A First Course in FUZZY and NEURAL CONTROL

212 CHAPTER 6. NEURAL CONTROL net1 = init(net1); net1.iw{1,1} net1.b{1} net2 = init(net2); net2.iw{1,1} net2.b{1} The training p ...

6.4. EXAMPLE: TEMPERATURE CONTROL 213 0.4-0 .6 -0 .4 -0 .2 0 0.2 0.4 0.6 0.8 0.5 0.6 0.7 0.8 0.9 1 1.1 Figure 6.13. Integral gai ...

214 CHAPTER 6. NEURAL CONTROL Figure 6.16. Proportional control network error surface Figure 6.17. Integral control network erro ...

6.4. EXAMPLE: TEMPERATURE CONTROL 215 p2(i)=5*(exp(-time))*sin(w*time); time=time+0.1; end; dp2=gradient(p2) The plots in Figure ...

216 CHAPTER 6. NEURAL CONTROL Figure 6.20. Variation in proportional gain to test pattern Figure 6.21. Variation in integral gai ...

6.5. NEURAL NETWORKS IN INDIRECT NEURAL CONTROL 217 This is similar to standard control in that a mathematical model is needed, ...

218 CHAPTER 6. NEURAL CONTROL in practice, system identification by neural networks works remarkably well for reasonably well-be ...

6.5. NEURAL NETWORKS IN INDIRECT NEURAL CONTROL 219 6.5.2 Example: system identification ............... As indicated previously ...

220 CHAPTER 6. NEURAL CONTROL corresponding vector of outputs. Select a suitable number of vector elements. In this example we h ...

6.5. NEURAL NETWORKS IN INDIRECT NEURAL CONTROL 221 function that updates weight and bias values according to Levenberg-Marquard ...

222 CHAPTER 6. NEURAL CONTROL Figure 6.23. Plant and trained neural network response to the same random input At this stage, as ...

6.5. NEURAL NETWORKS IN INDIRECT NEURAL CONTROL 223 xlabel(íTime Stepí); ylabel(íPlant (solid) NN Output (dotted)í); Figure 6.24 ...

224 CHAPTER 6. NEURAL CONTROL nonlinear neural network model at each sampling time. Assume that a neural network input-output mo ...

6.6. EXERCISES AND PROJECTS 225 where ζ(τ)=y(τ)+ Xn i=1 aiy(τ−i)− Xm i=0 biu(τ−i) is the bias term. The approximate model may th ...

226 CHAPTER 6. NEURAL CONTROL (a) Test the neural network performance to an input speciΩ fied byu(t)= 0. 2 e−^0.^02 πksin (0. 2 ...

6.6. EXERCISES AND PROJECTS 227 Assume that the ball position is measured using an optical sensor. Use the following set of para ...

228 CHAPTER 6. NEURAL CONTROL (a) Simulate the nonlinear equations for small perturbations around the equilibrium to obtain a su ...

Chapter 7 FUZZY-NEURAL AND NEURAL-FUZZY CONTROL So far we have discussed two distinct methods for building controllers: fuzzy an ...

230 CHAPTER 7. FUZZY-NEURAL AND NEURAL-FUZZY CONTROL to aneural-fuzzy systemñ a fuzzy system represented as a modified neural ne ...

7.1. FUZZY CONCEPTS IN NEURAL NETWORKS 231 Figure 7.1. Neural network with fuzzy neurons approximate functions from numerical in ...