PV maximum power point tracking based simplified fuzzy logic

(1)

PV MAXIMUM POWER POINT TRACKING BASED ON SIMPLIFIED FUZZY LOGIC

PERRY PAISLEY GOH HUA SENG

A project report submitted in partial fulfilment of the Requirements for the award of the degree of

Master of Engineering (Electrical – Power)

Faculty of Electrical Engineering Universiti Teknologi Malaysia

(2)

To my beloved mother, father and two sisters for their encouragement iii

(3)

ACKNOWLEDGEMENT

This is to dedicated and indebted to God the greatest loving and caring to all mankind, by his blessing that allowing me of progressing in this project preparation until completion.

I would like to express my sincere gratitude to my supervisor, Dr Shahrin Bin Md Ayob, who has supported me throughout my work with his guidance, patience, motivation, enthusiasm and enormous knowledge whilst allowing me to work in my own at comfort zone. I attribute the level of my Master Degree to his encouragement and effort which without him, this report would not have been possible to be written and completed. It is an honour for me to having this opportunity of doing the project research under his supervision.

Thank you to Mr Faridun for your kind assistance and guide towards into my project research references and supports. It is a pleasure to thank you those who made this project report possible. I would like to show my huge appreciations to my fellow classmate for their understanding, encouragement and moral support.

Last but not least, biggest special loving thank you and deepest appreciation to my father (Christi Goh), my mother (Sim Siang Eng) and both my sisters (Olivia Goh and Josie Goh) for supporting me through blessing and spiritually.

(4)

ABSTRACT

The thesis focus is to develop Maximum Power Point Tracking (MPPT) algorithm that based on the Simplified Fuzzy Logic Controller (SFLC). It is known that the output of the PV panel is always fluctuates due to the changes in the irradiation of the sunlight and surrounding temperature. This inconsistency of the output voltage is no good to the load. To compensate the problem, a power converter is used to reduce the fluctuation. However, the efficiency of the power converter is much depends on the maximum power point tracked of the solar panel. Therefore, there is a need for a MPPT algorithm to be implemented in the power converter. In this thesis, Simplified Fuzzy Logic Controller (SFLC) is employed. The proposed of Simplified Fuzzy logic Controller (SFLC) has several advantages as compared to the conventional Fuzzy Logic Controller (CFLC), such as less number of rules and tuning parameters. To verify, full system model is developed in MATLAB-Simulink software and simulated. From the results, it was shown that the features of the proposed Simplified Fuzzy Logic Controller (SFLC) are justified.

(5)

ABSTRAK

Tujuan fokus tesis ini adalah membangunkan algoritma penjejakan takat kuasa maksimum berdasarkan konsep kaedah dipermudahkan Pengawal Logik Kabur (SFLC) aplikasi. Dikenalpasti bahawa hasil keluaran panel PV sentiasa berubah-ubah kerana berdasarkan kepada perubahan penyinaran cahaya matahari dan suhu persekitarannya. Ketidakan konsisten perubahan kerap berterusan adalah tidak sesuai untuk beban pada keluaran. Untuk mengatasi masalah ini, maka memperkenalkan litar pernukar kuasa bagi mengurangkan kekerapan perubah-ubahan berlaku. Bagi kecekapan untuk litar pernukar kuasa adalah bergantung kepada penjejak takat kuasa maksimum pada panel PV tersebut. Oleh itu, algoritma penjejakan takat kuasa maksimum perlu ada dalam melaksanakan dalam litar penukar kuasa. Dalam tesis ini, dipermudahkan pengawal logik kabur (SFLC) diperkenalkan. Tujuan kaedah dipermudahkan pengawal logik kabur (SFLC) mempunyai banyak kebaikan berbandingkan kepada kaedah konvensional pengawal logik kabur (CFLC), seperti mengurangkan jumlah langkah peraturan logik dan penalaan parameter. Bagi kenalpastikannya, semua model keseluruhan dibangunkan di dalam MATLAB-simulink perisian dan disimulasikannya. Daripada keseluruhan keputusan, ini menunjukkan tujuan ciri-ciri dipermudahkan pengawal logik kabur (SFLC) telah dijustifikasikan.

(6)

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS & ABBREVIATIONS xviii

LIST OF APPENDICES xix

1 INTRODUCTION 1 1.1 General Background 1 1.2 Objectives 2 1.3 Scope 3 2 LITERATURE REVIEW 5 3 METHODOLOGY 9

3.1 Photovoltaic Solar Panel 10

3.2 DC-DC Boost Converter 14

3.3 Fuzzy Logic Controller 19

(7)

4 SIMULATION IMPLEMENTATION 26

4.1 PV Solar Panel 26

4.3 PV panel and DC-DC Boost Converter 29 4.4 Conventional Method of Fuzzy Logic Controller Set Up 31 4.5 Simplified Method of Fuzzy Logic Controller Set Up 35 4.6 Conventional Method Fuzzy Logic Controller 39 4.7 Simplified Method Fuzzy Logic Controller 40 4.8 PV Solar Panel and DC-DC Boost Converter circuit with Conventional Method of Fuzzy Logic Controller 41 4.9 PV Solar Panel and DC-DC Boost Converter circuit with Simplified Method of Fuzzy Logic Controller 42

5 SIMULATION RESULTS 44

4.1 PV Solar Panel 44

4.3 PV panel and DC-DC Boost Converter 58 4.4 Conventional Method Fuzzy Logic Controller 63 4.5 Simplified Method Fuzzy Logic Controller 64 4.6 PV Solar Panel and DC-DC Boost Converter circuit with Conventional Method of Fuzzy Logic Controller 66 4.7 PV Solar Panel and DC-DC Boost Converter circuit with Simplified Method of Fuzzy Logic Controller 69

(8)

6 DISCUSSIONS AND SUGGESTIONS 73

7 CONCLUSIONS 75

References 76

Appendix 79

(9)

LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 Conventional Fuzzy Logic Controller (CFLC) matrix 24 3.2 Simplified Fuzzy Logic Controller (SFLC) matrix 24 3.3 Conversion from conventional to simplified matrix 24 5.1 Change of Irradiance and fixed temperature at 25°C for

PV panel 55

5.2 Output results of the PV panel and DC-DC boost converter with changes on the PV panel input of temperature and

irradiance values 62

5.3 Output results of the PV panel and DC-DC boost converter with conventional method fuzzy logic controller (CFLC) with changes on the PV panel input of temperature and

5.4 Output results of the PV panel and DC-DC boost converter with simplified method fuzzy logic controller (SFLC) with changes on the PV panel input of temperature and

(10)

LIST OF FIGURES

FIGURE NO. TITLE PAGE

3.1 PV Maximum Power Point Tracking (MPPT)

full functions Block Diagram 9

3.2 Types of Solar Panel by materials 10

3.3 Solar Panel internal layout diagram 10 3.4 Solar/Cell panel internal diagrams 11 3.5 Solar panel schematic diagram circuit 11

3.6 Characteristic for solar panel 12

3.7 Characteristic of the solar panel at 25°C

temperature operation 13

3.8 Combination of single cell into module and

array of solar panel 14

3.9 DC-DC Boost Converter Circuit diagram 15 3.10 Graph diagrams of switching on and off time

for boost converter circuit 16 3.11 Pulse width modulation and Period of ON and

OFF time pulse 19

(11)

3.12 Perturb and Observe or Hill Climbing flow

chart diagram 21

3.13 Incremental Conductance flow chart diagram 21 3.14 Graph with dash line at Maximum Power Point

for different irradiance 22

3.15 Fuzzy Logic Controller flow application

function diagram 22

3.16 Fuzzy Logic Controller internal application

Function 23

3.17 Process progress flow of the fuzzification,

rule base and defuzzification diagram 23 4.1 Photovoltaic Solar Panel simulation diagram 27 4.2 Maximum Power Point Tracking (MPPT)

algorithm simulation setting curve 27 4.3 PV panel module set up simulation 28 4.4 DC-DC Boost Converter Circuit Diagram 29 4.5 Combine between PV Solar Panel and DC-DC

Boost Converter diagram 30

4.6 Fuzzy Logic Controller Conventional Method

set up at MATLAB software 31 4.7 Set up input setting pattern of the voltage site

for CFLC 31

4.8 Set up input setting pattern of the current site

for CFLC 32

(12)

4.9 Set up output setting pattern of the conventional

fuzzy logic controller site 32 4.10 Rule Editor 1 of the conventional fuzzy logic

controller (CFLC) 33

4.11 Rule Editor 2 of the conventional fuzzy logic

4.12 Rule Viewer of the conventional fuzzy logic

4.13 Surface Viewer of the conventional fuzzy logic

4.14 Surface Viewer of the conventional fuzzy logic

4.15 Fuzzy Logic Controller Simplified Method set up

at MATLAB software 35

4.16 Set up input setting pattern of the simplified fuzzy

logic controller (SFLC) 36

4.17 Set up output setting pattern of the simplified fuzzy

logic controller (SFLC) 36

4.18 Rule Editor of the simplified fuzzy logic controller

(SFLC) 37

4.19 Rule Viewer of the simplified fuzzy logic controller

(SFLC) 38

4.20 Surface Viewer of the simplified fuzzy logic

controller (SFLC) 38

(13)

4.21 Conventional Fuzzy Logic Controller (CFLC)

simulation diagram 39

4.22 Simplified Fuzzy Logic Controller (SFLC)

4.23 PV panel and DC-DC boost converter with Conventional Method Fuzzy Logic Controller

(CFLC) simulation diagram 42 4.24 PV panel and DC-DC boost converter with

simplified fuzzy logic controller (SFLC)

5.1 Voltage output result of the PV panel 45 5.2 Current output result of the PV panel 45 5.3 Power output result of the PV panel 46 5.4 Fixed Temperature at 25°C with irradiance of

0.4/0.7 on curve plotted 46

5.5 Change Temperature to 30°C with irradiance of

(14)

5.13 PWM pulses into DC-DC Boost Converter 56 5.14 Current output result of the DC-DC Boost

Converter 56

5.15 Current output result of the DC-DC Boost

Converter close up 57

5.16 Voltage output result of the DC-DC Boost

Converter 57

5.17 Voltage output result of the DC-DC Boost

Converter close up 58

5.18 PWM pulses into DC-DC Boost Converter 59 5.19 Current output results of the PV panel and

DC-DC Boost Converter 59

5.20 Current output results of the PV panel and

DC-DC Boost Converter at close up view 60 5.21 Voltage output results of the PV panel and

DC-DC Boost Converter 60

(15)

5.22 Voltage output results of the PV panel and

DC-DC Boost Converter at close up view 61 5.23 Voltage output result of the PV panel 61 5.24 Current output result of the PV panel 62 5.25 PWM pulse generated from Conventional Fuzzy

Logic Controller (CFLC) 63

5.26 Generated Carrier Signal waveforms 64 5.27 Output result of the Conventional Fuzzy Logic

Controller (CFLC) 64

5.28 PWM pulse generated from Simplified Fuzzy

Logic Controller (SFLC) 65

5.29 Generated Carrier Signal waveforms 65 5.30 Output result of the Simplified Fuzzy Logic

Controller (SFLC) 65

DC-DC Boost Converter with Conventional Fuzzy

Logic Controller (CFLC) at close up view 67 5.33 Voltage output results of the PV panel and

(16)

5.34 Voltage output results of the PV panel and

Logic Controller (CFLC) at close up view 68 5.35 Current output results of the PV panel and

DC-DC Boost Converter with Simplified Fuzzy

5.36 Current output results of the PV panel and DC-DC Boost Converter with Simplified Fuzzy

Logic Controller (SFLC) at close up view 70 5.37 Voltage output results of the PV panel and

DC-DC Boost Converter with Simplified Fuzzy

5.38 Voltage output results of the PV panel and DC-DC Boost Converter with Simplified Fuzzy

Logic Controller (SFLC) at close up view 71 xvii

(17)

LIST OF SYMBOLS & ABBREVIATIONS

PV - Photovoltaic

MPPT - Maximum Power Point Tracking FLC - Fuzzy Logic Controller

CFLC - Conventional Fuzzy Logic Controller SFLC - Simplified Fuzzy Logic Controller DC - Direct Current/Voltage

MF - Membership Function PWM - Pulse Width Modulation

(18)

LIST OF APPENDIX

APPENDIX TITLE PAGE

I SM Solar Panel 100W Specification 79

(19)

CHAPTER 1

INTRODUCTION

The world is offering the best natural resources of energy for human being to use it. Such as, sun, wind, ocean current wave, geothermal, biomass and lots more. One of the natural resources is the sun or sun radiation towards the earth atmosphere and surface. Sun had the strong energy onwards on earth around few hundred watts/meter square. In country like Malaysia which had the most sunlight from the sun, around 12 to 13 hours per daylight. This included direct sunlight, temperature and irradiation. Since fossil fuel which will run out sooner nor later, that’s why renewable energy now plays an important role to sustain for the usage of household appliances.

(20)

1.1 General Background

Research of this project is to develop and analyze PV Maximum Power Point Tracking (MPPT) algorithm that based on the Simplified Fuzzy Logic Controller (SFLC). Solar panel or PV panel will received incoming non linear energy from the sun direct sunlight, temperature and irradiation, which based on the weather condition changes. It’s had the wide available free natural clean energy, carbon emission free and environmental friendly. From the PV panel output, will be connected towards Maximum Power Point Tracking (MPPT) algorithm by using Fuzzy Logic Controller (FLC) to determine the algorithm progress process flow execution, and next connected to Boost Converter circuit to increase the output voltage level and retain or decrease output current level at suitable condition. The Fuzzy Logic Controller (FLC) is to reduce the numbers of inputs into one single input, which from conventional method to simplified method. The output of the DC-DC Boost Converter circuit is DC-DC voltage and current. Finally, both of the output is analyzed with the differences of two Fuzzy Logic Controller (FLC) methods applied.

1.2 Objectives

- To develop and analyze PV Maximum Power Point Tracking (MPPT) algorithm by using MATLAB software.

- To analyze the difference between conventional method and simplified method of the Fuzzy Logic Controller (FLC) cum MATLAB software based.

(21)

- To optimized and reduce numbers of Maximum Power Point Tracking (MPPT) algorithm by Fuzzy Logic Controller (FLC) concept.

- An able to do simulation and determine the algorithm of Maximum Power Point Tracking (MPPT) by using Fuzzy Logic Controller (FLC) based via MATLAB software.

- To determine and obtain the suitable output DC voltage and current values from the MATLAB simulation results.

1.3 Scope

Solar PV panel plays an important role as one of the renewable energy concept or alternative energy, which determine by it characteristic of current, voltage and power. It’s depends on the weather condition that can be changes around day light. Hereby, is to capture input of the non linear current based value of the solar PV panel. Output wise of the solar PV panel are in DC voltage and current values.

Maximum Power Point Tracking (MPPT) algorithm are consist Perturb and Observe or Hill Climbing, Incremental Conductance, fractional open circuit voltage and fractional short circuit current. All the functions of the Maximum Power Point Tracking (MPPT) stated as before, are in order to control the swing of the power maximum values. This is to prevent the power maximum values decrease sharply or rapidly drop neither left nor right of the characteristic Power vs. Voltage curve. On the other hand, by optimize and simplified its algorithm by using Fuzzy Logic Controller (FLC) cum MATLAB software application.

(22)

Fuzzy Logic Controller (FLC) is one of the concepts by using MATLAB software application to structure the outline between conventional method and simplified method. Conventional Fuzzy Logic Controller (CFLC) had multiples inputs and outputs or multiples inputs and single output. Simplified Fuzzy Logic Controller (SFLC) had single input and single output. Inside the structure of the Fuzzy Logic Controller (FLC) consist of Fuzzification, Rule base and Defuzzification. Both fuzzification and defuzzification, consist of Membership Functions (MF) either input or output structured. Rule base is an instruction of the process progress between both fuzzification and defuzzification structure, such as “if...and/or...then...”. Output of the Fuzzy Logic Controller (FLC) will be sending duty cycles signals to the DC-DC Boost Converter circuit.

DC-DC Boost Converter circuit is to convert or boost minimum DC voltage level at input to maximum DC voltage level at output. In order for it to function, which a duty cycle’s signals needed to input to the switching that an able to running the DC-DC Boost Converter circuit accordingly. So that, an able to obtain the suitable maximum DC voltage level as per requirement.

Lastly, it’s to analyze the difference both of the Conventional and Simplified Fuzzy Logic Controller from output voltage and current of the simulation obtained. Hereby, both of the end result will shown the similar or/and alike performance for output DC voltage and current.

(23)

References

[1] Ting-Chung Yu and Tang-Shiuan Chien, Analysis and Simulation of

Characteristics and Maximum Power Point Tracking for Photovoltaic Systems, 2009,

PEDS, pp 1339 – 1344.

[2] C. S. Chin, P. Neelakantan, H. P. Yoong and K. T. K. Teo, Optimisation of Fuzzy based Maximum Power Point Tracking in PV system for rapidly changing solar

irradiance, June 2011, Global Journal of Technology and Optimization, Vol. 2, pp

130 – 137.

[3] S. M. Ayob, Z. Salam, N. A. Azli and Malik E. Elbuluk, Control of A Single

Phase Inverter Using Fuzzy Logic, 2009, IEEE, 978-1-4244-3476-3/09, Faculty of

Electrical Engineering, University Technology Malaysia.

[4] Ting-Chung Yu and Yu-Cheng Lin, A study on Maximum Power Point Tracking

Algorithms for Photovoltaic Systems, December 2010, 3th Edition, University

Publications, Department of Electrical Engineering, Lung Hwa University of Science and Technology, pp 27 – 36.

[5] Yeong-Chau Kuo, Tsorng-Juu Liang and Jiann-Fuh Chen, Novel Maximum

Power Point Tracking Controller for Photovoltaic Energy Conversion System, June

2001, IEE Transactions on Industrial Electronics, Vol. 48, No 3, pp 594 – 601. [6] Joe-Air Jiang, Tsong-Liang Huang, Ying-Tung Hsiao and Chia-Hong Chen,

Maximum Power Tracking for Photovoltaic Power Systems, 2005, Tam Kang Journal

of Science and Engineering, Vol. 8, No 2, pp 147 – 253.

[7] Yuncong Jiang and Jaber A. Abu Qahouq, Study and Evaluation of Load Current

Based MPPT Control for PV Solar Systems, 2011, IEEE, 978-1-4577-0541-0/11,

Department of Electrical and Computer Engineering, The University of Alabama, pp 205 – 210.

[8] Kinal Kachhiya, Makarand Lokhande and Mukesh Patel, MATLAB/Simulink

Model of Solar PV Module and MPPT Algorithm, May 2011, National Conference

on Recent Trends in Engineering and Technology, B.V.M. Engineering College, V.V. Nagar, Gujarat, India, pp 1 – 5.

[9] Yousef Mahmoud, W. Xiao and H. H. Zeineldin, A Simple Approach to Modeling

and Simulation of Photovoltaic Modules, January 2012, IEEE Transactions on

sustainable energy, Vol. 3, No. 1, pp 185 – 186.

[10] Theodoros L. Kottas, Yiannis S. Boutalis and Athanassions D. Karlis, New Maximum Power Point Tracking for PV Arrays Using Fuzzy Controller in Close

Cooperation with Fuzzy Cognitive Networks, September 2006, IEEE Transactions on

energy conversion, Vol. 21, No. 3, pp 793 – 803.

[11] Mohamad Azab, A New Maximum Power Point Tracking for Photovoltaic

Systems, 2008, World Academy of Science, Engineering and Technology, 44, pp 571

– 574.

[12] Mohamad Azab, Improved Circuit Model of Photovoltaic Array, 2009,

International Journal of Electrical and Electronics Engineering, 3:11, pp 706 – 709. [13] Trishan Esram and Patrick L. Chapman, Comparison of Photovoltaic Array

Maximum Power Point Tracking Techniques, June 2007, IEEE Transactions on

energy conversion, Vol. 22, No. 2, pp 439 – 449.

[14] R. Ramaprabha and B. L. Mathur, Intelligent Controller based Maximum Power

Point Tracking for Solar PV System, International Journal of Computer Applications,

January 2011, Vol. 12, No. 10, pp 37 – 41.

[15] Manoj Kumar, Dr. F. Ansari and Dr. A. K. Jha, Maximum Power Point Tracking

using Perturbation and Observation as well as Incremental Conductance Algorithm,

(24)

December 2011, International Journal of Research in Engineering and Applied Sciences, Vol. 1, Issue 4, pp 19 – 31.

[16] Francisco M. Gonzalez-Longatt, Model of Photovoltaic Module in MATLAB, 2005, 2nd International Conferences of Electrical and Electronics Engineering and Applied Computations, pp 1 – 5.

[17] Mayssa Farhat and Lassaad Sbita, Advance Fuzzy MPPT Control Algorithm for

Photovoltaic Systems, March 2011, Science Academy Transactions on Renewable

Energy Systems Engineering and Technology, Vol. 1, No. 1, pp 29 – 36. [18] M. S. Ait Cheikh, C. Larbes, G. F. Tchoketch Kebir and A. Zerguerras,

Maximum Power Point Tracking using a Fuzzy Logic Control Scheme, 2007,

Renewable Energy, Vol. 10, No.3, pp 387 – 395.

[19] M. A. S. Masoum and M. Sarvi, A new Fuzzy Based Maximum Power Point Tracker for Photovoltaic Applications, January 2005, Iranian Journal of Electrical and Electronic Engineering, Vol. 1, pp 28 – 35.

[20] J. A. Ramos-Hernanz, J. J. Campayo, J. Larranaga, E. Zulueta, O. Barambones, J. Motrico, U. Fernandez Gamiz and I. Zamora, Two Photovoltaic Cell Simulation

Models in MATLAB/Simulink, March 2012, International Journal on Technical and

Physical Problems of Engineering, Vol. 4, Issue 10, No. 1, pp 45 – 51.

[21] Dr. Abu Tariq, Mohammed Asim and Mohd. Tariq, Simulink based modelling, simulation and performance Evaluation of an MPPT for maximum power generation on resistive load, 2011, 2nd International Conference on Environmental Science and Technology, pp 397 – 401.

[22] Pandiarajah N, Ramaprabha R. and Ranganath Muthu, Application of Circuit

Model for Photovoltaic Energy Conversion System, Circuit Modelling Process for

Photovoltaic Module, pp 1 – 11.

[23] Chun-hua Li, Xin-jian Zhu, Guang-yi Cao, Wan-qi Hu, Sheng Sui and Ming-ruo

Hu, A Maximum Power Point Tracker for Photovoltaic energy systems based on

fuzzy neural networks, 2009, Journal of Zhejiang University Science, Vol. 10, No. 2, pp 263 – 270.

[24] A. Al Nabulsi and R. Dhaouadi, Fuzzy Logic Controller based perturb and

observe maximum power point tracking, March 2012, International Conference on

Renewable Energies and Power Quality, pp 1 – 6.

[25] L. MacIsaac and A. Knox, Improved Maximum Power Point Tracking

Algorithm for Photovoltaic Systems, March 2010, International Conference on

Renewable Energies and Power Quality, pp 1 – 6.

[26] Karel Zaplatilek and Jan Leuchter, Behaviour Model of Photovoltaic Panel in

Simulink, 2011, Advances in Electrical and Computer Engineering, Vol. 11, No. 4,

pp 83 – 88.

[27] C. Liu, B. Wu and R. Cheung, Advanced Algorithm for MPPT Control of

Photovoltaic Systems, 2004, Canadian Solar, Buildings Conference, pp 1 – 7.

[28] Huan-Liang Tsai, Ci-Siang Tu and Yi-Jie Su, Development of Generalized

Photovoltaic Model using MATLAB/SIMULINK, 2008, Proceedings of the World

Congress on Engineering and Computer Science, ISBN 978-988-98671-0-2. [29] Pongsakor Takun, Somyot Kaitwanidvilai and Chaiyan Jettanasen, Maximum

Power Point tracking using Fuzzy Logic Control for Photovoltaic Systems, 2011,

Proceedings of the International Multi Conference of Engineers and Computer Scientists, Vol. 2, ISBN 978-988-19251-2-1.

[30] T. Chaitanya, Ch. Saibabu and J. Surya Kumari, Modeling and Simulation of PV

Array and its performance enhancement using MPPT (P&O) Technique, 2011,

(25)

International Journal of Computer Science and Communication Networks, Vol. 1, No. 1, pp 9 – 16.

[31] Fuzzy Logic Toolbox for use with MATLAB, User’s Guide, Version 2, The Math Works, 2002.

[32] Applications of Fuzzy Logic in Control Design, MATLAB Technical computing brief, The Math Works, 1996.