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E-raamat: Fuzzy Logic Type 1 and Type 2 Based on LabVIEW(TM) FPGA

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This book is a comprehensive introduction to LabVIEW FPGA™, a package allowing the programming of intelligent digital controllers in field programmable gate arrays (FPGAs) using graphical code. It shows how both potential difficulties with understanding and programming in VHDL and the consequent difficulty and slowness of implementation can be sidestepped.

The text includes a clear theoretical explanation of fuzzy logic (type 1 and type 2) with case studies that implement the theory and systematically demonstrate the implementation process. It goes on to describe basic and advanced levels of programming LabVIEW FPGA and show how implementation of fuzzy-logic control in FPGAs improves system responses.

A complete toolkit for implementing fuzzy controllers in LabVIEW FPGA has been developed with the book so that readers can generate new fuzzy controllers and deploy them immediately. Problems and their solutions allow readers to practice the techniques and to absorb the theoretical ideas as they arise.

Fuzzy Logic Type 1 and Type 2 Based on LabVIEW FPGA™, helps students studying embedded control systems to design and program those controllers more efficiently and to understand the benefits of using fuzzy logic in doing so. Researchers working with FPGAs find the text useful as an introduction to LabVIEW and as a tool helping them design embedded systems.



Downloadable LabVIEW toolkit and solutions to exercises
1 Literature Review for Digital Implementations of Fuzzy Logic Type-1 and Type-2
1(70)
1.1 Advances in Applications of Fuzzy Logic Systems
1(5)
1.2 FPGA and Microcontrollers Used for Fuzzy Logic Applications
6(4)
1.2.1 Microcontroller Application
7(1)
1.2.2 DSP Application
7(2)
1.2.3 FPGA Application
9(1)
1.3 Fuzzy Logic Concepts
10(10)
1.3.1 Type-1 Fuzzy Set (T1Fs)
13(1)
1.3.2 Membership Function
14(6)
1.3.3 Discourse Universe and Membership Degree
20(1)
1.4 Extension Principle
20(2)
1.4.1 Basic Identities
22(1)
1.5 Fuzzy Logic Rules
22(1)
1.6 Defuzzification Methods
23(2)
1.7 Fuzzy Inference Methods
25(4)
1.8 Takagi-Sugeno-Kang
29(3)
1.9 Numerical Example (Mandani)
32(3)
1.10 Basic Numerical Example (TSK)
35(1)
1.11 Type-2 Fuzzy Logic Set
36(3)
1.11.1 Historical Review of Advances
36(1)
1.11.2 Type-2 Fuzzy Sets (T2FS)
37(2)
1.11.3 Footprint of Uncertainty
39(1)
1.12 Fuzzy Sets Type 2 Representations
39(3)
1.12.1 Digital and Continuous Representation
39(3)
1.13 Interval Type 2 Fuzzy Sets (IT2FS)
42(2)
1.14 Type Reduction and Defuzzification
44(10)
1.14.1 Karnik--Mendel Iterative Procedure (KM)
44(2)
1.14.2 Wu-Mendel Uncertain Bounds
46(1)
1.14.3 Enhanced Karnik--Mendel Algorithm
47(2)
1.14.4 Type 2 Fuzzy Logic Systems Block Diagram
49(1)
1.14.5 Interval Type 2 Fuzzy Logic Numeric Example
50(4)
1.15 Experimental Implementation of a Fuzzy Logic Controller Type-2 in Quadrotors
54(3)
1.15.1 Introduction
54(1)
1.15.2 Quadrotor Basic Principles
55(1)
1.15.3 ANFIS
56(1)
1.16 Design of Fuzzy Logic Controller Tuned by an Expert
57(5)
1.17 Design of Fuzzy Logic Controller Tuned by an Anfis
62(2)
1.18 Experimental Results
64(7)
References
67(4)
2 LabVIEW™ FPGA
71(68)
2.1 Field-Programmable Gate Array (FPGA)
71(19)
2.1.1 How Do FPGA-Based Control Systems Compare to Processor-Based Systems?
72(2)
2.1.2 How Do I Program My Control Application Using the LabVIEW FPGA Module?
74(2)
2.1.3 How Does the LabVIEW Compiler Translate My Graphical Code into FPGA Circuitry?
76(1)
2.1.4 FPGAs Are Fast, but How Do Faster Loop Rates Improve Control System Performance?
77(1)
2.1.5 What FPGA Hardware Targets Are Available from NI?
78(2)
2.1.6 What Closed-Loop Control Performance Can I Achieve?
80(1)
2.1.7 How Much Jitter Can I Expect in My FPGA-Based Control Loops?
81(1)
2.1.8 Creating a New LabVIEW Real-Time Project and Adding I/O
82(8)
2.2 Developing the LabVIEW FPGA Application
90(11)
2.3 Compiling the FPGA Application
101(3)
2.3.1 Understanding the LabVIEW FPGA Compilation Process
102(1)
2.3.2 FPGA Clock Speed
103(1)
2.3.3 The Compilation Report
103(1)
2.4 Advanced Methods for LABVIEW FPGA
104(18)
2.4.1 Introduction
105(1)
2.4.2 Technique 1: Use Single-Cycle Timed Loops (SCTLs)
106(4)
2.4.3 Creating Counters and Timers
110(1)
2.4.4 Write Your FPGA Code as Modular, Reusable SubVIs
111(3)
2.4.5 Separate Logic from I/O
114(1)
2.4.6 Holding State Values in a Function Block
115(2)
2.4.7 Run-Time Updateable Look-up Table (LUT)
117(2)
2.4.8 Do not Place Delay Timers in the SubVI
119(1)
2.4.9 Reentrancy
120(2)
2.5 Use Simulation Before You Compile
122(6)
2.5.1 Providing Tick Count Values for Simulation
123(2)
2.5.2 Test the LabVIEW FPGA Code Using the LabVIEW Control Design & Simulation Module
125(3)
2.6 Synchronize Your Loops
128(4)
2.6.1 Latching Values
129(1)
2.6.2 Application Example
130(2)
2.7 Technique 5: Avoid "Gate Hogs"
132(7)
2.7.1 Avoid Front Panel Arrays for Data Transfer
133(1)
2.7.2 Use DMA for Data Transfer
134(1)
2.7.3 Use the Minimum Data Type Necessary
135(1)
2.7.4 Optimizing for Size
135(3)
2.7.5 Additional Techniques to Optimize Your FPGA Applications
138(1)
References
138(1)
3 Real-Time Fuzzy Logic Controllers
139(20)
3.1 Basic Parts in Real-Time Fuzzy Logic Controllers
139(1)
3.2 Case Study: The Karnik--Mendel Algorithms Performance Implemented in Real-Time LABVIEW FPGA
140(8)
3.2.1 Interval Type-2 Fuzzy Logic Systems
141(1)
3.2.2 The Karnik--Mendel Algorithm
142(1)
3.2.3 Non-iterative Version
142(2)
3.2.4 Iterative Version
144(2)
3.2.5 Enhanced Karnik--Mendel Algorithm
146(1)
3.2.6 Nie-Tan Method
147(1)
3.3 DC Servomotor
148(4)
3.3.1 Laplace Transform Model
149(1)
3.3.2 State-Space Transfer Function
150(1)
3.3.3 Servomotor Control System
151(1)
3.4 The Hardware Complexity
152(1)
3.5 Methodology
153(2)
3.6 Results and Discussion
155(4)
3.6.1 Reference Tracking
155(1)
3.6.2 The Hardware Performance
155(3)
References
158(1)
4 Fuzzy Logic Type 1 and Type 2 LabVIEW FPGA Toolkit
159(72)
4.1 Type-1 Fuzzy Sets
159(3)
4.1.1 Membership Function Parameters
160(1)
4.1.2 Normalization
161(1)
4.1.3 Membership Degree
161(1)
4.1.4 Error Handling
161(1)
4.2 Type-2 Fuzzy Sets
162(7)
4.2.1 Membership Function Parameters
162(1)
4.2.2 Normalization
162(1)
4.2.3 Uncertainty Widths
163(1)
4.2.4 Membership Degrees
163(1)
4.2.5 Error Handling
164(2)
4.2.6 Examples
166(3)
4.3 Creating a Knowledge Base
169(2)
4.3.1 Building a Rule Set
169(2)
4.4 The Inferred Set
171(9)
4.5 Defuzzification
180(6)
4.5.1 T1 Mamdani Model the Centroid
180(1)
4.5.2 T2 Mamdani Model the Karnik--Mendel Algorithm
181(1)
4.5.3 The Enhanced Karnik--Mendel Algorithm
182(1)
4.5.4 The Nie--Tan Method
182(1)
4.5.5 The Takagi--Sugeno Model
183(3)
4.6 Examples
186(1)
4.7 Study Cases
187(13)
4.7.1 T1FLS Validation
187(5)
4.7.2 Electric Wheelchair
192(8)
4.8 T2FLS Validation
200(2)
4.9 Performance T1 FLS DC Servomotor
202(2)
4.9.1 Electric Wheelchair
203(1)
4.10 T1FLS Versus T2FLS
204(6)
4.10.1 Noise Response
204(2)
4.10.2 Response Time
206(1)
4.10.3 Resource Utilization
206(4)
4.11 Included Examples
210(21)
4.11.1 Case Study: Experimental CNC Micromachine Controlled by Fuzzy Type 2
210(2)
4.11.2 Micromachines and Fuzzy Logic
212(1)
4.11.3 Reconfigurable Micromachine Tools
213(2)
4.11.4 Motion Control
215(2)
4.11.5 Control Design on Real-Time FPGA
217(5)
4.11.6 Experimental Results
222(6)
References
228(3)
Index 231
Professor Pedro Ponce studied automation and control engineering. Later, he studied for Master of science and Doctor of science, both degrees with specialization in electrical engineering automatic control option. Professor Pedro Ponce served as a field and design engineer in the Department of Speed Control, as well as projects of industrial development level II engineer. He has specialized in the areas of: automation industrial systems, industrial design, alternative energy, electric and hybrid vehicle systems, electronic power, electrical machines, electrical drives, electronics of power, conventional and digital control, intelligent, expert systems and artificial neural networks. He has been certified in several areas of engineering by companies and universities such as: Siemens, ABB, Rockwell, MIT among others. He has more than 60 publications in journals and conferences of academic reputation, 5 book chapters and 4 books. He was a member of the National System of Researchers and has received numerous national and international awards. He had research stays in Europe and the United States of North America. He has 16 engineering-related patents with two products in the process of technology transfer for the international market. Dr. Arturo Molina is researcher and titular Professor and Vice-Rector of research and innovation of the Tecnológico de Monterrey. He is a member of the National Research System of Mexico (level II), of the Mexican Academy of Sciences, the Academy of Engineering and of the Advisory Board of IFAC (the International Federation of Automation and Control). He is a consultant for the World Bank and Inter-American Development Bank. He has published 4 books, 43 articles in journals with arbitration, 58 book chapters and more than 60 articles in proceedings of refereed conferences. He holds 12 patents. He has been involved with three technology-based business start-ups: IECOS - Integration Engineering and Construction Systems, SMES - Solutions for Manufacturing Enterprise Systems and ALBIOMAR. Currently, he participates in a European 7 framework related to the creation of sustainable products and customizable manufacturing (sustainable mass customization) and transfer to Peru of the project creative small- and medium-size enterprises (SMEs) (creation of technologies of information for value-added networks) to support the development of SMEs manufacturing based on information technology funded by the Inter-American Development Bank. He is a member of the editorial board of the journals: Annals Review of Control and International Journal of Computer Integrated Manufacturing. He is a graduate career computer systems engineering and the master of science with specialization in computer science from the Tecnológico de Monterrey, campus Monterrey. He received the degree of Doctor in mechanics of the Budapest University of Technology and Economics, Hungary, and subsequently obtained his PhD in systems of manufacturing from the Department of Mechanical and Manufacturing Engineering of Loughborough University of Technology, England. He did his sabbatical of teaching and research at the Department of Mechanical Engineering of the University of California at Berkeley. Brian MacCleery helps small to medium businesses bring innovative clean energy products to market. He guides National Instruments strategic R&D and product development for embedded control and measurement with a focus on customer-oriented design tools for advanced control. In his 15-year tenure at NI, MacCleery led market research, product definition, launch and growth of the successful NI CompactRIO platform and product strategy for the popular LabVIEW FPGA tool chain. MacCleery holds bachelors and masters degrees in electrical and computer engineering from Virginia Tech where he now serves on the Industry Advisory Board. He completed his graduate research in power electronics and linear switched reluctance motor drives under the direction of Dr. Krishnan Ramu and led multidisciplinary teams in the development of novel magnetic levitation and propulsion vehicle systems.
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