状态时滞多采样率线性离散广义因果系统的最优输出调节器设计

Design of optimal output regulators for multirate linear discrete-time descriptor causal system with time delay

研究了带有状态时滞的多采样率线性离散时间广义因果系统的最优输出调节器的设计问题.首先利用离散提升技术将原系统转化为形式上无时滞的系统.再通过等价变换,利用系统的因果性特点将其化为一个正常系统.继续对系统进行离散提升,导出一个形式上简单的单采样率系统.然后将原系统的二次性能指标函数修正为单采样率系统的二次性能指标函数,进而利用最优调节原理,得到其最优调节器.再经过变换,得到多采样率系统的最优输出调节器.同时对导出的单采样率系统的能稳定性和能检测性进行了讨论,给出了严格的数学证明.最后的数值仿真表明,本文所设计的最优调节器是有效的.

This paper introduces the design problem of optimal output regulators for multirate linear discrete-time descriptor causal systems. At first, by making use of the discrete lifting technique the original system is transformed into no state time-delay system in form. Then thought the equivalent transformation, taking advantage of the causal characteristics of the system, it is changed into a nor-mal system. Continuing to apply discrete lifting into the system, a simple single-rate system in form is exported. The performance index function of the original system is modified to that of the single-rate system, and then an optimal output regulator is obtained by using the optimal regulator theory. Through transformation an optimal output regulator for the original system is finally derived. At meantime, the stabilizability and detectability of the exported single-rate system were discussed, and their rigorous mathematical proofs were given. Numerical simulations proved the effectiveness of the preview controller designed in this paper.