Takagi-Sugeno模糊控制器設計之研究

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：7

、訪客IP：18.118.195.208

姓名

孫建中(Chein-Chung Sun) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

Takagi-Sugeno模糊控制器設計之研究
(Design of Takagi-Sugeno Fuzzy Controller)

相關論文

★ 影像處理運用於家庭防盜保全之研究	★ 適用區域範圍之指紋辨識系統設計與實現
★ 頭部姿勢辨識應用於游標與機器人之控制	★ 應用快速擴展隨機樹和人工魚群演算法及危險度於路徑規劃
★ 智慧型機器人定位與控制之研究	★ 基於人工蜂群演算法之物件追蹤研究
★ 即時人臉偵測、姿態辨識與追蹤系統實現於複雜環境	★ 基於環型對稱賈柏濾波器及SVM之人臉識別系統
★ 改良凝聚式階層演算法及改良色彩空間影像技術於無線監控自走車之路徑追蹤	★ 模糊類神經網路於六足機器人沿牆控制與步態動作及姿態平衡之應用
★ 四軸飛行器之偵測應用及其無線充電系統之探討	★ 結合白區塊視網膜皮層理論與改良暗通道先驗之單張影像除霧
★ 基於深度神經網路的手勢辨識研究	★ 人體姿勢矯正項鍊配載影像辨識自動校準及手機接收警告系統
★ 模糊控制與灰色預測應用於隧道型機械手臂之分析	★ 模糊滑動模態控制器之設計及應用於非線性系統

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

針對以Takagi-Sugeno模糊器處理非線性控制問題，本論文提出數個創新的方法以改善現有設計方式的缺點，並細分為兩個方向來探討：(i)以傳統平行分配補償(Parallel Distribution Compensation)的設計方式，(ii) 以區域為基礎之控制架構。首先，針對PDC控制架構，本論文結合協方差控制之方法，藉由給定共同正定矩陣後反向求解里阿柏諾方程組，以取得模糊控制器，不過，現有的設計方式在設計靜態輸出迴授模糊控制器時，大多需要外加限制條件而導致設計結果太過保守，因此本論文結合基因演算法與線性矩陣不等式求解器，提出新的演算法來解決此問題，其優點在於設計過程簡單，且不需要外加任何的限制條件或假設，所以設計結果更加寬鬆，不過當非線性系統的複雜度增加，會導致模糊控制器的規則數增加時，此時以PDC控制架構的控制器製作成本將大幅提高(大量模糊規則在解模糊計算必須以高速的硬體來完成)，在設計上也更加複雜而提高無解的發生率，因此進一步提出模糊區域控制架構，並推導其穩定條件與設計方法，該控制架構不但能降低設計的複雜度而且設計結果也能夠以簡單的硬體來實現，由模擬結果可知，既使控制器規則數大量簡化，模糊區域控制架構仍然能提供如同PDC控制架構一般的性能，最後將上述的研究成果套用到單一模糊區域求解靜態輸出迴授增益，說明該方法也可解決多頂點模型(polytopic model)的靜態輸出迴授強健控制問題，以上所提出的方法都經由數值模擬的方式，以驗證其正確性與可行性。

摘要(英)

In this dissertation, several novel Takagi-Sugeno (T-S) fuzzy control approaches are developed for nonlinear control problems. These design approaches can be separated into two parts: (i) Parallel Distribution Compensation (PDC) design and (ii) Fuzzy Region Compensation (FRC) one.
The first type of T-S fuzzy control approach is developed for single input fuzzy control systems, in which all sub-models are represented as a controllability canonical form. The controller structure is based on the PDC control structure and the synthesis is derived from the covariance control techniques. Unfortunately, these state feedback designs are very difficult to deal with the static output feedback fuzzy control problems because the extra constraints or assumptions have to be attached. To overcome this problem, this dissertation proposes the mixed GA/LMI algorithm, which combines a standard Genetic Algorithm (GA) with LMI solver.
Even if PDC-based design approaches are very popular and ripe, it still has the following serious disadvantages when the fuzzy controller involving many IF-THEN rules: (i) The design result is difficult to implement with some simple hardware or cheap microcontroller. (ii) The total number of Lyapunov stability conditions is rapidly increased. (iii) The modeling errors between a T-S fuzzy model and a nonlinear model could result in the instability or undesired performances when applying the T-S fuzzy controller to the nonlinear models.
To improve the above problems, the FRC control structure is developed in this dissertation. The design idea is to partition the fuzzy model into several regions, and each region is redefined as a polytopic model. In this dissertation, this kind of fuzzy model is named T-S fuzzy region model or TSFRM for short. The proposed fuzzy controller is called T-S fuzzy region controller (TSFRC), in which the controller rule has to stabilize the polytopic model of the fuzzy region and the original nonlinear model is asymptotically stable. The stability analysis and control synthesis are derived from Lyapunov stability criterion, which is considered the robust compensation and is expressed in terms of Linear Matrix Inequalities (LMIs). Comparing with PDC-based designs, TSFRC is easy to design and to implement with simple hardware or a cheap microcontroller. Even if the total number of controller rules of TSFRC is reduced, TSFRC is able to provide competent performances as well as PDC-based designs. By combining the region-based control structure and GA/LMI algorithm, we further shows that the proposed ideas in the field of T-S fuzzy control can be applied to design the static output feedback robust control problems.
It should be noted that the merit of this dissertation is to provide simple design procedures and realizable solutions for state and static output feedback designs when the original T-S fuzzy model is complicated. From the synthesis point of view, these design approaches can deal with various performance constraints without complex mathematical derivations. From the implementation point of view, the design results can be implemented with simple hardware or a cheap microcontroller.

關鍵字(中)

★ 模糊控制
★ 非線性控制
★ 強健控制

關鍵字(英)

★ robust
★ nonlinear
★ Takagi-Sugeno
★ fuzzy
★ control

論文目次

Table of Contents
Abstract IV
Nomenclature VI
Acronyms VII
List of Tables VIII
List of Figures IX
Chapter 1 Introduction 1
1.1 Background and Motivation 1
1.2 Review of Previous Works 3
1.3 Purposes and Contributions 6
1.4 Chapter Outline of Dissertation 9
Chapter 2 Descriptions of T-S Fuzzy Control
and Problem Formulations 11
2.1 Introduction of T-S Fuzzy Control 11
2.2 Continuous-Time T-S Fuzzy Systems
and Its Stability Conditions 13
2.2.1 Continuous-Time T-S Fuzzy Model 13
2.2.2 Continuous-Time PDC-Based T-S
Fuzzy Controller 15
2.2.2.1 State Feedback T-S Fuzzy Controller 15
2.2.2.2 Static Output Feedback T-S
Fuzzy Controller 16
2.2.3 Stability Analysis 17
2.2.3.1 Stability Conditions for State
Feedback T-S Fuzzy Control Systems 18
2.2.3.2 Stability Conditions for Static
Output Feedback T-S fuzzy Systems 20
2.3 Discrete-Time T-S Fuzzy Systems and
Its Stability Conditions 22
2.3.1 Descriptions of Discrete T-S Fuzzy Model 22
2.3.2 PDC-Based Discrete State Feedback
T-S Fuzzy Controller 23
2.3.3 Stability and Performance analyses
for Discrete T-S Fuzzy Systems 24
2.4 Problem Formulations 27
2.5 Summaries 28
Chapter 3 Discrete Controllability Canonical T-S Fuzzy
Controller Design by Using Covariance
Control Technique 30
3.1 Introduction 30
3.2 System Descriptions and Problem Formulations 31
3.2.1 Descriptions of Controllability
Canonical T-S Fuzzy Model 31
3.2.2 Problem Formulations 33
3.3 Main Results 33
3.3.1 Stability Analysis of Closed-loop fuzzy
system via Generalized Inversed Theory 33
3.3.2 Numerical Algorithm for Seeking T-S
Fuzzy Controller 48
3.4 Numerical Example 50
3.5 Summaries 59
Chapter 4 Static Output Feedback Takagi-Sugeno
Fuzzy Controller Design via Genetic
Approaches and LMI Optimization 60
4.1 Introduction 61
4.2 Problem Formulations 62
4.3 Main Results 64
4.3.1 Preliminaries 66
4.3.2 Sequential Stability Requisites 68
4.3.3 Mixed GA/LMI Algorithm 69
4.3.3.1 Hierarchical Fitness Function Structure 69
4.3.3.2 Algorithm Structure 71
4.4 Numerical Example 74
4.5 Summaries 80
Chapter 5 Synthesis of Continuous-Time State Feedback
T-S Fuzzy Region Controller 81
5.1 Introduction 81
5.2 Problems Descriptions 83
5.3 Main Results 90
5.3.1 Continuous-Time T-S Fuzzy Region Model 91
5.3.2 Continuous-Time T-S Fuzzy Region Controller 95
5.3.3 Stability Analyses for Continuous-Time
T-S Fuzzy Region Systems 96
5.4 Numerical Example 100
5.5 Summaries 115
Chapter 6 H2 / H∞ Static Output Feedback Fuzzy
Controller Design for a Region of TSFRM 117
6.1 Introduction 117
6.2 System Descriptions and Problem Formulations 118
6.3 Main Results 121
6.4 Numerical Example 127
6.5 Summaries 132
Chapter 7 Conclusions 133
References 136
Vita 142
PUBLICATION LIST (2001-2005) 143

參考文獻

References
[1] Y. Bai, H. Zhuang, and Z. S. Roth, "Fuzzy Logic Control to Suppress Noises and Coupling Effects in a Laser Tracking System," IEEE Trans. Contr. Syst. Tech., Vol. 13, No. 1, pp. 113-121, 2005.
[2] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Orlando, FL: Academic Press, Inc., 1980.
[3] J. M. Jou, P. Y. Chen, and S. F. Yang, "An Adaptive Fuzzy Logic Controller: Its VLSI Architecture and Applications," IEEE Trans. VLSI Systs., Vol. 8, No. 1, pp. 52-60, 2000.
[4] B. J. LaMeres and M. H. Nehrir, "Fuzzy Logic Based Voltage Controller for a Synchronous Generator," IEEE Comput. Applicat. in Power, Vol. 12, No. 2, pp. 46-49, 1999.
[5] D. Nguyen and B. Widrow, "The Truck Backer-Upper: An Example of Self-Learning in Neural Networks," IEEE Contr. Syst. Mag., Vol. 10, No. 3, pp. 18-23, 1990.
[6] S. Chiu, S. Chand, D. Moore, and A. Chaudhary, "Fuzzy Logic for Control of Roll and Moment for a Flexible Wing Aircraft," IEEE Contr. Syst. Mag., Vol. 11, No. 4, pp. 42-48, 1991.
[7] W. J. M. Kickert and H. R. Van Nauta Lemke, "Application of a Fuzzy Control in a Warm Water Plant," Automatica, Vol. 12, No. 4, pp. 301-308, 1976.
[8] L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Englewood Cliffs, NJ: Prentice-Hall Inc., 1994.
[9] T. Takagi and M. Sugeno, "Fuzzy Identification of Systems and Its Applications to Modeling and Control," IEEE Trans. Systs., Man, Cybern., Vol. 15, No. 1, pp. 116-132, 1985.
[10] T. Tanaka and M. Sugeno, "Stability Analysis and Design of Fuzzy Control Systems," Fuzzy Sets & Systs., Vol. 45, No. 2, pp. 135-156, 1992.
[11] K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy Regulators and Fuzzy Observers - Relaxed Stability Conditions and LMI-Based Designs," IEEE Trans. Fuzzy Systs., Vol. 6, No. 2, pp. 250-265, 1998.
[12] H. O. Wang, K. Tanaka, and M. Griffin, "Parallel Distributed Compensation of Nonlinear Systems by Takagi and Sugeno's Fuzzy Model," Proceeding of FUZ-IEEE'95, pp. 531-538, 1995.
[13] W. J. Chang, "Model-Based Fuzzy Controller-Design with Common Observability Gramian Assignment," ASEM J. Dynam. Systs. Meas. & Contr., Vol. 123, No. 1, pp. 113-116, 2001.
[14] W. J. Chang, "Fuzzy Controller-Design via the Inverse Solution of Lyapunov Equations," ASEM J. Dynam. Systs. Meas. & Contr., Vol. 125, No. 1, pp. 42-47, 2003.
[15] B. S. Chen, C. S. Tseng, and H. J. Uang, "Mixed H2/H∞ Fuzzy Output-Feedback Control Design for Nonlinear Dynamic-Systems - An LMI Approach," IEEE Trans. Fuzzy Systs., Vol. 8, No. 3, pp. 249-265, 2000.
[16] D. J. Choi and P. G. Park, "Guaranteed Cost Controller Design for Discrete-Time Switching Fuzzy Systems," IEEE Trans. Systs., Man, Cybern., B, Vol. 34, No. 1, pp. 110-119, 2004.
[17] K. Kiriakidis, A. Grivas, and A. Tzes, "Quadratic Stability Analysis of the Takagi-Sugeno Fuzzy Model," Fuzzy Sets & Systs., Vol. 98, No. 1, pp. 1-14, 1998.
[18] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA: SIAM , 1994.
[19] P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Work Inc., 1995.
[20] M. F. Azeem, M. Hanmandlu, and N. Ahmad, "Generalization of Adaptive Neuro-Fuzzy Inference Systems," IEEE Trans. Neural Networks, Vol. 11, No. 6, pp. 1332-1346, 2000.
[21] K. Tanaka, S. Hori, and H. O. Wang, "Multiobjective Control of a Vehicle with Triple Trailers," IEEE/ASME Trans. Mechatron., Vol. 7, No. 3, pp. 357-368, 2002.
[22] K. Tanaka, T. Kosaki, and H. O. Wang, "Backing Control Problem of a Mobile Robot with Multiple Trailers - Fuzzy Modeling and LMI-Based Design," IEEE Trans. Systs. Man & Cynern., C, Vol. 28, No. 3, pp. 329-337, 1998.
[23] K. Tanaka and M. Sano, "Trajectory Stabilization of a Model Car via Fuzzy Control," Fuzzy Sets & Systs., Vol. 70, No. 2-3, pp. 155-170, 1995.
[24] K. Tanaka and T. Kosaki, "Design of a Stable Fuzzy Controller for an Articulated Vehicle," IEEE Trans. Systs., Man, Cybern., B, Vol. 27, No. 3, pp. 552-558, 1997.
[25] S. G. Cao, N. W. Rees, and G. Feng, "Stability Analysis and Design for a Class of Continuous-Time Fuzzy Control-Systems," Int. J. Contr., Vol. 64, No. 6, pp. 1069-1087, 1996.
[26] G. Feng and D. Sun, "Generalized H2 Controller Synthesis of Fuzzy Dynamic Systems Based on Piecewise Lyapunov Functions," IEEE Trans. Circuits & Syst., I, Vol. 49, No. 12, pp. 1843-1850, 2002.
[27] G. Feng, "H∞ Controller Design of Fuzzy Dynamic Systems Based on Piecewise Lyapunov Functions," IEEE Trans. Systs., Man, Cybern., B, Vol. 34, No. 1, pp. 283-292, 2004.
[28] K. Tanaka, T. Hori, and H. O. Wang, "A Multiple Lyapunov Function Approach to Stabilization of Fuzzy Control Systems," IEEE Trans. Fuzzy Systs., Vol. 11, No. 4, pp. 585-589, 2003.
[29] W. J. Wang and C. H. Sun, "A Relaxed Stability Criterion for T-S Fuzzy Discrete Systems," IEEE Trans. Systs., Man, Cybern., B, Vol. 34, No. 5, pp. 2155-2158, 2004.
[30] T. Taniguchi, K. Tanaka, H. Ohtake, and H. O. Wang, "Model Construction, Rule Reduction, and Robust Compensation for Generalized Form of Takagi-Sugeno Fuzzy-Systems," IEEE Trans. Fuzzy Systs., Vol. 9, No. 4, pp. 525-538, 2001.
[31] Y. C. Chang, S. S. Chen, S. F. Su, and T. T. Lee, "Static Output Feedback Stabilization for Nonlinear Interval Time-Delay Systems via Fuzzy Control Approach," Fuzzy Sets & Systs., Vol. 148, No. 3, pp. 395-410, 2004.
[32] J. C. Lo and M. L. Lin, "Robust H∞ Nonlinear Control via Fuzzy Static Output Feedback," IEEE Trans. Circuits & Syst., I, Vol. 50, No. 11, pp. 1494-1502, 2003.
[33] L. Wang and R. Langari, "Building Sugeno-Type Models Using Fuzzy Discretization and Orthogonal Parameter Estimation Techniques," IEEE Trans. Fuzzy Systs., Vol. 3, No. 4, pp. 454-458, 1995.
[34] E. M. Abdelrahim and T. Yahagi, "A New Transformed Input-domain ANFIS for Highly Nonlinear System Modeling and Prediction," Proceeding of Canadian Conf. on Electr. and Comput. Eng., Vol. 1, pp. 655-660, 2001.
[35] K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, NY: John Wiley & Son, Inc., 2001.
[36] S. G. Tzafestas and K. C. Zikidis, "NeuroFAST: On-Line Neuro-Fuzzy ART-Based Structure and Parameter Learning TSK Model," IEEE Trans. Systs., Man, Cybern., B, Vol. 31, No. 5, pp. 797-802, 2001.
[37] M. L. Hadjili and V. Wertz, "Takagi-Sugeno Fuzzy Modeling Incorporating Input Variables Selection," IEEE Trans. Fuzzy Systs., Vol. 10, No. 6, pp. 728-742, 2002.
[38] J. S. Jang and N. Gulley, Fuzzy Logic Toolbox, Natick, MA: The MathWorks, Inc., 1995.
[39] W. J. Chang and C. C. Sun, "Fuzzy Controller Design for Nonlinear TORA Systems," Int. Jour. Fuzzy Systs., Vol. 2, No. 1, pp. 60-66, 2000.
[40] C. S. Tseng, B. S. Chen, and H. J. Uang, "Fuzzy Tracking Control Design for Nonlinear Dynamic-Systems via T-S Fuzzy Model," IEEE Trans. Fuzzy Systs., Vol. 9, No. 3, pp. 381-392, 2001.
[41] K. Tanaka, M. Iwasaki, and H. O. Wang, "Switching Control of an R/C Hovercraft: Stabilization and Smooth Switching," IEEE Trans. Systs., Man, Cybern., B, Vol. 31, No. 6, pp. 853-863, 2001.
[42] A. Hotz and R. E. Skelton, "Covariance Control Theory," Int. Jour. Cont., Vol. 46, No. 1, pp. 13-32, 1987.
[43] W. J. Chang and K. Y. Chang, "Variable Structure Controller Design with Norm and Variance Constraints for Stochastic Model Reference Systems," Proceeding of IEE Contr. Theory Appl., Vol. 146, No. 6, pp. 511-516, 1999.
[44] R. E. Skelton, Dynamic Systems Control: Linear Systems Analysis and Synthesis, New York: John Wiley & Son, 1988.
[45] R. E. Skelton, T. Iwasaki, and K. M. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, London, U.K.: Taylor & Francis, 1998.
[46] Y. Park, M. J. Tahk, and J. Park, "Optimal Stabilization of Takagi-Sugeno Fuzzy-Systems with Application to Spacecraft Control," J. Guid. Contr. & Dynam., Vol. 24, No. 4, pp. 767-777, 2001.
[47] D. Z. Liao and L. F. Yeung, "Design Method and Application for Fuzzy Logical Controller Based on L∞ Lyapunov Functions," Proceeding of IEE Contr. Theory Appl., Vol. 146, No. 1, pp. 17-24, 1999.
[48] K. R. Lee, E. T. Jeung, and H. B. Park, "Robust Fuzzy H∞ Control for Uncertain Nonlinear-Systems via State-Feedback - An LMI Approach," Fuzzy Sets & Systs., Vol. 120, No. 1, pp. 123-134, 2001.
[49] S. K. Hong and R. Langari, "An LMI-Based H∞ Fuzzy Control-System Design with TS Framework," Inform. Sci., Vol. 123, No. 3-4, pp. 163-179, 2000.
[50] W. J. Chang and C. C. Sun, "Constrained Fuzzy Controller-Design of Discrete Takagi-Sugeno Fuzzy Models," Fuzzy Sets & Systs., Vol. 133, No. 1, pp. 37-55, 2003.
[51] K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms, NY, USA: John Wiley & Sons, Inc., 2004.
[52] M. A. Abramson, Genetic Algorithm and Direct Search Toolbox, Natick, MA: The Math Work Inc., 2004.
[53] Q. W. Yang, J. P. Jiang, and G. Chen, "How to Select Optimal Control Parameters for Genetic Algorithms," Proceeding of 2000 IEEE Int. Symposium on Indust. Electr., pp. 37-41, 2000.
[54] L. G. Komartsova, "Research of a Genetic Algorithms Designer," Proceeding of IEEE Int. Conf. on Artificial Intelligence Syst., pp. 395-397, 2002.
[55] G. H. Gates, L. D. Merkle, G. B. Lamont, and R. Pachter, "Simple Genetic Algorithm Parameter Selection for Protein Structure Prediction," Proceeding of IEEE Int. Conf. on Evolutionary Comput., pp. 620-624, 1995.
[56] M. Chilali and P. Gahinet, "H∞ Design with Pole-Placement Constraints - An LMI Approach," IEEE Trans. Automat. Contr., Vol. 41, No. 3, pp. 358-367, 1996.
[57] M. Chilali, P. Gahinet, and P. Apkarian, "Robust Pole-Placement in LMI Regions," IEEE Trans. Automat. Contr., Vol. 44, No. 12, pp. 2257-2270, 1999.
[58] P. Gahinet, P. Apkarian, and M. Chilali, "Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty," IEEE Trans. Automat. Contr., Vol. 41, No. 3, pp. 436-442, 1996.
[59] A. Weinmann, Uncertain Models and Robust Control, New York: Springer-Verlag Wien, 1992.
[60] A. Leonessa, W. M. Haddad, and V. S. Chellaboina, "Nonlinear System Stabilization via Hierarchical Switching Control," IEEE Trans. Automat. Contr., Vol. 46, No. 1, pp. 17-28, 2001.
[61] D. Angeli and E. Mosca, "Lyapunov-Based Switching Supervisory Control of Nonlinear Uncertain Systems," IEEE Trans. Automat. Contr., Vol. 47, No. 3, pp. 500-505, 2002.
[62] M. L. Corradini, L. Jetto, and G. Orlando, "Robust Stabilization of Multivariable Uncertain Plants via Switching Control," IEEE Trans. Automat. Contr., Vol. 49, No. 1, pp. 107-114, 2004.
[63] C. Scherer, P. Gahinet, and M. Chilali, "Multiobjective Output-Feedback Control via LMI-Optimization," IEEE Trans. Automat. Contr., Vol. 42, No. 7, pp. 896-911, 1997.
[64] B. V. Sheela, "An Optimized Step Size Random Search," Comput. Methods in Appl. Mech. & Eng., Vol. 19, pp. 99-106, 1979.

指導教授

鍾鴻源(Hung-Yuan Chung)

審核日期

2005-6-27

推文