倒單擺定位系統之多自由度H∞ 控制器設計

Abstract

在建立受控系統數學模型，再怎麼精確的鑑別一個系統，我們所得到的也僅是一個“近似”於實際系統的數學模型。因此我們希望利用一種控制器設計，能夠接受系統數學模型建立時所產生的不確定性，在一個可容許的誤差範圍內，設計控制器來達到良好的控制效果。藉由這個觀念，本篇論文採用“normalized left coprime factorization”的方式來考慮系統數學模型建立時產生的不確定性，目的就是為了要利用 設計出來的控制器容許在我們數學系統建立時所造成的誤差，而依然能提供穩定的控制效果。在控制器的設計上，我們採用“Loop Shaping Design Procedure”的方式來設計控制器；接著以倒單擺的系統，用以作為設計控制器的觀察對象，觀察在 控制器下，倒單擺穩定以及效能的情況，用以探討此種控制理論的可行性以及優缺點。並且考慮到一般的實際受控系統都為多自由度的系統，所以我們在此篇論文中也將會對多自由度系統的控制器作一設計(雙自由度的設計)，希望能達到預期的效果。

In modeling the controlled plant, the mathematical model is at best the approximation to the actual system. This motivates the authors to design a controller which is able to accept the uncertainty produced by the mathematical model to enhance the performance of the controller in acceptable tolerance range. In this monograph, the concept of the “normalized left coprime factorization” to design a controller is therefore adopted for considering problem of uncertainty of the model system. The purpose for applying the controller in this paper is to tolerate the modeling error and further maintain a stable control performance. After that, the“Loop shaping design procedure”method is in use to design the controller. In this work, the experimental objective of the design will be the inverted pendulum system. By looking into the performance of the inverted pendulum system, the authors will discuss feasibility, advantages and disadvantages of the control theory.