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, H 2 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 Contribution 1- This thesis present the design of fuzzy controller of the Magnetic Levitation Model CE 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 was the birth of fuzzy logic techniques 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 ORNOT

11 Fuzzy Control Operations of Fuzzy Sets : 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 population 3- 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

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. Let us find the maximum value of the function (15x  x 2 ) where parameter x varies between 0 and 15. For simplicity, we may assume that x takes only integer values. Thus, chromosomes can be built with only four genes:

32 Suppose that the size of the chromosome population N is 6, the crossover probability p c equals 0.7, and the mutation probability p m equals The fitness function in our example is defined by f(x) = 15 x  x 2

33

34 Genetic Algorithm Genetic Fuzzy Systems:

35 Genetic Algorithm Genetic Fuzzy Systems: 1- Genetic Tuning of The Data Base Tuning scaling gains Tuning 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 FPGA and Xfuzzy CAD Tool

38 FPGA and Xfuzzy CAD Tool

39 FPGA and Xfuzzy CAD Tool

40 FPGA and Xfuzzy CAD Tool The Spartan-3E Development System

41 FPGA and Xfuzzy CAD Tool Xfuzzy CAD Tool:

42 FPGA and Xfuzzy CAD Tool Xfuzzy CAD Tool: 1- Description Stage

43 FPGA and Xfuzzy CAD Tool Xfuzzy CAD Tool: 2- Tuning Stage

44 FPGA and Xfuzzy CAD Tool Xfuzzy CAD Tool: 3- Vervication Stage

45 FPGA and Xfuzzy CAD Tool Xfuzzy CAD Tool: 4- Synthesis Stage 1- Generat VHDLcode. 2- C code. 3- sysgen code.

46 Application and Results Magnetic Levitation CE152 Model

47 Application and Results Magnetic Levitation CE152 Model

48 Application and Results Magnetic Levitation CE152 Model open loop poles of the system: : (Stable pole), -63: (Stable pole), 61: (Unstable pole)

49 Application and Results 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 Application and Results 1- Fuzzy controller

51 Application and Results 1- Fuzzy controller elnmnsnzspmplp ce ln mnsnz mnln mnsnzsp snln mnsnzspmp zlnmnsnzspmplp spmnsnzspmplp mpsnzspmplp zspmplp

52 Application and Results 1- Fuzzy controller

53 Application and Results 1- Fuzzy controller Fuzzy Subsystem PI Subsystem

54 Application and Results 1- Fuzzy controller

55 Application and Results 1- Fuzzy controller Set Point Time Set Point Time Ts is nearly 0.15 sec Tr is nearly sec

56 Application and Results 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 Application and Results 2- Fuzzy Controller Design with GA

58 Application and Results 2- Fuzzy Controller Design with GA Set Point Time overshot is nearly 6%, Ts is sec Tr is sec. Set Point Time

59 Application and Results 3- VHDL Fuzzy Controller Implementation PIC 16f877 as ADC DAC 0800.

60 Application and Results 3- VHDL Fuzzy Controller Implementation

61 Application and Results 3- VHDL Fuzzy Controller Implementation

62 Application and Results 3- VHDL Fuzzy Controller Implementation Change of error Time Error

63 Application and Results 3- VHDL Fuzzy Controller Implementation Set Point Time Set Point Time

64 Application and Results 3- VHDL Fuzzy Controller Implementation

65 Application and Results 3- VHDL Fuzzy Controller Implementation

66 Application and Results 3- VHDL Fuzzy Controller Implementation

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