
系統識別號 
U00261807201613163900 
論文名稱(中文) 
廣義最佳線性二次追蹤器暨其在控制系統上的應用 
論文名稱(英文) 
Generalized Optimal Linear Quadratic Trackers and Their Applications to Control Systems 
校院名稱 
成功大學 
系所名稱(中) 
電機工程學系 
系所名稱(英) 
Department of Electrical Engineering 
學年度 
104 
學期 
2 
出版年 
105 
研究生(中文) 
伊法 
研究生(英文) 
Faezeh Ebrahimzadeh 
學號 
n28017031 
學位類別 
博士 
語文別 
英文 
論文頁數 
246頁 
口試委員 
召集委員王伯群 口試委員蘇德仁 口試委員林君明 口試委員蔡清池 口試委員莊智清 口試委員李祖聖 口試委員王振興 指導教授王醴 指導教授蔡聖鴻

中文關鍵字 
最佳線性二次伺服機制
非極小相位系統
頻域塑型
干擾估測
最佳疊代式學習控制
模型預測控制
比例–積分–微分控制
控制零點
系統辨識
輸入限制
時延系統
製鐵高爐

英文關鍵字 
Optimal linear quadratic tracker
Nonminimum phase systems
Disturbance estimation
Frequency shaping
Optimal iterative learning control
Model predictive control
PID control
Control zeros
System identification
Input constraints
Timedelay system
Ironmaking blast furnace

學科別分類 

中文摘要 
本論文探討廣義最佳線性二次追蹤器暨其在控制系統上的應用。基於性能指標函數中頻域塑型法的發展，頻域的設計概念得以融入時域的最佳方法論，然而，針對一個不具有額外輸入∕輸出信號的嚴格適當系統，引入頻域的比例–積分–微分權重函數於追蹤性能指標項，理論上等同於擴增一個比例–積分–微分濾波器於該系統的輸出端，導致擴增後的系統變成一個適當系統模型（具有一輸入–輸出直接傳輸項）且具有額外的輸入與輸出信號。然而，針對這樣的一個系統模型，如何決定最佳的伺服控制卻未在現有的文獻中適當地被提出。尤其，如果涉及在某些隔離的時間點上，具有劇烈變化的指令輸入，此類系統模型的最佳化追蹤器設計更是具有挑戰性。然而，針對非隨機的連續與離散廣義系統模型，廣義最佳線性二次類比與數位追蹤器分別於本論文中首度被提出，接著，基於上述的數學工具－廣義最佳線性二次追蹤器，多種新的系統控制應用相繼被提出，包括：一、一種計算非方陣系統「控制零點」的新方法；二、針對非方陣、非極小相位系統，待控制後，其閉迴路系統足以達到類似最小相位系統之追蹤性能的一種新的最佳濾波器塑型比例–積分狀態迴授二次化設計。然而，針對一個方陣、非最小相位系統，儘管於系統輸入端、輸出端或輸出、入端擴增比例–積分–微分濾波器或控制器，該擴增型系統依然是非極小相位。為解決上述問題，針對方陣、非最小相位系統，同時又具有未知外部干擾的系統，一種基於當下輸出資訊之比例–積分觀測器所建構的改善型最佳線性二次追蹤器在本論文中被提出；三、針對適當系統（具有輸出–輸出直接傳輸項）且具有未知的系統干擾，一種基於比例–積分觀測器所建構的改良型最佳線性二次追蹤器，亦本論文被提出，其中比例–積分觀測器得以估測系統狀態與未知的外部干擾。本論文中，更以多個電腦模擬範例驗證了所提方法的優異性；四、針對具有未知的系統干擾與量測干擾，且控制輸入受到限制之可重複式運作系統，一種僅需一次學習代數的最佳線性二次學習追蹤器在本論文中被提出。
為了完整性考量，具有未知干擾與正值控制輸入限制的未知隨機系統其未知干擾估測與性能補償，亦在本論文中首度被提出。其創新性或貢獻包括：一、發展一種改良的觀測器／卡爾曼濾波器識別法，其中，使用當下輸出資訊以估測當下系統狀態；二、針對未知非線性時延系統，建構等效的線性非時延模型；三、基於當下資訊的卡爾曼濾波器，建構性能良好的系統輸出估測器；四、基於當下資訊的卡爾曼濾波器，提出一種通用的系統建模法；五、量化未知系統其隨機與非隨機成份；六、當測試或實際運作系統中的部分(有效)輸出資訊無法得到時，以所建構的仿真系統輸出當作虛擬量測值，取代不可得的(有效)輸出資訊；七、針對具有正值輸入的未知非線性隨機時延系統，提出一種修正型的基於觀測器之模型預測控制法；八、針對具有正值輸入的未知非線性隨機時延資料取樣系統，發展一種通用的模擬器與追蹤器設計法則；九、伴隨著所建構的仿真系統其虛擬量測值與修正型模型預測控制法，得以做長時間的閉迴路輸入與輸出資訊預測。本論文更以實際運作中的製鐵高爐溫度控制為例，驗證了所提方法的優異性。

英文摘要 
Generalized optimal linear quadratic trackers and their applications to control systems are investigated in this dissertation. With the deployment of the frequencydomain shaping on the timedomain performance index function, the frequencydomain design concept can be merged into the optimization methodology in the time domain. However, for the strictly proper system without having any extra input or output signal, inducing the frequencydomain proportionalintegralderivative (PID) weighting function on the item of timedomain output tracking performance is equivalent to augmenting PID filter at the output terminal of the given strictly proper plant, theoretically. Consequently, the augmented plant arises in a proper system model with extra input and output signals. Nevertheless, how to resolve the optimal tracking for this generic system model has not been properly addressed in literature. Specifically, if an arbitrary timevarying command signal with enormous variations at some isolated time instants is involved, the design methodology for the optimal tracking of this kind of system arises in more challenge. Nevertheless, in this dissertation we first derive generalized optimal linear quadratic analog and digital trackers for the deterministic continuoustime and discretetime general system models, respectively. Then, some new applications of the generalized optimal linear quadratic trackers on control systems are investigated. These include: (i) A new approach for computing the control zeros of the given nonsquare systems, (ii) A new optimal PID filtershaped proportionalplusintegral (PI) statefeedback linear quadratic design for nonsquare nonminimum phase system to achieve a minimum phaselike tracking performance. However, a square nonminimum plant is still nonminimum phase, even though through appending PID filter(s)/controller(s) at either the input terminal, output terminal, or both terminals. To solve for the abovementioned issues, in this dissertation we have designed a new PI currentoutput observerbased optimal linear quadratic tracker for square nonminimum phase system with an unknown external disturbance, (iii) A new PI observerbased optimal linear quadratic tracker for the proper system, using PI observer to estimate the system state and the unknown external disturbance. Some illustrative examples are given to demonstrate the effectiveness of the proposed methodologies, and (iv) A onelearningepoch optimal linear quadratic tracker with an inputconstrained for the repetitive proper system with unknown process disturbance and unknown measurement noise.
For completeness, disturbance estimation and performance compensation of unknown stochastic system with disturbances and positive input constraint are presented in this dissertation. Its novelties and contributions include: (i) Developing an improved observer/Kalman filter identification (OKID) method, which uses the current output measurement to estimate the current state, (ii) Proposing a modelling of a delayfree linear model for the unknown nonlinear timedelay system, (iii) Constructing a wellperformed system output estimation by utilizing the current outputbased Kalman filter, (iv) Formulating a universal approach for constructing artificial system models, based the current outputbased Kalman filter, (v) Conducting of quantitative analysis to determine the stochastic and deterministic components of the unknown system of interest, (vi) Presenting a mechanism for virtual measurement, which allows us to use the output of the constructed artificial system model as virtual measurement to replace those missing and/or abnormal output measurements during the phases of testing and/or practical operation, (vii) Developing a modified observerbased model predictive control (MPC) with input constraints for the unknown nonlinear timedelay stochastic system with positive input constraints, (viii) Developing a universal mechanism for creating simulator and tracker design for positive inputconstrained unknown nonlinear input timedelay stochastic sampleddata systems, and (ix) Carrying out the closedloop type longtime prediction of future inputoutput sets, along the associated virtual measurements of the proposed artificial system with the modified MPC. Finally, a case study on the real stochastic nonlinear input timedelay blast furnace temperature control is demonstrated to show the effectiveness of the proposed methodology.

論文目次 
Contents
中文摘要 i
Abstract iii
Acknowledgement v
Contents vi
List of Tables x
List of Figures xi
Symbols xviii
Abbreviations xx
Chapter 1 Introduction 1
1.1 Motivation 1
1.1.1 Generalized optimal linear quadratic analog and digital trackers 1
1.1.2 Optimal PID filtershaped PI statefeedback LQT designs for nonsquare nonminimum phase systems 2
1.1.3 Optimal LQDTs for the discretetime systems with an unknown disturbance 4
1.1.4 Onelearningepoch inputconstrained optimal LQT designs for the repetitive systems 4
1.1.5 Modelling and tracker design for unknown nonlinear stochastic delay systems with positive input constraints 4
1.2 Contributions 5
1.3 Organization 7
Chapter 2 Generalized Optimal Linear Quadratic Trackers for Proper Systems with Known System Disturbances 9
2.1 Overview 9
2.2 A generalized optimal linear quadratic analog tracker for continuoustime proper systems with known system disturbances 11
2.3 A generalized optimal linear quadratic digital tracker for the discretetime proper system with known system disturbances 16
2.4 Illustrative examples 22
2.5 Summary 30
Chapter 3 Optimal PI StateFeedback Linear Quadratic Trackers for NonMinimum Phase Systems 32
3.1 Overview 32
3.2 Controlzero computation of nonsquare systems 39
3.3 A new optimal PI statefeedback linear quadratic analog tracker for nonsquare nonminimum phase continuoustime systems 51
3.4 A new optimal PI statefeedback linear quadratic digital tracker for nonsquare nonminimum phase discretetime systems 58
3.5 Illustrative examples 64
3.6 Summary 74
Chapter 4 Optimal Linear Quadratic Trackers for DiscreteTime Systems with an Unknown Disturbance 76
4.1 Overview 76
4.2 Currentoutput observerbased LQDT for square nonminimum phase strictly proper discretetime system with an unknown disturbance 77
4.3 Observerbased optimal digital tracker for proper discretetime system with an unknown disturbance 85
4.4 Illustrative examples 89
4.5 Summary 104
Chapter 5 OneLearningEpoch Optimal Trackers with Input Constraint for Repetitive Proper Systems with Unknown Disturbances 106
5.1 Overview 106
5.2 A onelearningepoch optimal LQAT with input constraint for the repetitive proper system with unknown disturbances 107
5.3 A onelearningepoch optimal LQDT with input constraint for the repetitive proper system with unknown disturbances 112
5.4 Illustrative examples 117
5.5 Summary 126
Chapter 6 Modelling and Tracker Design for Unknown Nonlinear Stochastic Delay Systems with Positive Input Constraints: A Case Study on the Blast Furnace Temperature Control 127
6.1 Overview 128
6.2 An improved observer/Kalman filter identification 135
6.2.1 The proposed current outputbased OKID method 136
6.2.2 Delayfree linear modelling of a nonlinear system with timedelay 142
6.3 A novel approach for formulating artificial system models 150
6.3.1 The unified statespace innovation form 151
6.3.2 The wellperformed output estimatorbased simulator 155
6.3.3 Quantification of the dynamic characteristic of the system between stochastic and deterministic 158
6.4 Improved OKIDbased modified model predictive control 159
6.4.1 Model predictive control 159
6.4.2 Inputconstrained model predictive control 161
6.4.3 Improved OKIDbased modified observerbased model predictive control with input constraints 163
6.4.31 Improved OKIDbased modified observerbased model predictive control 163
6.4.32 A new input constraint design method based on the modified observerbased model predictive control 165
6.5 A universal mechanism for creating simulator and tracker design for unknown nonlinear timedelay stochastic systems with input constraints 167
6.6 An Illustrative example 174
6.7 Summary 189
Chapter 7 Conclusion 191
7.1 Conclusions 191
7.2 Future work 192
References 194
Appendix A Mathematical Modeling of NonMinimum Phase Plants and Related Systems 206
A.1 Statespace model with inputtooutputfeedthrough term [46] 206
A.2 Nonminimum phase CtoD and DtoC model conversations [10] 207
A.3 Nonminimum phase PWM systems [4] 215
A.4 Nonminimum phase unmanned aerial vehicles [11] 219
A.5 Nonminimum phase vertical takeoff and landing aircraft [39] 221
A.6 Nonminimum phase conventional takeoff and landing aircraft [98] 224
A.7 Nonminimum phase beamball systems [129] 225
A.8 Nonminimum phase flexible onelink robots [86, 22] 227
A.9 Nonminimum phase behavior in a class of chemical reaction systems [53] 233
Appendix B Proof of Theorem 6.1 237
Appendix C AutoCorrelation Matrix 242
Biography 244
Publication List 245

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