连续时间多胞线性变参数系统变增益H_∞/H_2输出反馈控制

Gain-scheduled H_∞/H_2 output feedback controller synthesis for continuous-time polytopic linear parameter varying systems

针对一类同时具有参数不确定性和外界干扰的非线性系统,提出了一种连续时间多胞线性变参数(LPV)系统变增益H_∞/H_2输出反馈控制方法.首先,对连续时间多胞LPV系统的变增益混合目标(H_∞/H_2指标和区域极点约束)输出反馈控制器综合方法进行了数学描述;其次,引入新的结构化松弛矩阵变量和参数依赖Lyapunov函数,将满足期望性能的混合目标鲁棒动态输出反馈控制问题转化为线性矩阵不等式框架内的有限维凸优化问题,进一步降低了所设计LPV控制器的保守性.最后,以四分之一车辆模型主动悬架系统为研究对象进行仿真,仿真结果验证了本文控制器的有效性.

This paper focuses on the problem of gain-scheduled H1/H2 output feedback controller synthesis forcontinuous-time linear parameter varying (LPV) systems with parameter uncertainty and external disturbance simultaneously.First, the mathematical formulation and control objectives, including the H1/H2 performance and regional poleplacement, of gain-scheduled mixed-objective robust dynamic output feedback controller for continuous-time LPV systemsare presented. Second, in order to further reduce the conservatism of this algorithm, several slack variables andparameter-dependent Lyapunov functions are employed to the well-established performance conditions. Then the desiredgain-scheduled mixed-objective robust dynamic output feedback controllers are reformulated as efficiently tractable finitedimensionalconvex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical examples of aquarter car model with an active suspension are given to illustrate the effectiveness of the proposed methods.