## A First Course in Fuzzy and Neural Control (Google eBook)Although the use of fuzzy control methods has grown nearly to the level of classical control, the true understanding of fuzzy control lags seriously behind. Moreover, most engineers are well versed in either traditional control or in fuzzy control-rarely both. Each has applications for which it is better suited, but without a good understanding of both, engineers cannot make a sound determination of which technique to use for a given situation. A First Course in Fuzzy and Neural Control is designed to build the foundation needed to make those decisions. It begins with an introduction to standard control theory, then makes a smooth transition to complex problems that require innovative fuzzy, neural, and fuzzy-neural techniques. For each method, the authors clearly answer the questions: What is this new control method? Why is it needed? How is it implemented? Real-world examples, exercises, and ideas for student projects reinforce the concepts presented. Developed from lecture notes for a highly successful course titled The Fundamentals of Soft Computing, the text is written in the same reader-friendly style as the authors' popular A First Course in Fuzzy Logic text. A First Course in Fuzzy and Neural Control requires only a basic background in mathematics and engineering and does not overwhelm students with unnecessary material but serves to motivate them toward more advanced studies. |

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### Contents

1 | |

3 | |

5 | |

13 Stable and unstable systems | 9 |

14 A look at controller design | 10 |

15 Exercises and projects | 14 |

MATHEMATICAL MODELS IN CONTROL | 15 |

inverted pendulum on a cart | 20 |

311 Universal approximation | 126 |

312 Exercises and projects | 128 |

FUZZY CONTROL | 133 |

42 Main approaches to fuzzy control | 137 |

421 Mamdani and Larsen methods | 139 |

422 Modelbased fuzzy control | 140 |

43 Stability of fuzzy control systems | 144 |

44 Fuzzy controller design | 146 |

22 State variables and linear systems | 29 |

23 Controllability and observability | 32 |

24 Stability | 34 |

241 Damping and system response | 36 |

242 Stability of linear systems | 37 |

243 Stability of nonlinear systems | 39 |

244 Robust stability | 41 |

25 Controller design | 42 |

26 Statevariable feedback control | 48 |

262 Higherorder systems | 50 |

27 Proportionalintegralderivative control | 53 |

temperature control | 61 |

controlling dynamics of a servomotor | 71 |

28 Nonlinear control systems | 77 |

29 Linearization | 78 |

210 Exercises and projects | 80 |

FUZZY LOGIC FOR CONTROL | 85 |

32 Fuzzy sets in control | 86 |

33 Combining fuzzy sets | 90 |

332 Triangular norms conorms and negations | 92 |

333 Averaging operators | 101 |

34 Sensitivity of functions | 104 |

342 Average sensitivity | 106 |

35 Combining fuzzy rules | 108 |

351 Products of fuzzy sets | 110 |

353 Larsen model | 111 |

354 TakagiSugenoKaiig TSK model | 112 |

355 Tsukamoto model | 113 |

36 Truth tables for fuzzy logic | 114 |

37 Fuzzy partitions | 116 |

38 Fuzzy relations | 117 |

381 Equivalence relations | 119 |

382 Order relations | 120 |

392 Heightcenter of area method | 121 |

393 Max criterion method | 122 |

395 Middle of maxima method | 123 |

3101 Extension principle | 124 |

3102 Images of alphalevel sets | 125 |

controlling dynamics of a servomotor | 151 |

45 Exercises and projects | 157 |

NEURAL NETWORKS FOR CONTROL | 165 |

52 Implementing neural networks | 168 |

53 Learning capability | 172 |

54 The delta rule | 175 |

55 The backpropagation algorithm | 179 |

training a neural network | 183 |

training a neural network | 185 |

58 Practical issues in training | 192 |

59 Exercises and projects | 193 |

NEURAL CONTROL | 201 |

62 Inverse dynamics | 202 |

63 Neural networks in direct neural control | 204 |

641 A neural network for temperature control | 205 |

642 Simulating PI control with a neural network | 209 |

65 Neural networks in indirect neural control | 216 |

651 System identification | 217 |

system identification | 219 |

653 Instantaneous linearization | 223 |

66 Exercises and projects | 225 |

FUZZYNEURAL AND NEURALFUZZY CONTROL | 229 |

71 Fuzzy concepts in neural networks | 230 |

72 Basic principles of fuzzyneural systems | 232 |

73 Basic principles of neuralfuzzy systems | 236 |

731 Adaptive network fuzzy inference systems | 237 |

732 ANFIS learning algorithm | 238 |

74 Generating fuzzy rules | 245 |

75 Exercises and projects | 246 |

APPLICATIONS | 249 |

82 Cooling scheme for laser materials | 250 |

83 Color quality processing | 256 |

84 Identification of trash in cotton | 262 |

85 Integrated pest management systems | 279 |

86 Comments | 290 |

291 | |

297 | |

### Common terms and phrases

algorithm ANFIS applied approach approximation backpropagation bark behavior characteristic consequent parameters control actions control law control problem control system control theory controller design defined delta rule derivative develop differential equation discussed dynamics example feedback control fuzzy control fuzzy control systems fuzzy inference system fuzzy logic fuzzy rules fuzzy sets fuzzy subset fuzzy systems hidden layer identify illustrated implement input input-output insects integral gain inverse dynamics inverted pendulum linear system linguistic Mamdani mathematical model MATLAB matrix membership functions method neural control neuron node nonlinear system obtain open-loop control operator output layer overshoot pattern vector Pepper Pepper performance PID controller plant polynomial position proportional gain sample shown in Figure sigmoidal functions simulation Simulink stability steady-state error Step response Sugeno system identification t-conorm t-norm Table temperature theorem trained neural network training data trash objects trash type triangular tristimulus values variables velocity error voltage weights zero