1 design ga-fuzzy controller for magnetic levitation using fpga prepared by hosam.m abu elreesh...

1

Design GA-Fuzzy Controller for Magnetic Levitation

Using FPGA

Prepared by

Hosam .M Abu Elreesh

Advisor Dr. Basil Hamed

2

Contents

• Introduction• Fuzzy Logic• Genetic Algorithm (GA)• FPGA and Xfuzzy CAD Tool• Application and Results• Conclusion• Future Works

3

Introduction

• Control systems have been in use for decades.• Power systems, computer control, space

technology, robotics, weapon systems and many others.

• Types of Control Systems:1- Conventional Control Techniques.

2- Intelligent Control Techniques.

4

Introduction

• Conventional Control Techniques:1- Classical Control (PID).

2- Modern Control (deadbeat, sliding mode). 3- Optimal Control (LQR, H2 and H∞).

• Intelligent Control Techniques: 1- Knowledge-base-expert systems (fuzzy

logic).2- Neural networks.

5

Introduction

• Fuzzy Logic hardware Implementation:

1- General-purpose fuzzy processor (µP, µC, digital signal processor (DSP)).

2-Dedicated fuzzy hardware

3- FPGA

6

Introduction

• Thesis Contribution1- This thesis present the design of fuzzy

controller of the Magnetic Levitation Model CE152.

2- Matlab program for applying the GA to optimize the memberships of the fuzzy controller.

3- Design the hardware of fuzzy controller using Xilinx Spartan 3e FPGA.

7

Fuzzy Control

Fuzzy Sets

Classical Sets

8

Fuzzy Control

Fuzzy History:• Fuzzy logic idea was born in July 1964.Lotfi A. Zadeh father of

fuzzy.

• 1965 was the birth of fuzzy logic techniques.

• 1979 was the first application of the fuzzy logic in industrial world cement kiln controller.

• In 1985 Japanese starts to make the first general-purpose fuzzy logic controller.

• Japanese start to use it in control systems, and they designed the first automatic subway train controller in 1987.

9

Fuzzy Control Why Use Fuzzy Logic?

• Fuzzy logic is used to control the complex, and nonlinear systems without make analyzing for these systems.

• Fuzzy control enables the engineers to implement the control technique by human operators

• Fuzzy logic is flexible with any given systems. • Fuzzy logic can be blended with conventional technique, to

simplify their implementation.

10

Fuzzy Control

Operations of Fuzzy Sets :

x

AND OR NOT

11

Fuzzy Control

Operations of Fuzzy Sets :

5.0)5.0,7.0min()(),(min)( xxx BABA

7.0)5.0,7.0max()(),(max)( xxx BABA

5.05.01)(1)( xx AAc

If there are two fuzzy sets A and B, and there is element (x).element (x) can be set A and has degree (0.5), element (x) can be in set B and has degree (0.7),

12

Fuzzy Control

Fuzzy Concepts:

• Membership Function.• Linguistic Variables.

• IF – THEN Rules

13

Fuzzy Control

Membership Function:

14

Fuzzy Control

Linguistic Variables:

• Age (old, young, very young, very old).• Tall (tall, short, very short, very tall).• Error( P big, P small, zero,N big, N small)

15

Fuzzy Control

IF – THEN Rules

• IF (input1 is MFa) AND (input2 is MFb) )

THEN (output is MFc)

• IF (Food is bad) and (Serves is bad ) THEN (Tip is cheap)

Antecedent consequent

16

Fuzzy Control

Fuzzy Logic Control (FLC)

• Mamdani model.• Takagi- Sugeno-Kang (TSK) model.• Kosko's additive model (SAM).

17

Fuzzy Control

Mamdani Model:

18

Fuzzy Control

Mamdani Model:• Fuzzification.

• Fuzzy Associative Memory (FAM) 1- Knowledge base.(Membership Functions, IF-THEN rules)

2- Decision-Making.

• Defuzzification Mean of Maximum method (MOM).

Center of Area (COA). Center of Maximum (CoM):

19

Fuzzy Control

Mamdani Model:

20

Genetic Algorithm

GA• Genetic Algorithms are reliable and robust methods for searching

solution spaces.

GA must address five issues. 1- A genetic representation 2- Initial population3- Fitness Function 4- Genetic operators 5- Values for the parameters of the GA, such as population size,

21

Genetic Algorithm

22

Genetic Algorithm

GA differs from conventional optimization techniques in following ways:

• GA does not deals with data directly but works with encoded data.

• GA uses least information such as fitness function to solve problems an does not need

derivation.

• GA uses probability laws rather than certain laws.

• GA generate populations of answer not just one answer.

• Almost all conventional optimization techniques search from a single point but

GA always operate on a whole population of points (parallelism).

23

Genetic Algorithm

GA Elements:

1- Individuals

2- Population

24

Genetic Algorithm

Chromosome coding

25

Genetic Algorithm

Fitness Function

0

2 )(. dttevaluefitness

dttevaluefitness

0

)(.

dtttevaluefitness

0

2 )(.

26

Genetic Algorithm

GA Operations:

1- Selection (Roulette Wheel Selection).

Roulette Wheel Selection

27

Genetic Algorithm

GA Operations:

1- Selection (Stochastic Universal Selection).

Stochastic Universal Sampling

28

Genetic Algorithm

GA Operations:

2- Crossover (Single-Point Crossover)

Single-Point Crossover

29

Genetic Algorithm

GA Operations:

2- Crossover ( Two-Point Crossover)

Two-Point Crossover

30

Genetic Algorithm

GA Operations:

3- Mutation

Mutation means swap one bit in binary coding or changes one number if the chromosome consist of numbers

4- Elitism

31

A simple example will help us to understand how a GA works. A simple example will help us to understand how a GA works. Let us find the maximum value of the function (15 Let us find the maximum value of the function (15xx xx22) ) where parameter where parameter xx varies between 0 and 15. For simplicity, varies between 0 and 15. For simplicity, we may assume that we may assume that xx takes only integer values. Thus, takes only integer values. Thus, chromosomes can be built with only four genes:chromosomes can be built with only four genes:

32

Suppose that the size of the chromosome population Suppose that the size of the chromosome population NN is 6, the is 6, the crossover probability crossover probability ppcc equals 0.7, and the mutation probability equals 0.7, and the mutation probability

ppmm equals 0.001. The fitness function in our example is defined equals 0.001. The fitness function in our example is defined

byby

ff((xx) = ) = 15 15 xx xx22

33x

50

40

30

20

60

10

00 5 10 15

f(x)

(a) Chromosome initial locations.

x

50

40

30

20

60

10

00 5 10 15

(b) Chromosome final locations.

34

Genetic Algorithm

Genetic Fuzzy Systems:

35

Genetic Algorithm

Genetic Fuzzy Systems:

1- Genetic Tuning of The Data Base

Tuning scaling gainsTuning fuzzy membership functions.

2- Genetic Learning of The Rule Base

36

FPGA and Xfuzzy CAD Tool

FPGA:

FPGA is digital integrated circuits (ICs) that have electronics blocks which can be programmed, and these blocks has configurable interconnection between them.

37


38


39


40


The Spartan-3E Development System

41


Xfuzzy CAD Tool:

42


Xfuzzy CAD Tool:

1- Description Stage

43


Xfuzzy CAD Tool:

2- Tuning Stage

44


Xfuzzy CAD Tool:

3- Vervication Stage

45


Xfuzzy CAD Tool:

4- Synthesis Stage

1- Generat VHDLcode.2- C code.

3- sysgen code.

46

Application and Results

Magnetic Levitation CE152 Model

47


1 12c 00 c 00

2 23 2kk 00 0 k 00 0

3 3 i DA

1

x AD 2

3

0 1 0x 0

-2*k *i -k 2*k *ix 0 u(t)

mm x -x m x -xx K K

1 T0 0T

y= K K 0 0

fv

a

a

x

x

x

x

x

x


3 2

8.883e8 G(s)=

s + 5.349e4 s + 1.312e5 s - 2.054e8

The plant

48



open loop poles of the system:

-53492: (Stable pole), -63: (Stable pole), 61: (Unstable pole)

2Controlability Matrix B AB A B

0 0 5.5697e6

= 0 5.5697e6 -2.9795e11

1.5873e5 -8.49

08e9 4.519e14

Rank 3

Sytem is controllable

n

49


1- Fuzzy controller

•All universes of discourses are normalized to lie between –1 and 1 with scaling •assumed that the first and last membership functions have their apexes at –1 and 1 respectively.

•Triangular, Z and S membership functions are to be used.

•The number of fuzzy sets is constrained to be an odd integer greater than unity.

•The base vertices of membership functions are coincident with the apex of the adjacent membership functions

50


1- Fuzzy controller

51


1- Fuzzy controller

e ln mn sn z sp mp lp

ce

ln ln ln ln ln mn sn z

mn ln ln ln mn sn z sp

sn ln ln mn sn z sp mp

z ln mn sn z sp mp lp

sp mn sn z sp mp lp lp

mp sn z sp mp lp lp lp

lp z sp mp lp lp lp lp

52


1- Fuzzy controller

53


1- Fuzzy controller

Fuzzy Subsystem

PI Subsystem

54


1- Fuzzy controller

55


1- Fuzzy controller

Set Point

Time

Set Point

Time

Ts is nearly 0.15 sec Tr is nearly 0.106 sec

56


2- Fuzzy Controller Design with GA

some simplification is used in writing GA code: 1- The interval of the inputs and output will still at [-1 1] range.2- The symmetric point will still at zero.3- The inputs and output will have the same shape.

The number of individuals per one population will be 50.

the number of generation will be 100.

the crossover probability will be 0.7

57



dttevaluefitness

0

)(.

58



Set Point

Time

overshot is nearly 6%,Ts is 0.046 sec Tr is 0.023 sec.

Set Point

Time

59


3- VHDL Fuzzy Controller Implementation

PIC 16f877 as ADC DAC 0800.

60



61



62



Change of error

Time

Error

63



Set Point

Time

Set Point

Time

64



65



66



67

CONCLUSION

•Fuzzy logic and fuzzy controller.•GA •FPGA •Xfuzzy CAD tool.• The Magnetic Levitation CE152.• Fuzzy controller with and without GA are tested.•Implementation of fuzzy controller using FPGA.

68

Thank You

1 design ga-fuzzy controller for magnetic levitation using fpga prepared by hosam.m abu elreesh...

Documents

fuzzy hardware

fuzzy logic controller

fuzzy logic idea

fuzzy controlmamdani

hardware of fuzzy controller

design of fuzzy controller

expert systems fuzzy

fuzzy controlfuzzy concepts