CAJ | 학술논문

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。
연구료대유상태시체적다채양솔선성리산시간엄의인과계통적최우수출조절기적설계문제。수선이용리산제승기술장원계통전화위형식상무시체적계통。재통과등개변환，이용계통적인과성특점장기화위일개정상계통。계속대계통진행리산제승，도출일개형식상간단적단채양솔계통。연후장원계통적이차성능지표함수수정위단채양솔계통적이차성능지표함수，진이이용최우조절원리，득도기최우조절기。재경과변환，득도다채양솔계통적최우수출조절기。동시대도출적단채양솔계통적능은정성화능검측성진행료토론，급출료엄격적수학증명。최후적수치방진표명，본문소설계적최우조절기시유효적。
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.