科技在人類發展之下，不斷地向前演進，然而在科技快速演進下，智慧型控制器逐漸成為關鍵角色，由於智慧型控制器的運算大多較為複雜，因此運算效能的優劣將決定該控制器的控制效果，過去的設計上大多透過軟體實現控制器，然而由於軟體的單步執行，減低了整體運算的效果，為了提升控制器之效能，本文透過硬體的方式實現小腦模型控制器。
　　在硬體實現的同時，將面臨浮點數處理的問題，然而過去的解決方式，是透過IEEE-754的方式來制定浮點數的運算格式，但由於IEEE-754的運算較為複雜，因此將會耗掉較多的運算時間，然而，本文透過整數法的運算處理浮點數的議題。
　　在實現T-S小腦模型控制器時，以指數運算最為複雜，由於指數運算時較其他運算複雜，過去設計指數硬體時，較多透過記憶體存取的方式做表格化的建置，然而這樣的設計將占用許多寶貴的存取空間，因此本文透過泰勒展開式之運算，將指數的運算近乎完整的呈現出來，最終本文整合各個運算模組，而實現T-S小腦模型控制器的硬體化設計。

The technology is improving by the human developing. As the technology fast improving, the intelligence control becoming a key point. Because the process of the intelligence control is quite complex, the performance of operating will decide the performance of controller. In the past, the intelligence controller was usually designed by the software system. But the step by step software process will make the performance decreasing. To improve it this thesis use hardware to implement the T-S CAMC. 
  In hardware implementation we need to face the floating point process problem. In the past, the IEEE-754 is the methodology of solution. But the operating of IEEE-754 is complex. Therefore, the process will take a lot of process time. This thesis use integer numeric system to solve this issue. 
  While implement the T-S CMAC, the exponential operating is the most complex part in the process. In the past, look up table wad used as the solution. But the method will cost a lot of memory. Therefore, in this thesis the Tylor series was used to solve the exponential problem. Finally, this thesis connect all of the operating modules and realized the T-S CMAC.

Contents
Abstract in Chinese I
Abstract in English II
List of Figures V
1 INTRODUCTION 1
1.1 Research Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Fuzzy Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Takagi-Sugeno Fuzzy . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Cerebellar Model Articulation Controller . . . . . . . . . . . . . 2
1.1.4 T-S Fuzzy Model Cerebellar Model Articulation Controller . . . 4
1.1.5 Floating-Point Numeric System . . . . . . . . . . . . . . . . . . 7
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Problem statement and Motivations . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 System Structure 10
2.1 Equipment information . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 FPGA Development main board . . . . . . . . . . . . . . . . . . 10
2.2 Hardware Design TS-CMAC . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Gaussian function . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Multiple and summation . . . . . . . . . . . . . . . . . . . . . . 14
3 Experiment Result 16
3.1 Error Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Gaussian function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Weight Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Multiple and summation . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 PWM module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Conclusions and Future works 38
Bibliography 39
List of Figures
1.1 CMAC structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 CMAC Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 TS-CMAC structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 IEEE754 Formate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 Error Generating Block Diagram. . . . . . . . . . . . . . . . . . . . . . 16
3.2 Error generator Functional wave form. . . . . . . . . . . . . . . . . . . 17
3.3 Error generator Timing wave form. . . . . . . . . . . . . . . . . . . . . 18
3.4 Gaussian Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5 Power Number Module Block Diagram. . . . . . . . . . . . . . . . . . . 19
3.6 Exponential Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . . 20
3.7 Reciprocal Calculating Block Diagram. . . . . . . . . . . . . . . . . . . 20
3.8 Power number in Gaussian Function wave form. . . . . . . . . . . . . . 21
3.9 Power number in Gaussian Timing wave form. . . . . . . . . . . . . . . 22
3.10 Exponential function wave form. . . . . . . . . . . . . . . . . . . . . . . 23
3.11 Exponential Timing wave form. . . . . . . . . . . . . . . . . . . . . . . 24
3.12 Reciprocal of Exponential Functional wave form. . . . . . . . . . . . . . 25
3.13 Reciprocal of Exponential Timing wave form. . . . . . . . . . . . . . . 26
3.14 Gaussian Function wave form. . . . . . . . . . . . . . . . . . . . . . . . 27
3.15 Gaussian Timing wave form. . . . . . . . . . . . . . . . . . . . . . . . . 28
3.16 Update Rule Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . . 29
3.17 Weight update wave form. . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.18 Weight update timing wave form. . . . . . . . . . . . . . . . . . . . . . 31
3.19 Multiple and ADD Block Diagram. . . . . . . . . . . . . . . . . . . . . 32
3.20 Multiple and summation functional wave form. . . . . . . . . . . . . . . 33
3.21 Multiple and summation timing wave form. . . . . . . . . . . . . . . . . 34
3.22 PWM Module Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . 35
3.23 PWM functional wave form. . . . . . . . . . . . . . . . . . . . . . . . . 36
3.24 PWM timing wave form. . . . . . . . . . . . . . . . . . . . . . . . . . . 37

[1] Y. C. Hsueh, S. F. Su, and M. C. Chen, “Decomposed fuzzy systems and their
application in direct adaptive fuzzy control,” IEEE Transactions on Cybernetics,
vol. 44, no. 10, pp. 1772–1783, Oct 2014.
[2] D. Ramot, R. Milo, M. Friedman, and A. Kandel, “Complex fuzzy sets,” IEEE
Transactions on Fuzzy Systems, vol. 10, no. 2, pp. 171–186, Apr 2002.
[3] G. Ayala, T. Leon, and V. Zapater, “Different averages of a fuzzy set with an
application to vessel segmentation,” IEEE Transactions on Fuzzy Systems, vol. 13,
no. 3, pp. 384–393, June 2005.
[4] D. S. Yeung, D. Chen, E. C. C. Tsang, J. W. T. Lee, and W. Xizhao, “On the
generalization of fuzzy rough sets,” IEEE Transactions on Fuzzy Systems, vol. 13,
no. 3, pp. 343–361, June 2005.
[5] T. Takagi and M. Sugeno, “Ieee transactions on systems, man, and cybernetics,”
ACM Computing Surveys (CSUR), vol. SMC-15, no. 1, pp. 116–132, Jan 1985.
[6] R. Qi, G. Tao, and C. Tan, “Adaptive control of discrete-time state-space t-s
fuzzy systems,” in Control Conference (CCC), 2011 30th Chinese, July 2011, pp.
2496–2501.
[7] W. Rui, H. Jiang, and L. Liu, “Continuously dynamic output feedback control for
t-s fuzzy nonlinear networked control systems,” in 2012 International Conference
on System Science and Engineering (ICSSE), June 2012, pp. 454–458.
[8] D. Zhang, X. Han, H.Wang, and Z.Wang, “Multiobjective fault detection observer
design for a class of t-s fuzzy nonlinear systems,” in Advanced Control of Industrial
Processes (ADCONIP), 2011 International Symposium on, May 2011, pp. 486–
491.
[9] J. Dong, Y.Wang, and G. H. Yang, “Control synthesis of continuous-time t-s fuzzy
systems with local nonlinear models,” IEEE Transactions on Systems, Man, and
Cybernetics, Part B (Cybernetics), vol. 39, no. 5, pp. 1245–1258, Oct 2009.
[10] Y. Wang, C. Haoguang, W. Wang, and T. Xiao, “Adaptive control for a class of
nonlinear systems via t-s fuzzy logic systems with nonlinear rule consequents,” in
The 27th Chinese Control and Decision Conference (2015 CCDC), May 2015, pp.
376–381.
[11] X. J. Zeng, “A comparison between t-s fuzzy systems and affine t-s fuzzy systems
as nonlinear control system models,” in 2014 IEEE International Conference on
Fuzzy Systems (FUZZ-IEEE), July 2014, pp. 2103–2110.
[12] J. Albus, “A new approach to manipulator control: The cerebellar model articulation
controller (cmac),” Dynamic System, Measurment, and Control, no. 1, pp.
220–227, Sep 1975.
[13] ——, “Data storage in the cerebellar model articulation controller (cmac),” Dy-
namic System, Measurment, and Control, no. 1, pp. 220–227, Sep 1975.
[14] J.-S. Ker, Y.-H. Kuo, R.-C. Wen, and B.-D. Liu, “Hardware implementation of
cmac neural network with reduced storage requirement,” IEEE Transactions on
Neural Networks, vol. 8, no. 6, pp. 1545–1556, Nov 1997.
[15] C.-S. Chiu and T.-S. Chiang, “Robust output tracking cmac control: the t-s fuzzy
model-based approach,” in Proceedings. 2005 IEEE International Joint Conference
on Neural Networks, 2005., vol. 4, July 2005, pp. 2290–2295 vol. 4.
[16] D. Goldberg, “What every computer scientist should know about floating-point
arithmetic,” ACM Computing Surveys (CSUR), vol. 23, no. 1, pp. 5–48, 1991.
[17] Z. w. Hu, D. x. Duan, Z. y. Xie, and X. Yang, “Pipeline design of transformation
between floating point numbers based on ieee754 standard and 32-bit integer
numbers,” in Intelligent Information Technology and Security Informatics, 2009.
IITSI '09. Second International Symposium on, Jan 2009, pp. 92–96.
[18] Z. w. Hu, Z. y. Xie, and G. x. Luo, “32 bits comparator for multi-number systems,”
in Intelligent Ubiquitous Computing and Education, 2009 International
Symposium on, May 2009, pp. 445–448.
[19] X. D. Sun, K. H. Koh, B. G. Yu, and M. Matsui, “Fuzzy-logic-based v/f control
of an induction motor for a dc grid power-leveling system using flywheel energy
storage equipment,” IEEE Transactions on Industrial Electronics, vol. 56, no. 8,
pp. 3161–3168, Aug 2009.
[20] P. Guillemin, “Fuzzy logic applied to motor control,” IEEE Transactions on In-
dustry Applications, vol. 32, no. 1, pp. 51–56, Jan 1996.
[21] P. Xiaohong, M. Zhi, and X. Laisheng, “Research and application on ga-based
two-stage fuzzy temperature control system for a type of industrial furnace,” in
Electrical and Control Engineering (ICECE), 2010 International Conference on,
June 2010, pp. 1558–1561.
[22] Y. X.Wang, F. F. Qin, K. Ou, and Y. B. Kim, “Temperature control for a polymer
electrolyte membrane fuel cell by using fuzzy rule,” IEEE Transactions on Energy
Conversion, vol. 31, no. 2, pp. 667–675, June 2016.
[23] T.-S. Chiang, K.-Y. Lian, P. Liu, and C.-S. Chiu, “Lmi-based fuzzy chaotic synchronization
and communication,” in Fuzzy Systems, 2000. FUZZ IEEE 2000.
The Ninth IEEE International Conference on, vol. 2, 2000, pp. 900–905 vol.2.
[24] J.-Q. Huang and F. L. Lewis, “Neural-network predictive control for nonlinear dynamic
systems with time-delay,” IEEE Transactions on Neural Networks, vol. 14,
no. 2, pp. 377–389, Mar 2003.
[25] F. Hong, S. S. Ge, and T. H. Lee, “Practical adaptive neural control of nonlinear
systems with unknown time delays,” in American Control Conference, 2004.
Proceedings of the 2004, vol. 3, June 2004, pp. 2409–2414 vol.3.
[26] S.-F. Su, Z.-J. Lee, and Y.-P. Wang, “Robust and fast learning for fuzzy cerebellar
model articulation controllers,” IEEE Transactions on Systems, Man, and
Cybernetics, Part B (Cybernetics), vol. 36, no. 1, pp. 203–208, Feb 2006.
[27] D. Job, V. Shankararaman, and J. Miller, “Combining cbr and ga for designing fpgas,”
in Computational Intelligence and Multimedia Applications, 1999. ICCIMA
'99. Proceedings. Third International Conference on, 1999, pp. 133–137.
[28] A. Savran and S. Unsal, “Hardware implementation of a feedforward neural network
using fpgas,” Master’s thesis, EGE University, Dep. of Electrical and Electronic
Egineering, 2003.
[29] Anjanasasidharan and P. Nagarajan, “Vhdl implementation of ieee 754 floating
point unit,” in Information Communication and Embedded Systems (ICICES),
2014 International Conference on, Feb 2014, pp. 1–5.
[30] Terasic, “De2i-150 fpga development kit.” [Online]. Available:
https://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=
English&CategoryNo=165&No=529