適用於同向與非同向誤差系統之回授輸出滑動模式控制設計

Abstract

當系統模型中具有誤差時，滑動模式控制（sliding-mode control）能有效消除誤差，因而廣泛應用於理論設計及工程實務，惟其應用仍受限於天生控制震顫（chattering）及系統狀態資訊難以完整取得。近年來，許多研究單位致力於消除此限制；然時至今日，已知研究成果及文獻仍未能提出一有效解決方案。 本篇論文針對此現存缺點提出一新式回授輸出之滑動模式設計。此研究具有三大特點：首先，作者提出一新式強韌觀測器－－LTR觀測器，於系統模型中具有大振幅誤差時仍可產生一準確系統狀態估測。此觀測器明顯優於傳統高增益觀測器（high-gain observer），傳統設計儘能應用於相對階數為一之控制系統，然本文之新設計不受此一條件限制。 其次，一新式震顫消除方法亦首見於本文中。此控制方法以積分運算消除傳統設計中運入訊號帶有之高頻震顫，並大幅消少所需計算量及安裝複雜度；當狀態量測帶有雜訊時，此設計仍能有效達成震顫消除。 最後，基於LTR 觀測器及轉移函數之非最簡表示（non-minimal realization），本文提出一適用於具有非同向誤差系統之回授輸出滑動模式控制。此新設計不受現存研究成果之嚴格系統假設限制，且文中所需用之設計工具皆有嚴謹數學分析證明其控制成果及穩定性。

Sliding-mode control has been a widely accepted control design for controlling systems with uncertainties. Even with it popularity, the sliding-mode control still has some obstacles that hinder its applications. These obstacles include the chattering phenomenon in the control signal and the difficulty in obtaining full state measurement. Even though there has been different sliding-mode control designs proposed to overcome these problems, these problems are considered not completely solved nowadays.

In view of these problems, this dissertation proposes a new output-feedback sliding-mode control. The new control has three contributions. First, a new robust observer called the LTR observer is proposed to provide accurate state estimate in the face of large uncertainties. The LTR observer is superior to the conventional robust observers such as the high-gain observer. Conventional high-gain observer only applies to systems with the relative degree equal to the system dimension, while the new LTR observer can apply to systems with arbitrary relative degree.

Second, a new chattering reduction control is proposed in this dissertation. The new control puts the switching control term inside an integration so that the high frequency oscillations caused by the switching control is smoothed out by the time integration. This new control chattering reduction mechanism is more efficient and compact than previous chattering reduction control designs, especially in noisy environments.

Third, based on the LTR observer and a non-minimal realization of the system transfer function, a new output-feedback sliding-mode control is proposed to deal with systems with mis-matched uncertainties. This new approach relaxes many stringent assumptions posed by previous sliding mode control designs. Rigorous stability and performance analysis are presented to prove the efficacy of all the new designs in this dissertation.