The fuzzy control

Fuzzy logic asserts itself as an operational technique. Used alongside other techniques for advanced control, it makes a discreet entrance but popular in industrial control automation. Fuzzy controller is divided into three steps illustrated in figure 2-11

.

Figure 2-11: Steps of fuzzy control ^[1]

Figure 2-10: P&O Block in Simulink^[1]

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 STEP 1:"FUZZIFICATION"

This section transforms inputs into fuzzy variables. The inputs are transformed into linguistic variables described by membership functions. These functions can take many forms: triangular, trapezoidal, bell or other. This fuzzy controller uses trapezoidal and triangular membership functions. The input and output variables will be transformed to the following linguistic variables:

1. NG: Grand negative 2. NM: Middle negative 3. N: Negative

4. ZE: Zero 5. P: Positive

6. PM: Middle positive 7. PG: Grand positive

The schematic of the fuzzy controller (Mamdani-type fuzzy controller) is given in figure 2-12

.

Figure 2-12: Adopted fuzzy controller^[1]

Figures 2-13 and 2-14 show the membership functions of the various variables.

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Figure 2-13: Membership functions of input variables: (A) E and (B) ΔE^[1]

Figure 2-14: Membership functions of the output variable dD ^[1]

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(a)

(c)

(b)

Table 2-1: Numerical Intervals of different variables (E, ΔE and dD): (a) E, (b) ΔE and (c) dD (Trap: trapezoidal and Triang:

triangular) ^[1]

The first fuzzy controller input E is the slope of the P-V characteristic curve:

E Lower

PURSUIT OF THE MAXIMUM POWER POINT (PMPP) IN A PHOTOVOLTAIC SYSTEM The output parameter dD represents the variation of the duty cycle.

 S^TEP 2:"I^NFERENCE"

It gives the relationship between input and output variables in language form. There are several methods of inference: MAX-MIN, MAX-PROD and SUM-PROD. Each method takes its own operators and each rule has the following form:

If (Condition), Then (Conclusion)

The method used by this fuzzy controller is the MAX-MIN method. In this method the operators AND, OR and Then are represented by the MIN and MAX:

At the condition level: → → At the conclusion level: → → The rule base of this fuzzy controller has the following form:

If ("E Condition 1" AND "ΔE Condition 2"), Then "Conclusion 1" OR If ("E Condition 1" AND "ΔE Condition 3 "), Then "Conclusion 2" OR

...

...

Before giving the basic rules, a little example is used to explain how to fill the database

.

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Figure 2-15: Characteristic of a SP ^[1]

Figure 2-15 shows two successive slopes: E (k) and E (k-1).When E (k)> 0 and ΔE (k) <0, the voltage must be increased to reach a point close to the MPP and so on. Therefore the variations of the voltage difference depend on the position between the operating point and the MPP. When this point is approached, there must be further incrementing the voltage to reach the highest stable state. Note that the variation of the voltage is represented by a variation in the duty cycle in the same sense.

After reviewing all the cases the base rules of table 2-2 will be adopted.

E ΔE NG NM N ZE P PM PG

This base rule presents the variation of the conclusion according to the variation of E and ΔE. Then these basic rules are implemented in MATLAB using the "Fuzzy Logic" toolbox.

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 STEP 3:"DEFUZZIFICATION"

During this step, the result provided by the fuzzy inference output dD is converted to real value or numerical value. We distinguish several methods of defuzzification: the maximum method, the weighted average method, simplified method of centroid, the centroid method and others. The used method by the used fuzzy controller is the centroid method. This method will then convert the result of the fuzzy output variable dD to the duty ratio variations that will be acceptable by the converter.

The centroid method calculates the center of gravity of the fuzzy surface obtained by the inference block (figure 2-16).

Figure 2-16: Numeric result obtained by inference block for E=0 and ΔE=0.5^[1]

2.4 Conclusion

In this chapter, we presented different MPPT control algorithms: Adaptive control, Hill Climbing, Increment of conductance, Perturb and Observe and the fuzzy control algorithms. In the next chapters, we will introduce the theory of PSO; also we will make a comparison between PSO, P & O and fuzzy control for the single peak power tracking, and a similar comparison between PSO and neural-fuzzy control algorithms for multi-peaks power.

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CHAPTER THREE

3 THEORY OF PARTICLE SWARM OPTIMIZATION

(PSO)

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3.1 Introduction

Particle swarm optimization (PSO) is a heuristic global optimization method put forward originally by Kennedy and Eberhart in 1995(Kennedy J, Eberhart R, 1995). It is developed from swarm intelligence and is based on the research of bird and fish flock movement behavior (figure 3.1).

While searching for food, the birds are either scattered or go together before they locate the place where they can find the food. While the birds are searching for food from one to another, there is always a bird that can smell the food very well, that is, the bird is perceptible of the place where the food can be found, having the better food resource information. Because they are transmitting the information, especially the good information at any time while searching the food from one place to another, conducted by the good information, the birds will eventually flock to the place where food can be found. As far as particle swam optimization algorithm is concerned, solution swam is compared to the bird swarm, the birds’ moving from one place to another is equal to the development of the solution swarm, good information is equal to the most optimist solution, and the food resource is equal to the most optimist solution during the whole course. The most optimist solution can be worked out in particle swarm optimization algorithm by the cooperation of each individual. The particle without quality and volume serves as each individual, and the simple behavioral pattern is regulated for each particle to show the complexity of the whole particle swarm.

Figure 3-1: How can birds or fish exhibit such a coordinated collective behavior? ^[2]

This algorithm can be used to work out the complex optimist problems. Due to its many advantages including its simplicity and easy implementation, the algorithm can be used widely in the fields such

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as function optimization, the model classification, machine study, neutral network training, the signal procession, vague system control, automatic adaptation control and etc.