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 μ 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.