雙互質分解干擾觀測器

Abstract

本論文旨在提出一個採用雙互質分解之干擾觀測器，此干擾觀測器乃基於雙互質分解 (Doubly coprime) 及 Bezout Identity加以延伸演變而來。以往干擾觀測器方面之研究多數採用Ohnishi於1987年所提出之概念加以延伸，不過該種干擾觀測器架構無法應用於非極小相位系統。本論文所提出之雙互質分解干擾觀測器則可應用於穩定、非穩定、極小相位及非極小相位等線性系統，文中對於不同系統狀況之內部穩定及穩健性皆加有詳細分析，並對於非極小相位系統不穩定零點之影響有較深入之探討。當應用於非穩定系統，除了採用外迴路控制器穩定外，本文亦結合此干擾觀測器與Vidyasagar's structure發展一新穎獨立雙參數架構，除保證系統穩定外，亦可獨立設計干擾抑制參數與追跡響應參數。當系統為多輸入多輸出時，方陣系統可同時抑制輸入與輸出干擾，倘若系統為非方陣型態時，干擾抑制能力則受限於輸入與輸出頻道相對個數。 對於探討系統非確定性與穩健干擾觀測器的發展上，本文則採用Small gain theorem設計觀測器參數以滿足系統穩健性。對於穩健雙互質分解干擾觀測器，吾人亦利用McFarlane 及 Glover發展之迴路整形法設計觀測器參數，藉此滿足系統穩健性與響應規格。在最後一章節中，本文提供數個數值模擬來驗證各章節之論點與推導正確性並以交流馬達定位控制實驗來抑制鈍齒力干擾用以驗證穩定性與系統響應。

In this thesis, one provides a disturbance observer which is based on “Bezout Identity” and doubly coprime factorization. Previous studies about disturbance observer were extended from the concept that provided by Ohnishi in 1987. Unfortunately, that structure cannot be applied to non-minimum phase systems. The disturbance observer we proposed is quite general, which can be applied to stable, unstable, minimum-phase and non-minimum-phase linear systems. Besides, this thesis also discusses the internal stability and robust stability for each different plant cases, and studies about the influences and limitations caused by non-minimum-phase zeros. For unstable systems, in this thesis, we combined the proposed disturbance observer and Vidyasagar’s structure to develop a novel two degree of freedom structure containing two independent parameters which can not only stabilize the system but eliminate the disturbances and improve the tracking performance. When multi-input-multi-output systems are applied, the rejection capability is restricted by the relative numbers of input / output channels. Roughly speaking, the capability of the input and output disturbances rejections is good when the plant is square and is deteriorated when the plant is non-square. A robust disturbance observer is developed to treat plant uncertainty. We applied the small gain theorem to design the disturbance observer that satisfies the robust stability criteria. Also, to guarantee the robust stability and robust performance, we used H_inf - loop shaping method developed by McFarlane and Glover to design the observer parameter. In the final chapter, we provided some numerical examples and an experimental result of positioning control and cogging force rejection of an AC servomotor to verify the correctness of the theoretical developments.