A First Course in FUZZY and NEURAL CONTROL

3.12. EXERCISES AND PROJECTS 131 Find formulas for all the functions involved and also plot them. LetA(x)=sinπx,B(x)=x^2 ,A^0 ( ...

132 CHAPTER 3. FUZZY LOGIC FOR CONTROL 0 0.2 0.4 0.6 0.8 246810 B 1 [1, 4 ,6]andB 2 [4, 8 ,9] and 0 0.2 0.4 0.6 0.8 246810 C 1 [ ...

Chapter 4 FUZZY CONTROL Fuzzy logic controllers serve the same function as the more conventional con- trollers, but they manage ...

134 CHAPTER 4. FUZZY CONTROL To balance an upright pendulum, we know from naive physics that the con- trol forceu(t)should be ch ...

4.1. A FUZZY CONTROLLER FOR AN INVERTED PENDULUM 135 ANGULAR VELOCITY B 1 =NB B 2 =NM B 3 =NS B 4 =PS B 5 =PM B 6 =PB Fuzzy sets ...

136 CHAPTER 4. FUZZY CONTROL The look-up table θ\θ^0 NB NM NS PS PM PB NB NB NB NB NM NS PS NM NB NB NM NS PS PS NS NB NM NS PS ...

4.2. MAIN APPROACHES TO FUZZY CONTROL 137 FORCE C 3 =NS C 4 =PS Ψ(u)=[0. 6 ∧C 3 (u)]∨[0. 82 ∧C 4 (u)] To produce an actual contr ...

138 CHAPTER 4. FUZZY CONTROL control laws using logical rules. That is why we sometimes call this methodology fuzzy logic contro ...

4.2. MAIN APPROACHES TO FUZZY CONTROL 139 also be assessed by using a concept known asVapnik-Chervonenki dimensionof a class of ...

140 CHAPTER 4. FUZZY CONTROL Cjx,j=1,...,N. In the Mamdani and Larsen methods, this is done by taking the maximum. In the Mamdan ...

4.2. MAIN APPROACHES TO FUZZY CONTROL 141 Note that the premise is in the same form as for the Mamdani and Larsen methods, but t ...

142 CHAPTER 4. FUZZY CONTROL each having value 1 on one of the pieces of the mapping and 0 on the other. -3 -2 -1^01 x 2 3 A 1 ( ...

4.2. MAIN APPROACHES TO FUZZY CONTROL 143 are state and input matrices, respectively, andz(t)=(z 1 (t),...,zp(t))is the p-dimens ...

144 CHAPTER 4. FUZZY CONTROL 4.3 Stability of fuzzy control systems.................. Fuzzy control designs seem appropriate for ...

4.3. STABILITY OF FUZZY CONTROL SYSTEMS 145 For a given pair(x(k),u(k)),thenextstatex(k+1)is obtained from the aboverulebaseasfo ...

146 CHAPTER 4. FUZZY CONTROL Then, in view of the hypothesis and the fact that ifA,B,Paren◊nmatrices withP positive definite and ...

4.4. FUZZY CONTROLLER DESIGN 147 providing as much force as needed to bring the velocity to the desired level. If the actual vel ...

148 CHAPTER 4. FUZZY CONTROL (c) Engine force Figure 4.3. Prototype membership functions for automobile cruise control With the ...

4.4. FUZZY CONTROLLER DESIGN 149 If velocity error is PE and acceleration is NA, then engine force is Max. If velocity error is ...

150 CHAPTER 4. FUZZY CONTROL velocity is set up as a constant that feeds a signal to a summer. Since this is a reference signal, ...