Chapter 6: FUZZY LOGIC CONTROLLER

6.1. Introduction

Fuzzy logic is a powerful problem-solving methodology with a myriad of application in embedded control and information processing. Fuzzy provides a remarkable a sense, fuzzy logic resembles human decision making with its ability to work from approximate data and find precise solution. Unlinked classical logic which requires a deep understanding of a system, exact equations, and precise numeric values, fuzzy logic incorporation an alternative way of thinking, which allows modeling complex systems using a higher level of abstraction organizing from our knowledge and experience. Fuzzy logic allows expressing this knowledge with subjective concepts such as very hot, medium cold, and a long time which are mapped into exact numeric ranges. Fuzzy logic is recently finding wide in various applications which cover a variety of practical systems, such as the control of cement kilns, train operation, parking control of car, heat exchangers, and in many other system, such as home appliances, video cameras, elevators, aero space, etc [10, 14]. Nearly every application can potentially realize some of the benefits of fuzzy logic, such as performance simplicity lower cost, and productivity [9, 13]. Fuzzy logic was first introduced by Zadeh in 1965, whereas the first fuzzy logic controller was implemented by Mamdani in 1974 [10, 14].

In this work, different types of fuzzy based controllers are designed for an automatic generation control in single power system.

6.2. Basic Control of Fuzzy Logic

A fuzzy logic, unlike the crispy logic in Boolean theory that uses two logic (0 to 1) is a branch of logic that admits infinity logic level (from 0 to 1) to solve a problem that has uncertainties or imprecise situations. A variable in fuzzy logic has sets of values which are characterized by linguistic expressing, such a SMALL, MEDIUM, LARGE, etc. linguistic expressions are represented numerically by fuzzy sets. Even Fuzzy set is characterized by a membership function, which varies from 0 to1 .Although fuzzy theory deals with imprecise information; it is based on sound quantitative mathematical theory [8, 14].

Again fuzzy control is a process that is based on fuzzy logic and is normally characterized by if-THEN rules. A fuzzy control algorithm for a process control system embeds the intuition and experience of operator, designer and researcher. The control does not need accurate mathematical model of a plant, and therefore, it suits well to a process where the model is unknown or ill defined. The fuzzy control also works well for complex nonlinear multi dimensional system, system with parameter variation problem, or where the sensor signals are not precise. The fuzzy control is basically nonlinear and adaptive in nature, giving robust performance under parameter variation and load disturbance effect [8, 14].

To gain an in depth on fuzzy logic, the following terms the need to be studied.

  1. Degree of Membership (µ): It is a number between (0 to 1) that expresses the confidence that a given element belongs to a fuzzy set.
  2. Fuzzy Set (fuzzy subset): This is defined as a set consisting of elements having degree of membership varying between 0 (member) to 1 (full member). It is usually characterized by a membership function, and associated with linguistic valuably characterized by a membership function, and associated with linguistic values, such as SMALL, MEDIUM, and LARGE etc.
  3. Membership Function: It is a function that defines a fuzzy subset, by associating every element in the set with a number between 0 and 1.
  4. Linguistic Variables: Any variable (such as temperature, speed, etc) whose values are defined by language, such as LAGE, SMALL, etc. is called a linguistic variable or fuzzy variable.
  5. Universe of Discourse: It is the range of values associated with a fuzzy variable.

6.3. Advantages of Fuzzy Logic Controller (FLC)

When compared to classical control theory a fuzzy logic approach to control offers the following advantages [14].

  1. It can be used in systems which cannot be easily modeled mathematically in particular, systems with non linear responses are difficult to analyze may respond to a fuzzy control approach.
  2. It is inherently robust since it does not require precise, noise free inputs. The output control is a smooth control function despite a wide range of input variations.
  3. Since the fuzzy logic controller (FLC) processes user defines rules governing the target control system, it can be modified easily to improve or drastically alter system performance.
  4. Continuous variable may be represented by linguistic terms that are easier to understand, making the controller easier to implement and modify. For example, instead of using numeric values, temperature may be represented as “cold, cool warm, or hot”.
  5. Complex processes can often be controlled by relatively few logic rules, allowing a more understandable controller design and faster computation for real time applications.

 

6.4. Design of Fuzzy Logic Controller (FLC)

Fuzzy control is special form of knowledge-based control. In designing a fuzzy control system, the precise mathematical model of target plant is not needed. Only the relevant experiences and heuristics concerning the pant are utilized to from a set of fuzzy control rules. These are linguistic in nature and often use the simple cause- effect relationship to link a fuzzy partitioning of certain state-space of the plant with a fuzzy petitioning of the control action. The final control signal is generated by an appropriate defuzzifying process [15].

The reference signal and plant output, which are crisp values but non-fuzzy variables, must be fuzzified by a fuzzification procedure. Similarly, the fact that the controlled plant can not directly respond to FL controls accounts for the reason why the FL control signal generated by the fuzzy algorithm must be defuzzification before applied to control the actual plant. A rule base consists of a set of fuzzy rules. The data base contains the membership functions of the fuzzy subsets. A fuzzy rule may contain fuzzy variables and fuzzy subsets characterized by membership functions and conditional statement. The fuzzy control algorithm

Fig: 6.1 Block diagram of a typical close-loop fuzzy control system

6.4.1. Fuzzification:

The fuzzification procedure consists of finding appropriate membership function to describe crisp data. The membership functions for the fuzzy variables may have several shapes. The most popular choices for the shape of the membership function include, triangular trapezoidal, and bell-shaped functions. Among them, triangular membership function is the most economic one because of its minimal use of memory & efficiency, in terms of real time requirements, by the inference engine. To design the fuzzy controller in the work, the triangular membership functions for an input & output variables. The memberships functions are system dependent. The membership functions used for the fuzzy logic controller (FLC) design in this work. Usually, membership functions are determined by trail & error. In this work, the membership functions have been determined by trail & error method. The precise numerical values are obtained by measurements that are converted to membership values of the various linguistic variables. For the FLC controller the inputs are defined as:

Input 1: error =∆f=fnom– ft=et

Input 2: change in error=∆f2-∆f1=cet.

Usually, two input variables (error of the variable of interest for the control and change of error) are used fore fuzzy logic controller (FLC) design [18]. However, in this work, two input and single output are used for FLC design. The use of two input and single output variable makes the design of the controller very straightforward [9-13].

6.4.2. Fuzzy Rule Base:

The rule base is the heart of a fuzzy controller, since the control strategy used to control the closed-loop system is stored as a collection of control rules. The heuristic rules of the knowledge base are used to determine the fuzzy controller action.

Controller has 2 inputs et, and cet,and one output ut. Then a typical control rule has the form.

If et, is A and cet, is B then and uis C. …………………………(6.1)

Where A, B and C are linguistic terms, such as very low, very high and medium, etc. the control rule (6.1) is composed of two parts: ‘if’ part and the ‘then’ part. The ‘if’ part is the input to the controller and the ‘then’ part is the output of the controller. The ‘if ’part is called the premise (or antecedent or condition) and the ‘then’ part is called the consequence (or action).

Though it is possible to derive a membership value for this variable in many possible ways, one of the rules that has been chosen is,

µ(et,cet.)=min[µ(et.),µ(cet.)] ……………………………(6.2)

The fuzzy rules are system dependent. The most usual source fore constructing linguistic control rules is human experts. However, it is often the case that no expert is available.

Therefore trial and error method is usually used to find fuzzy control rules.

6.4.3. Fuzzy Inference

The basic operation of the inference engine is that it infers i.e. it is deduces (from evidence or data) a logical conclusion. Let us consider the following example describe by the logical rule known as modus ponens:

Premise 1: If and animal is a cat, then it has four legs.

Premise 2: My pet is a cat.

Conclusion: My pet has four legs.

Here, premise 1 is the rule base, 2 are the fact (or the data) and the conclusion is the consequence. Actually, the inference engine is a program which uses the rule base and the input data of the controller to draw the conclusion, very much in the manner shown by the above the modus ponens rule [9]. The conclusion of the inference engine is the fuzzy output of the controller, which subsequently becomes the input to the defuzzification interface.

Usually, two types of fuzzy inference are available in the literature. One is Takagi-Sugeno-Kang (TSK) fuzzy inference and other is Mamdani type fuzzy inference. For the inference mechanism of the fuzzy logic controller in this work, Mamdanis method [8] has been utilized. Compared to other methods, the advantages of Mamdant’s are:

  1. Calculation time is very short;
  2. Inference mechanism is very simple;
  3. Parameters can be changed easily.

6.4.4. Defuzzification

In this last operation, the fuzzy conclusion of the inference engine is defuzzified, i.e. it is converted into a crisp signal .this last signal is the final product of the FLC which is of course, the crisp control single to the process. There are several methods for defuzzification  available in the fuzzy interaction, such as Center -of -Area  or  Center -of –Gravity defuzzification Center -of –Sums defuzzification Center -of –Largest-Area, defuzzification  first- of- Maxima defuzzification Middle-of- Maxim defuzzification, Height defuzzification etc. the Center -of -Area  or  Center -of –Gravity method which is implemented in this work to determine the output crisp value. The well-known center of gravity defuzzification method is given by the following expression:

……………………………………….. (6.3)

Where, Z is the crispy output function and symbols have already been defined in the previous section. The membership function, knowledge base and method of defuzzification essentially determine the controller performance [1].

6.5. The Proposed Fuzzy Logic Control

Fig (6.2): fuzzy controller for the SMES unit

The proposed controller along with SMES unite is shown in fig (6.2), the ∆f are the input to the corresponding fuzzy controllers. The output of the Fuzzy Frequency Controller (FFC) is KI. ∆f is changing with changing KI.

Unlikely, the conventional controller, in the proposed method  the change in  ∆f the signal are also consider as explained below. In general, the input variables considered in the fuzzy rule base are:

E(k)=R(k)-C(k)

CE(k)=E(k)-E(k-1)

Where E(k) is the loop error (present deviation), CE(k) is the change in loop error, R(k) is the reference signal, C(k) is the present signal, and k is the sampling interval.

The structure of a general rule can be given as:

IF E(K) is X AND CE(K) is Y THEN U(K) is Z

The variable can be expressed as per unit quantities as follows:

e(p.u) = E(k)/GE

ce(p.u) = E(k)/GCE

Where, GE and GCE are the respective gain factor of the controllers. Fig (6.4) shows the membership function of e(p.u), ce(p.u) and their respective output variable.

Note that the fuzzy the subsets for output variable have an asymmetrical shape causing more crowding near the origin. This allows precision control near the steady state operating point. Also large number of subsets is selected to obtain accurate control.

Table 1 gives the rule base matrix for frequency control can be summarized as follows:

  1. Sample the reference frequency f* and the actual frequency fact
  2. Compute error (e) and change of error (ce) in their respective p.u. values are as follows:

                                                       e(k)=(f*(k)-f(k))/GE

                                                      ce=(e(k)-e(k-1))/GCE

  1. Identify the interval indices for e (p.u) and ce(p.u) respectably, by the comparison method.
  2. Compute the degree of membership of e (p.u) and ce (p.u) for the relevant fuzzy subsets.
  3. Identify the four valid rules in table 1 and calculate the degree of membership µRi MIN operation.

Fig (6.4): Membership function of fuzzy frequency control (FFC)

            6. Integrating gain KI for each rule from table

           7. Calculate the crisp value of KI higher defuzzification  method as follow:

………………………. (6.4)

Table 1: Rule base of frequency control

The fuzzy sets of the each linguistic variable adopted in this work are: NVB: Negative very Big, NB: Negative Big; NM: Negative Medium NS: Negative small; NVS: Negative Very small Z: Zero; PVS: Positive Very small; PS: Positive small; PM: Positive Medium PB: Positive Big. PVB: Positive Very Big. Each fuzzy set has a triangular shape and is determined by three parameters consequently, if a linguistic variable is supported by N fuzzy sets, then the total number of parameters needed is N+1, considering that the zero.

6.6. Simulation Results and Discussion:

In Order to Demonstrate the beneficial damping effect of the proposed fuzzy set theory based-gain scheduling of automatic generation controller in a single area power system, computer simulations results based on system non-liner differential equations have been carried out for different load changes. The differential equations have been solved by using MATLAB environment. Figure 6.5, 6.6 and Fig 6.7 depict the simulation results with & without considering the load changes of ∆PL =0.01, 0.015, and 0.02 P.U M W respectively.

The system frequency is not found satisfactory with fixed integral gain, KI. With the addition of proposed schemes, the damping is improved significantly. The generator frequency is almost diminished with the proposed mode of control. It is clearly shown that considering governor is greatly minimized error. Moreover, this eventually reduces the settling time of the speed for both cases, which in turn brings the FGPI controller in more advantageous position for subsequent use. The frequency deviation is diminished with the Fuzzy controller. The system frequency deviation is almost minimized. The settling time becomes smaller.

Fig: 6.5 Frequency deviation and variation of KI of a typical single area power system with the step load ΔPL =0.01(p.u)

Fig: 6.6 Frequency deviation and variation of KI of a typical single area power system with the step load ΔPL =0.015(p.u)

Fig: 6.7 Frequency deviation and variation of KI of a typical single area power system with the step load ΔPL =0.02(p.u)

6.7. Effect of Variable Load

Fig: 6.8. Frequency deviation for single area power system with variable load change

Table: 2 Table for frequency deviation for single area power system with variable load change. In the table 2 that get from the fig 6.8., Load change from .005(pu) to 0.25(pu), then maximum deviation, settling time, overshoot change. Above table settling time is nearly 4.5(s).

6.8. Conclusion

Fuzzy logic is getting increasing acceptance in control application over the past few years. In this work the fuzzy logic control (FLC) is used for the designed of some controllers for an Automatic Generator Control (AGC) of single and single-area power system. Again in order to see how well, robust and effect designed of the fuzzy controllers are and its performance compare to that of the control. This chapter presents overview of fuzzy controller, design of fuzzy logic control.

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