臺灣博碩士論文加值系統

本論文主要目的是針對實驗用雙螺旋多輸入多輸出模組之控制問題設計控制機構，其中包含四組模糊補償器與四組PID控制器。控制機構中所有參數都將利用與ITSE系統性能指標為適應性函數之實數型基因演算法來最佳化，其中所引用的ITSE性能指標可以將系統表現以更有效率的方式分析。最佳化的過程也以分區最佳化的方式以及引用解耦合後之設計結果設為初始範圍，讓實數型基因演算法收斂過程更有效率，並使收斂結果更加接近全域最佳解。目的在於使實驗模組在耦合的情況下穩定與完成二自由度的定位與追跡控制，同時改善系統的輸出誤差與減少控制能量，由電腦的模擬實驗可以看出，本論文所設計的控制機構在經過最佳化後，確實可以大幅增進系統表現，改善以往研究所無法克服之缺點。在即時控制部份，利用HCTL21016晶片擷取位置信號，並以撰寫VHDL語言的方式，將最佳化後的控制機構以FPGA晶片的形式實現，再透過數位類比的轉換完成即時控制。

This thesis presents a new approach based on PID controller and Fuzzy compensator to an experimental propeller setup that is called the twin rotor multi-input multi-output system (TRMS). The goal of control is to stabilize the TRMS in significant cross coupling condition and to reach desired set-point and trajectory efficiently. The control scheme includes four Fuzzy compensators and four PID controllers with independent inputs. In order to reduce total error and control energy, all parameters of the controllers are obtained by real-type genetic algorithm (RGA) with system performance index as fitness function. The system performance index applies the integral of time multiplied by the square error criterion (ITSE) to build a suitable fitness function in RGA. We also investigate a new method for RGA to solve control parameters. This new method leads chromosomes in RGA to converge to optimal solutions in complicated hyperplan more quickly. Computer simulations show that the proposed control scheme can overcome system nonlinearities and influence between two rotors successfully. For real-time control, the Xilinx Spartan II SP200 FPGA (Field Programmable Gate Array) is employed to construct a hardware-in-the-loop system. We built a linear-like fuzzy PID controller in coupled condition through writing VHDL on this FPGA. Performance of the hardware controller is demonstrated by real-time experiments.

Abstract (Chinese) i
Abstract ii
Acknowledgement (Chinese) iii
Content iv
List of Figures vii
List of Tables xi
Chapter 1 Introduction 1
1.1 Research Motivation and Goal 1
1.2 Papers Review 2
1.2.1 Research on TRMS Control 2
1.2.2 Research on Fuzzy Controller 3
1.2.3 Research on the Genetic Algorithm 3
1.3 Thesis Contribution 4
1.4 Thesis Overview 4
Chapter 2 Mathematical Model of the TRMS 6
2.1 Introduction of the TRMS 6
2.2 Mathematical Model 7
2.2.1 Non-Linear Model 8
2.3 Mathematical Model and Parameter of TRMS
Decoupled 18
2.3.1 Mathematical Model of Vertical Part of
TRMS 18
2.3.2 Mathematical Model of Horizontal Part of
TRMS 19
2.4 Simulink Models of the TRMS 20
2.4.1 Simulink Model of the Horizontal Part of the
TRMS 20
2.4.2 Simulink Model of Vertical Part of the
TRMS 22
2.4.3 Simulink Model of the 2-DOF TRMS 24
Chapter 3 Fuzzy PID Controller Structure 25
3.1 Structure of Fuzzy Controller 25
3.1.1 Preprocessing 25
3.1.2 Fuzzification 26
3.1.3 Rule Base 27
3.1.4 Connectives 29
3.1.5 Modifiers 29
3.1.6 Membership Function 30
3.1.7 Inference Engine 34
3.1.9 Defuzzification 37
3.2 Structure of Fuzzy PID Controller 39
3.3 Fuzzy PID Control 42
3.4 Fuzzy Compensator and PID Controller with TRMS
Model 48
3.4.1 Fuzzy Compensator and PID Controller in
decoupled condition 48
3.4.2 Fuzzy Compensator and PID Controller in Cross
Coupled Condition of TRMS 52
Chapter 4 Genetic Algorithms and TRMS Control 54
4.1 Introduction to Genetic Algorithms 54
4.2 Real Type Genetic algorithms 55
4.2.1 Fundamental of RGA 55
4.2.2 Procedure of RGA 58
4.3 System performance index 60
4.4 Parameters Optimizing for TRMS Control 62
4.4.1 Parameters Optimizing for PID in Horizontal
Plane 62
4.4.2 Parameters Optimizing for PID in Vertical
Plane 65
4.4.3 Parameters Optimizing for Fuzzy Controller in
Horizontal Plane 67
4.4.4 Parameters Optimizing for Fuzzy Controller in
Vertical of Plane 70
4.4.5 Parameters Optimizing for Fuzzy Compensator and
PID Controller in Horizontal Plane 72
4.4.6 Parameters Optimizing for Fuzzy Compensator and
PID Controller in Vertical Plane 75
4.4.7 Parameters Optimizing PID Controller in Cross-
Coupled Condition 79
4.4.8 Parameters Optimizing for FLC and PID Controller
in Cross-Coupled Condition 84
4.4.9 Summary 88
Chapter 5 Implementation of Controller 90
5.1 Introduction of HCTL-2016 91
5.2 Xilinx Spartant II XC2S200 FPGA 93
5.2.1 Introduction 93
5.2.2 Development System 94
5.3 Implementation of controller 96
Chapter 6 Conclusions and Recommendations 102
6.1 Conclusion 102
6.2 Future Work 103
Appendix 104
Appendix B 109
References 111

[1] Feedback Instiude Ltd, Twin Rotor MIMO system 33-220 User’s Manual
33-000M5, 1998.

[2] 黃明德,莊季高,“結合基因演算與PID控制法於非線性TRMS之應用,”第七屆人工智慧與應用研討會論文集, pp. 734-739, 2002.

[3] 黃明德, 基因演算法與PID控制法於非線性雙旋轉翼多輸入多輸出系統之應用, 碩士論文, 國立台灣海洋大學導航與通訊系, 2002.

[3] 蔡政郁,黃明德,莊季高, “應用實數型基因演算法於非線性TRMS之定位控
制,” 2003自動控制研討會, pp.1267-1273, 2003.

[4] 范浚宏,莊季高,“最佳適應函數參數搜尋之分析及FPGA控制之實現,”人工智慧與應用研討會, FP4-1, 2004.

[5] 范浚宏、蔡政郁、莊季高,“最佳適應函數於非線性 TRMS 1-DOF 及 2–
DOF PID控制參數搜尋之分析,”Proc. Automatic Control Conference. 2004

[6] W.K. Liu, J.H. Fan, and J.G. Juang, “Application of Genetic Algorithm base on System Performance Index on PID Controller,” in the Ninth Conference on Artificial Intelligence and Application ,2004.

[7] E.H. Mamdani, “Application of fuzzy algorithms for control of simple
dynamic plant,” Proc. Inst. Elect. Eng. Contr. Sci., vol. 121, pp.1585-1588,1974.

[8] L.A. Zadeh, “Outline of a new approach to the analysis of complex systems
and decision processes,” IEEE Trans. Syst., Man, Cybern., vol. SMC-3, pp.28
-44,1973

[9] N. Zhang, D.C. Wunsch II, “An Extended Kalman Filter (EKL) Approach on
Fuzzy System Optimization Problem,” IEEE Intl. Conference on Fuzzy System
pp.1465-1470, 2003



[10] Q. LU, Z. Peng, F. Chu, and J. Huang, “Design of fuzzy controller for smart structures using genetic algorithms,” Inst. Of Physics Publish, Smart Materials and Structures pp.979-986 Dec, 2003.

[11] W.R. Hwang, Z.S. Saleh, “Fuzzy Controller Using Genetic Algorithms”

[12] D. Park, A. Kandel and G. Langholz, “Genetic based new fuzzy reasoning models with application to fuzzy control” IEEE. Trans. Syst. Man Cybern vol.24, pp.39-47, 1994.

[13] H. Hagras, V. Callaghan, and M. Colly, “Online learning of fuzzy behavior co-ordinate for autonomous agent using genetic algorithms and real-time interaction with the environment,” Fuzzy Sets Syst., vol.2, pp.853-858, 2000.

[14]J.H. Holland, Adaption in Nature and Artificial system,University of Michigan
Press, 1975.

[15]D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine
Learning. Reading, MA: Addison-Wesley, 1989.

[16]L. Davis, Ed.,Handbook of Genetic Algorithms. NewYork:Van Nostrand
Reinhold , Kluwer Academic, Boston, pp. 299–305,1991.

[17] J.T. Alander,. “An indexed bibliography of genetic algorithms with fuzzy logic,” in W. Pedrycz (ed.), Fuzzy Evolutionary Computation, Kluwer Academic, Boston, pp. 299–318, 1997.

[18]C.L. Karr, “Genetic Algorithm for Fuzzy Controllers,” AI Expert, vol.6 pp.
26-33, 1991.

[19] A. Bonarini,. Evolutionary Learningof Fuzzy rules: competition and cooperation,
in W. Pedrycz (ed.), Fuzzy Modelling:Paradigms and Practice, Norwell, MA:
Kluwer Academic Press, pp. 265–284, 1996.

[20]S.F. Lee, H.C. Lu, and T.H. Hung, “Optimal Design GA-based Fuzzy PID
Controllers,” Proc. IEEE. International Conference on SMC, vol. 2, pp.215 –
220, 2002.

[21] G. Rovithakis, M. Maniadakis, and M. Zervakis, “A Genetically optimized
artificial Network structure for Feature Extraction and Classification of
vascular tissue fluorescence spectrums,” Proc. Fifth IEEE International workshop on Computer Architectures for Machine Perception, pp. 107-111, 2000.

[22] H.-J. Cho, K.-B. Cho, and B.-I. Wang, “Automatic Rule Generation Using Genetic Algorithms for Fuzzy-PID Hybrid Control,” Proc. IEEE International Symposium on Intelligent Control, pp. 271-276, 1996.

[23] B. Hu, G. K. I. Mann, and G. Raymond, “New Methodology for Analytical and Optimal Design of Fuzzy PID Controllers,” Proc. IEEE Transactions on Fuzzy Systems, vol. 7, no. 5, pp. 521-539, 1999.

[24] Y.-S. Zhou and L.-Y. Lai, “Optimal Design for Fuzzy Controllers by Genetic Algorithms,” IEEE Trans. on Industrial Application, vol. 36, no. 1, pp. 93-97, 2000.

[25] K. Belarbi and F. Titel, “Genetic Algorithm for the Design of a class of Fuzzy Controllers : An Alternative,” IEEE Trans. on Fuzzy Systems, vol. 8, no. 3, pp. 398-405, 2000.

[26] C.L. Chen, P.C. Chen, and C.K. Chen, “Analysis and design of fuzzy control systems,” Fuzzy Sets Syst., vol. 57, pp. 125–140, 1993.

[27] C.W. de Silva, Intelligent Control: Fuzzy Logic Applications. New York: CRC, 1995.

[28] C.W. de Silva and A.G.J. MacFarlane, Knowledge-Based Control with Application to Robots. Berlin, Germany: Springer-Verlag, vol. 123, 1989.

[29] G. Hill, E. Horstkotte, and J. Teichrow, Fuzzy-C development system user’s manual, Togai Infralogic, 30 Corporate Park, Irvine, CA 92714, USA.1990.

[30] M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, 1998.


[31] M. Jakiela, C. Chapman, J. Duda, A. Adewuya, and K. Saitou,
“Continuum structural topology design with genetic algorithms,” Computer
Methods in Applied Mechanics and Engineering, 2000.