闭环两尺度系统复合LQR控制建模与设计方法

分析了Kokotovic提出的复合LQR控制器设计方法,以复合控制与最优控制的性能指标差异为依据,评判了设计控制器过程中所建立的标准两尺度系统模型是否符合系统内在的时间尺度特性;指出了以开环时间尺度特性分解系统的缺陷,分析了系统参数变化对闭环时间尺度特性的影响; 基于闭环时间尺度特性分析,提出了将一般线性动力学方程转换为标准两尺度系统形式的方法, 并分析了小参数mu在复合控制器设计中的影响.依据该标准两尺度模型设计的控制器能够敏感由系统参数变化或反馈控制变化导致的时间尺度特性的改变, 并能够得到满意的控制效果.

Modelling and design of composite LQR with close-loop two time scales

According to the analysis of the composite LQR design method proposed by Kokotovic, whether the standard two-scale model established during controller design meets the inherent system time scale characteristic is judged based on the difference between the performance index of composite and optimal control. The defect of system decomposition according to open-loop characteristic is presented and the influence of the system parameter change to closed-loop time scale characteristic is also analyzed. A method to convert the general linear dynamic equations to a standard two-scale model is proposed based on the closed-loop time scale characteristic analysis. The influence of the small parameter mu on the composite control design is also analyzed. Finally, according to the standard two-scale model, the controller can be sensitive to the change of the time scale characteristics caused by the change of system parameters or feedback control, and can get satisfactory control effect.