1. A Presentation on Adaptive Neuro-Fuzzy Inference System using Particle Swarm Optimization and it’s Application By Sumanta Kundu (En.R.No ) System Modeling & Control Under the guidance of Dr.M.J.Nigam

2. OUTLINES
Introduction.
Neural Network.
Fuzzy Logic.
Adaptive Neuro-Fuzzy Inference System.
Particle Swarm Optimization Technique.
Simulation results.
Conclusions.

3. INTRODUCTION
The Adaptive Neuro-Fuzzy Inference System combines the concept of Fuzzy logic and Neural network to form a hybrid intelligent system that enhances the ability to automatically learn and adapt.
The Particle Swarm Optimization algorithm used to get the optimal values and parameters of our ANFIS model.

4. NEURAL NETWORK
A Neural network can be described as a system composed of many simple processing elements operating in parallel .
The function of NN is determined by network structure, connection strengths and the processing performed at computing elements or nodes.
It resembles the brain in two respects:
1. Knowledge is acquired by the network through a learning process.
2. Interneuron connection strengths known as synaptic weights are used to store the knowledge.

5. NEURAL NETWORK ARCHITECTURE
Single Layer Architecture:
It has one input layer and one output layer.
The assigned weight matrix is
Here Wij Denotes the weight between j th source to the i th neuron

6. NEURAL NETWORK ARCHITECTURE
Multiple Layer Architecture
Here each single layer is connected in cascade form.
Each layer has it’s own weight matrix , bias vector , input vector , output vector.

7. LEARNING
Learning of NN means to find the best value of weights and bias inputs by an iterative procedure with some sets of sample data.
Two forms of learning procedures are:
Supervised Learning.
Unsupervised Learning.

8. BACK PROPAGATION IN NEURAL NETWORK
Back Propagation learns by iteratively processing a set Of training data (samples). For each sample, weights are modified to minimize the error between network’s classification and actual classification.
The steps involved in back propagation are:
Initialize the weights and biases.
Feed the training sample.
Propagate the inputs forward; The net input has been computed and so as the output of each unit in the hidden and output layers.
Back propagate the error.
Update weights and biases to reflect the propagated errors.
Terminating conditions.

9. APPLICATION OF NEURAL NETWORK
Useful in the identification and control of dynamic
systems.
Optical character recognition.
Voice recognition.
Industrial process control.
Customer research.
Risk management.

10. FUZZY LOGIC
Fuzzy logic is introduced by Lotfi Zadeh in 1960’s.
It is a superset of Boolean or Crisp logic.
Decision making with its ability to work from approximate data and find precise solutions.
Modeling of complex systems using a higher level of abstraction originating from expertise knowledge.

11. MODEL OF FUZZY LOGIC CONTROLLER

12. ADVANTAGES
Fuzzy logic reduces the design development cycle.
It simplifies design complexity.
It simplifies implementation.
It improves control performance
Easy extension of the base of knowledge through the addition of new rules.
Robustness in relation of the possible disturbances in the system.

13. DISADVANTAGES
Highly dependent on expertise knowledge.
Not robust in relation to topological changes.
Incapable to generalize.

14. ADAPTIVE NEURO-FUZZY PRINCIPLE
Finding the membership functions and rules is not easy task.
This deficiency demands learning algorithm.
Neural Network has efficient learning algorithm.
The combined Neuro-Fuzzy principle has the advantage of both.

15. ARCHITECTURE OF ANFIS MODEL

16. ARCHITECTURE OF ANFIS MODEL
The common rule set for two if then rules can be expressed as:
Rule 1: if x is A1 and y is B1 , then z1=p1x+q1y+r1
Rule 2: if x is A2 and y is B2 , then z2=p2x+q2y+r2
Layer 1: Oi = µAi(x), i = 1, 2
Oi = µBi(y), i = 3, 4
Layer 2: Oi2 = w i= µAi(x). µBi(y) , i=1,2
Layer 3:   
ARCHITECTURE OF ANFIS MODEL

17. Layer 4:
Layer 5:
ARCHITECTURE OF ANFIS MODEL

18. PARTICLE SWARM OPTIMIZATION TECHNIQUE
Population based optimization method.
No gradient information is required.
Particles changes their position in a hyperspace until
terminating conditions are reached.

19. PSO ALGORITHM
Particles are put into the d-dimensional search space with randomly chosen velocities and positions.
The velocity of each particle, adjusted according to its own flying experience and the other particle’s flying experience.
the i-th particle is represented as xi = (xi,1 ,xi,2 ,…, xi,d) in the d-dimensional space.
The best previous position of the i-th particle is recorded and represented as: Pbesti = (Pbesti,1, Pbesti,2,..., Pbesti,d)

20. The index of best particle in the group is gbestd.
The velocity of particle i is vi=(vi,1 ,vi,2 ,……… vi,d).
The modified velocity  
The modified position
Here i=1,2,…..n; m=1,2,……,d;
The fitness function
PSO ALGORITHM

21. APPLICATION OF PSO TECHNIQUE
Model selection is the task of picking the model that best describe a data set.
Task assignment is one of the core steps of effectively exploit the capabilities of distributed or parallel computing system.
Adjustment of weights in Neural Network.

22. SPEED CONTROL OF DC MOTOR
Mathematical model of dc motor
………..(1)
………….(2)
……………(3)

23. MODEL OF DC MOTOR IN SIMULINK

24. ADAPTIVE NEURO-FUZZY CONTROLLER
The output of ANFIS controller changes according to error and change of error.
The Sugeno type fuzzy rule is
if e is Ai and de is Bi then z = f(e, de)
Fig: ANFIS controller architecture

25. ADAPTIVE NEURO-FUZZY CONTROLLER
Layer 1:
Layer 2:
Layer 3:
Layer 4:
ADAPTIVE NEURO-FUZZY CONTROLLER

26. ADAPTIVE NEURO-FUZZY CONTROLLER
Layer 5:

27. MEMBERSHIP FUNCTIONS OF ANFIS CONTROLLER
Input variable “e”
Input variable “de”

28. SPEED RESPONSE OF ANFIS CONTROLLER

29. ANFIS CONTROLLER WITH PSO
It gives the optimal range of ‘universe of discourse’ for ‘e’ and
‘de’.
It defines the optimal range of each membership functions.

30. THE OPTIMAL MEMBERSHIP FUNCTIONS
Input variable ‘e’
Input variable ‘de’

31. SPEED RESPONSE OF ANFIS CONTROLLER WITH PSO

32. From the above comparison, the ANFIS controller with PSO is
CONCLUSIONS
The problem of finding proper membership functions and rules can be overcome by introducing ANFIS controller.
The optimal value of universe of discourse and range of each membership functions are obtained with the help of PSO technique.
Results
ANFIS controller
ANFIS controller with PSO
Rise time[sec]
Overshoot[%]
Steady State error[%]
From the above comparison, the ANFIS controller with PSO is
best from other two.