基于内模方法的离散时间不确定系统的鲁棒预见控制

Robust Preview Control of Uncertain Discrete Systems Based on An Internal Model Approach

本文主要研究了基于周期信号的离散时间不确定系统的鲁棒预见控制问题。首先针对离散时间不确定系统,通过向前差分,构造包含状态向量、输入向量以及可预见目标值信号的扩大误差系统,该过程中利用内模方法的假设引入另一状态量处理周期性目标信号。然后针对该扩大误差系统的闭环系统,引入Lyapunov函数,并通过线性矩阵不等式(LMI)方法,得到扩大误差系统的鲁棒控制器。这个控制器就是原系统的一个鲁棒预见控制器。数值仿真结果表明了本文所得结论的正确性和有效性。

In this paper, the problem of robust preview control for uncertain discrete-times systems with previewable periodic signal is considered. First of all, by employing the methods of forward differences for uncertain discrete-time systems, the augmented error system with the state vector, the input control vector and the previewable desired tracking signal is derived. An internal model approach was used to deal with the periodic signal during the process. Then, a Lyapunov function for the augmented error closed-loop system is introduced. And by applying LMI method, the robust controller for the augmented error system is obtained, which is regarded as the robust preview controller for the original system. At last, the numerical simulation shown the correctness and effectiveness of the results.