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系統識別號 U0026-1108202016352300
論文名稱(中文) 不同模式預測控制演算法之推導與其性能及穩定性之比較分析
論文名稱(英文) Derivation of Different Model Predictive Control Algorithms and Comparative Analysis on Their Performance and Stability
校院名稱 成功大學
系所名稱(中) 化學工程學系
系所名稱(英) Department of Chemical Engineering
學年度 108
學期 2
出版年 109
研究生(中文) 洪憶倫
研究生(英文) Yi-Lun Hung
學號 N36074364
學位類別 碩士
語文別 中文
論文頁數 133頁
口試委員 指導教授-黃世宏
口試委員-張珏庭
口試委員-吳煒
口試委員-邱繼正
中文關鍵字 模式預測控制  動態矩陣控制  狀態空間模式預測控制  廣義預測控制  無偏預測模式  閉環轉移函數 
英文關鍵字 Model predictive control  dynamic matrix control  state-space model predictive control  generalized predictive control  unbiased prediction model  closed-loop transfer function 
學科別分類
中文摘要   本研究探討基於不同程序模式之各種預測控制演算法,並分析與比較其性能與強健穩定性。模式預測控制利用模式來預測控制系統在給定未來時間範圍內的輸出,並優化目標函數以計算指定時間範圍內的最佳輸入變化,實務上僅執行控制計算的第一步,同時以真實輸出測量進行實時回饋,以減少模式不確定性和未知擾動的影響。目前的相關研究多針對單一特定模式進行演算法探討,未能提供針對多種不同模式的比較分析。
  本文首先介紹六種演算法,包括基於階梯應答模式的動態矩陣控制、基於狀態空間模式的四種預測控制及基於受控自迴歸積分滑動平均模式的廣義預測控制。經過確保無穩態誤差的分析及目標函數的選擇,共篩選出四種演算法,分別為動態矩陣控制、含積分狀態空間模式預測控制、含穩態估測狀態空間模式預測控制及廣義預測控制。接著在設定點改變、擾動或雜訊的存在下,針對模型匹配與否,比較四種演算法在單一輸入/單一輸出(SISO)系統和多重輸入/多重輸出(MIMO)系統中的性能優劣。模擬結果顯示,四種演算法中除了含積分狀態空間模式預測控制在處理MIMO系統時產生稍許穩態誤差,其餘演算法均能保證無穩態誤差。廣義預測控制能有效排除擾動,但對雜訊的消除效果較差。動態矩陣控制在所有情況下皆能保證相對良好的性能。
  本文另外推導出模式預測控制的閉環轉移函數,除了可用以分析控制系統的強健穩定性,亦可快速計算其性能指標。接著利用特徵方程式生成模型參數不確定範圍內的穩定區域圖,來評估四種演算法的強健穩定性。模擬結果顯示,動態矩陣控制的強健穩定性最佳,而當時延參數不匹配時,廣義預測控制的強健穩定區域會急遽縮小。
英文摘要 This research investigates various predictive control algorithms based on different process models, and analyzes and compares their performance and robust stability. Model predictive control utilizes a model to predict the output of a control system over a specified future time horizon, and optimizes an objective function to calculate the best input movements over a specified control horizon. In practice, only the first step of the control calculation is implemented. The actual output measurement is applied for real-time feedback to reduce the impact of model uncertainty and unknown disturbances. The available researches mostly discuss algorithms for single specific models, and fails to provide comparative analysis for various models.
This thesis first introduces six algorithms, including dynamic matrix control based on a step response model, four predictive control based on a state-space model, and generalized predictive control based on a controlled autoregressive integrated moving average model. After the analysis to ensure no steady-state error and the selection of the objective function, a total of four algorithms are selected, namely dynamic matrix control, state-space model predictive control with integral action, state-space model predictive control with steady-state estimation, and generalized predictive control. Then, in the presence of set-point changes, disturbances, or noise, the performance of the four algorithms are compared for single-input/single-output (SISO) systems and multiple-input/multiple-output (MIMO) systems when model mismatch is encountered. The simulation results show that, except for state-space model predictive control with integral action, which produces a slight steady-state error when processing a MIMO system, the remaining algorithms can ensure no steady-state error. Generalized predictive control can effectively reject disturbances, but the effect of eliminating noise is poor. Dynamic matrix control can ensure relatively good performance in all cases.
In addition, this thesis derives the closed-loop transfer function of model predictive control, which can not only analyze the robust stability of the control system, but also quickly calculate its performance indices. Then the characteristic equation is applied to generate stability diagrams for the uncertain ranges of model parameters to evaluate the robust stability of the four algorithms. The simulation results show that dynamic matrix control possesses the best robust stability, and when the time delay parameters do not match, the robust stability region of generalized predictive control will shrink sharply.
論文目次 摘要 I
Abstract II
誌謝 XIV
目錄 XV
表目錄XVIII
圖目錄XXIV
符號表XXX
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 章節與組織 3
第二章 模式預測控制系統理論 4
2.1 動態矩陣控制(Dynamic Matrix Control) 4
2.1.1 離散摺積模式 4
2.1.2 動態矩陣控制之設計 5
2.2 狀態空間模式預測控制 9
2.2.1 狀態空間模式 9
2.2.2 含積分狀態空間模式預測控制之設計 11
2.2.3 含穩態估測狀態空間模式預測控制之設計 13
2.3 廣義預測控制(Generalized Predictive Control) 15
2.3.1 轉移函數模式 15
2.3.2 廣義預測控制之設計 16
第三章 模式預測控制之性能分析與比較 19
3.1 目標函數之選擇 19
3.2 穩態誤差的消除 22
3.3 SISO系統模式預測控制之模擬研究及性能分析 24
3.3.1 模式正確且系統無時延 24
3.3.2 模式正確且系統有時延 29
3.3.3 模式不吻合且系統無時延 34
3.3.4 模式不吻合且系統有時延 48
3.4 MIMO系統模式預測控制之模擬研究及性能分析 63
3.4.1 模式正確且系統無時延 63
3.4.2 模式正確且系統有時延 67
3.4.3 模式不吻合且系統無時延 71
3.4.4 模式不吻合且系統有時延 83
第四章 模式預測控制穩定性分析 95
4.1 動態矩陣控制之閉環轉移函數 95
4.2 狀態空間模式預測控制之閉環轉移函數 99
4.2.1 含積分狀態空間模式 99
4.2.2 含穩態估測狀態空間模式 102
4.3 廣義預測控制之閉環轉移函數 105
4.4 SISO系統模式預測控制穩定性分析模擬 107
4.4.1未含時延之系統108
4.4.2含時延之系統110
4.5 MIMO系統模式預測控制穩定性分析模擬 113
4.5.1 未含時延之系統 113
4.5.2 含時延之系統 116
第五章 結論與未來展望 119
5.1 結論 119
5.2 未來展望 120
參考文獻 121
附錄A 125
附錄B 126
附錄C 129
附錄D 132
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