使用廣義型取樣資料保持器的最佳數位控制器設計

Abstract

本篇論文旨在研究以廣義型取樣資料保持器架構的數位控制器設計.由於 過去數位控制理論的發展,大部份均以最常見的零階保持器作考慮,很少注 意到使用廣義型保持器時可引起之特性.直到最近數年來,一些研究者發 現,以廣義型保持器的數位結構,能在許多方面比尋常結構發揮更大的控制 潛能.本篇論文以廣義型數位結構為基礎作最佳控制器設計,提出兩個重要 設計公式.一個是擴充型線性調整公式,另一是將類比狀態回授直接變成廣 義型數位輸出回授的轉換公式.另外本文也應用廣義型的數位結構去解決 一些更為複雜的控制問題 (例如, 無漣波的強健數位伺服控制系統設計, 週期性線性時間延遲系統最佳控制設計等),事實上若非廣義型保持器的引 用,上述之問題在已往被認為是很困難以尋常數位結構去解決的. In this thesis, optimal design approaches of digital controller using generalized sampled-data hold are developed. In the past two decades, almost all developed digital control theories are based on the use of zero-order hold, only few studies are beyond this copies. In recent years, some reseachers have shown that in many practical applications, the design of a digital control system using generalized sampled-data hold exhibits more advantages and control potentials over that of using zero- order hold. This thesis presents two basic algorithms for the optimal design. One is the optimal algorithm which solves the "extended linear quadratic regulation" (ELQR) control problem, and the other is the conversion algorithm which directly coverts the analog optimal state-feedback control scheme into an output feedback control scheme. These two algorithms plays a fundamental stone for the optimal design approach of instantaneous output feedback controllers using generalized sampled-data hold. Moreover, approaches for solving some more complicated control design problems (such as, ripple-free sampled-data robust servomechanism controller design, multirate controller design of linear periodic time delay system, etc) are also developed. Such control problems, unless by employing generalized sampled-data structure, are difficult to solve by using ordinary sampled-data approach.