增益调度积分型切换项滑模控制器设计

Design of sliding-mode controller with gain-scheduling integral switched term

针对一类不确定离散系统,提出了一种增益调度积分型滑模控制器,并分析其鲁棒H∞性能。首先,通过状态扩维,得到含有输出误差积分项的离散模型,并利用理想滑模运动性质得出滑模等效控制律,利用输出误差积分项设计增益调度滑模补偿控制律。然后,将滑模闭环控制系统等效为切换系统,基于切换系统相关理论推导了滑模控制参数与闭环控制系统的二次稳定性、鲁棒H∞性能指标的关系。最后,通过对不确定项和非线性项的处理得到线性矩阵不等式(linear matrix inequality,LMI),再求解该不等式,得出满足控制性能要求的滑模控制参数。仿真实验中分析了控制算法的暂态性能和扰动抑制能力,证明了该方法的有效性。

For a class of discrete systems with uncertainties, a gain-scheduled integral sliding-mode controller is proposed, and the controller＇s robust H∞ performance is analyzed. The discrete model containing an out- put error integral term is obtained by states dimension extension. The sliding-mode equivalent control law is derived using the property of the ideal sliding-mode motion; the gain-scheduled compensation control law is derived using the output error integral term. The sliding-mode closed loop control system is regarded as a switched system. The relationships between sliding-mode control parameters, quadratic stability and robust H∞ performance are derived from the theory of switched systems. The linear matrix inequality （LMI） is obtained by dealing with uncertainties and the nonlinear terms. By solving the LMI, the control parameters of the slidingmode meeting the performance requirement is given. The transient performance and disturbance rejection of the controller are analyzed in simulation, and the simulation results show the effectiveness of the proposed method.