臺灣博碩士論文加值系統

在控制多變數系統時，有二種類型的控制器最常被使用，一是多環路控制器，另一種則是多變數控制器。多環路控制具有架構簡單及容易處理環路失效等優點，不過環路之間的交互作用，往往導致控制性能上的限制；同時每個環路的控制器彼此會互相影響，造成在設計上有困難。理論上，可以使用多變數控制器來消除環路間的交互作用。然而，大部分的研究都只設計其中一種控制器，例如：多環路控制器或多變數控制器。且只處理一種控制問題，例如：設定點追蹤問題或干擾排除問題，絕大部分的方法仍以處理設定點追蹤問題為主。事實上，干擾輸入為化學工業程序最常面臨的狀況。本論文中，將提出一個系統化的方法來對多變數系統設計一般化控制器，此一般化控制器可適用於各種架構且可以同時滿足二種控制目標。
對干擾排除方面，首先提出單環路控制器的合成方法，此控制器可適用於一些常見的穩定程序，甚至是含有右半平面零值的情況。在多環路控制系統方面，導出負荷對程序輸出的總影響，將其定義為等效擾動，藉此將其他環路交互作用對擾動的影響考慮進去，並結合等效開環路程序，形成多個對等單環路系統。相同地，在多變數控制系統中，使用逆轉基式去耦合器將環路去耦合成多個獨立的單環路程序，此逆轉基式去耦合器可以經由一個系統化的步驟來得到，在此設計下，可以確保去耦合器的可行性。由於上述二種控制架構皆可分解成多個對等單環路系統。因此，單環路控制器合成方法便可應用至此二種控制架構中。
對設定點追蹤方面，大部分的控制器設計方法都針對穩定程序設計。事實上，有些化學單元為積分程序。例如：液位系統等。在本文中，將提出含積分程序的多變數系統之多環路控制器設計方法。在設計多環路控制器前，須先進行環路配對，對於含有積分程序的系統，無法使用相對穩態增益矩陣來進行配對。為了解決這個問題，將相對穩態增益矩陣做一些修正，並利用修正後的結果來進行環路配對。
對於單一控制目標，傳統單一自由度控制器就可以處理得很好，若要同時達到二個設計目標，例如：干擾排除及設定點追蹤。則需使用二自由度控制器才能達成，本文中提出一個可以簡單應用到多變數系統的三元件控制結構，其中一個主回饋環路用來處理干擾排除問題，另外二個元件則用來獲得較好的設定點追蹤響應，在設定點追蹤性能上，可以獲得與Smith預測器相同的控制結果。在干擾排除方面，分別評估多環路控制及多變數控制理論上及實際上所能達到的控制性能為何，再定義一些指標來比較二種架構的控制性能。然後，將這些指標延伸至控制器控制架構的選擇上，並提出一套適用於這些結構的設計方法。最後，建立一套多變數系統控制器的系統化設計方法。

The multi-loop controller and multivariable controller have been used in the control of multi-input-multi-output chemical plants. The simple controller structure and the easiness to handle loop failure are the most attractive advantages of multi-loop control. Because of loop interactions, the design of such controllers is more difficult to meet specifications. Theoretically, loop interactions can be eliminated by making use of multivariable controller. However, most research works are focused on one controller (i.e., a multi-loop or a multivariable controller) and one design objective (i.e., set-point tracking or disturbance rejection). In this thesis, a systematic design method is proposed to design generalized controllers for multi-input-multi-output systems.
For disturbance rejection, a new design of controllers based on the synthesis approach is proposed for single-loop systems. The controllers are derived for several common types of process models including one that contains right-half-plane zeros. In multi-loop control systems, an effective disturbance is derived to consider the total effects of a load input on a process output. Then, a muli-loop control system can be treated as several equivalent single-loop systems with equivalent open-loop processes and effective disturbances. Similarly, in multivariable control system, an inverse-based decoupler is given to decouple the system into several individual single-loop systems. The design of this inverse-based controller emphasizes on a systematic procedure to obtain physically realizable controllers for practical implementation. By the equivalent single-loop systems in multi-loop control and decoupled open-loop process in multivariable control, the method of controller synthesis in single-loop systems can be applied to both control systems.
For set-point tracking, most methods have been proposed to design the multi-loop controller for stable processes. Actually, some chemical units are integrating processes. An extension is presented to design a multi-loop PI/PID controller for a transfer function matrix whose some elements having pure integrators. Moreover, a modified RGA is given to overcome the difficulty encountered in computing the RGA of an integrating process for loop pairing.
To achieve both control objectives, a three-element multivariable control system with two-degree-of-freedom is proposed. Among the three elements, one in the main loop is designed for rejecting disturbance, and the other two that serve as pre-filter and dynamic preset are devised for set-point tracking. For set-point tracking, the two elements are designed to have a dead-time compensated response as that of a Smith predictor. For disturbance rejection, the theoretically and practically achievable performances are assessed in both controls and indices are defined to compare their control performances. Then, these indices are extended to select the structure of controller in multivariable control systems. Finally, a systematic approach is proposed to design the generalized controller for multi-input-multi-output processes.

誌 謝 I
中文摘要 III
Abstract V
目 錄 VII
附圖目錄 XI
附表目錄 XV
英文縮寫符號表 XVII
第一章 緒論 1
1.1. 前言 1
1.2. 文獻回顧 2
1.2.1. 多環路控制系統 2
1.2.2. 多變數控制系統 6
1.3. 研究動機與目的 9
1.4. 組織章節 11
第二章 含積分程序之多環路PID控制器設計13
2.1. 前言 13
2.2. RGA的修正及環路配對 14
2.2.1. RGA的修正 15
2.2.2. 範例說明 18
2.3. 單環路積分程序的控制器設計 21
2.3.1. 控制架構 21
2.3.2. 控制器之合成 23
2.3.3. 系統的可控制度分析 28
2.4. 含積分程序的多環路控制器設計 29
2.4.1. 設計步驟 30
2.4.2. 穩定性分析 34
2.5. 模擬範例 35
2.5.1. 2×2系統 36
2.5.2. 3×3系統 42
2.5.3. 有緩慢動態的系統 44
第三章 針對干擾排除之多環路系統控制器合成
47
3.1. 前言 47
3.2. 單環路系統對干擾移除之控制器合成
48
3.2.1. 一階帶時延模式 51
3.2.2. 二階帶時延及高階模式 52
3.2.3. 含有右半平面零值的程序模式 53
3.2.4. 控制性能及系統韌性 53
3.2.5. 範例說明 58
3.3. 多環路控制中對等干擾輸入之推導61
3.3.1. 2×2系統 61
3.3.2. n×n系統 64
3.4. 針對干擾排除之多環路控制器合成69
3.4.1. 對等單環路系統之近似 70
3.4.2. 控制器合成 71
3.4.3. 範例說明 72
第四章 對干擾排除之多變數控制器設計 79
4.1. 前言 79
4.2. 多變數去耦合控制設計 80
4.2.1. 以程序逆矩陣為基礎的去耦合器設計 80
4.2.2. 以程序伴隨矩陣為基礎的去耦合器設計 82
4.2.3. 多變數控制器之設計 85
4.2.4. 系統的穩定性及韌性 87
4.2.5. 感測器及促動器失效之韌性分析 88
4.3. 針對干擾移除之多變數預測控制 89
4.3.1. 多變數預測控制設計 90
4.3.2. 系統的穩定性及韌性 92
4.3.3. 去耦合產生之額外時延的消除 93
4.3.4. 範例說明 95
第五章 二自由度之單變數及多變數控制 99
5.1. 前言 99
5.2. 二自由度單環路控制系統 100
5.3. 二自由度之線上適應性切換控制 101
5.3.1. 二自由度切換控制設計 101
5.3.2. 線上適應性控制 104
5.3.3. 含領先及延遲之補償器 107
5.3.4. 範例說明 108
5.4. 多變數程序之二自由度控制系統 113
5.4.1. 設定點追蹤 114
5.4.2. 2×2多變數程序範例 116
5.4.3. 3×3多變數程序範例 124
第六章 控制架構選擇及MIMO系統之整體設計 131
6.1. 前言 131
6.2. MLC及MVC系統之範例比較 133
6.2.1. 基礎之設計方法 133
6.2.2. MLC及MVC性能比較 135
6.3. 理論上及實際上最好的控制效能 139
6.3.1. 理論上之最佳效能 139
6.3.2. 實際上之最佳效能 144
6.4. 控制架構的選擇 147
6.4.1. 使用穩態增益來評估 147
6.4.2. 使用動態來評估 150
6.4.3. 範例說明 151
6.5. 部分去耦合控制 161
6.5.1. 部分去耦合控制器及一般化去耦合控制器之設計
161
6.5.2. 去耦合器之可行性分析 163
6.5.3. 其他特殊結構之去耦合 165
6.6. MIMO系統控制器之整體設計方式 168
6.6.1. 使用RLG來評估一般化之結構 168
6.6.2. 對MIMO系統之一般化控制器設計 170
6.6.3. 範例說明 171
第七章 結論與未來展望 175
7.1. 結論 175
7.2. 未來展望 176
A. 線性分式轉換（LFT） 177
B. 方塊矩陣逆轉換 181
參考文獻 183

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