基于LMI的4WS-4WD车辆H_∞鲁棒控制器设计

H_∞ robust controller design for 4WS-4WD vehicle based on LMI

基于线性矩阵不等式(LMI)设计了H_∞鲁棒最优控制器以及H_∞鲁棒非脆弱控制器.通过两自由度(2-DOF)车辆模型推导并建立H_∞鲁棒控制系统,此外,定义系统摄动并对摄动矩阵进行分解,进而利用线性矩阵不等式求解控制器.仿真结果表明,H_∞鲁棒最优控制器对侧偏角及横摆角速度的控制效果显著优于LQR控制器.同时,在控制器存在摄动及对侧偏角及横摆角速度进行控制的情况下,H_∞鲁棒非脆弱控制器的鲁棒性能显著优于普通鲁棒H_∞控制器.因此,H_∞鲁棒最优控制器解决了普通鲁棒H_∞控制器控制性能差的问题,H_∞鲁棒非脆弱控制器则解决了普通H_∞鲁棒控制器对参数变化敏感的问题.

H∞ robust optimal controller and H∞ robust non-fragile controller were designed based on linear matrix inequality （LMI）. Two degrees of freedom （2-DOF） vehicle model was used to derive and establish the H∞ robust control system. In addition, the perturbation matrix of the system was defined and decomposed. And then the controller was obtained by using LMI. Simulation results show that the control effects on the sideslip angle and the yaw rate with H∞ robust optimal controller are significantly better than those of LQR （linear quadratic regulator） controller. Meanwhile, when the perturbation of controller in the vehicle system exists, the control effects on side angle and yaw rate with H∞ robust non-fragile robust are significantly better than those with of ordinary H∞ robust controller. Thus, H∞ robust optimal control solves the problem with bad control performance for H∞ robust control. H∞ robust optimal control can guarantee control performance and robust performance at the same time. H∞ robust non-fragile controller solves the problem that the controller is sensitive to parameters.