustness,the design of the controller was verified by the actual project.