20-01-2010, 11:30 PM
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ABSTRACT
Fuzzy logic, a relatively new cutting edge technology, is nowadays gaining popularity. Fuzzy control is a practical alternative for a variety of challenging control applications since it provides a convenient method for constructing no-linear controllers via the use of heuristic information. Such heuristic information may come from an operator who has acted as a human in the loop controller for a process. A fuzzy controller emulates human decision-making process. Fuzzy control provides a user-friendly formalism for representing and implementing the ideas we have about how to achieve high performance control. This paper discusses the automation of sugar factory by the use of fuzzy controller for controlling the pH of sugar solution. The structure, working, and design of a fuzzy controller for this purpose is very well dealt with in this paper. With its ability to simulate a human decision making process, the technology seems to be lucid and natural to the human. In short, fuzzy logic is a car with an engineer in its driverâ„¢s seat. With proper design of its four components along with a wisely chosen set of rules, fuzzy control is all set to crack the most complex of control problems- thanks to Lotfi A. Zedah, who is regarded as the father of Fuzzy Logic.
INTRODUCTION
Fuzzy control is a practical alternative for a variety of challenging control applications since it provides a convenient method for constructing non-linear controllers via the use of heuristic information. Since heuristic information may come from an operator who has acted as a human in the loop controller for a process. In the fuzzy control design methodology, a set of rules on how to control the process is written down and then it is incorporated into a fuzzy controller that emulates the decision making process of the human. In other cases, the heuristic information may come from a control engineer who has performed extensive mathematical modelling, analysis and development of control algorithms for a particular process. The rest of the process is the same as the earlier case. The ultimate objective of using fuzzy control is to provide a user-friendly formalism for representing and implementing the ideas we have about how to achieve high performance control. Apart from being a heavily used technology these days, fuzzy logic control is simple, effective and efficient. In this paper, the structure, working and design of a fuzzy controller is discussed in detail through an in-depth analysis of the development and functioning of a fuzzy logic pH controller.
FUZZY CONTROL - The Basics
The primary goal of control engineering is to distill and apply knowledge about how to control a process so that the resulting control system will reliably and safely achieve high performance operation. Here, the effort made is to show how fuzzy logic provides a methodology for representing and implementing our knowledge about how best to control a process.
Figure 1. Fuzzy Controller
The general block diagram of a fuzzy controller is shown in figure 1. The controller is composed of four elements, viz
¢ A Rule Base
¢ An Inference Mechanism
¢ A Fuzzification Interface
¢ A Defuzzification Interface
RULE BASE
This is a set of If ¦¦..then¦.. rules which contains a fuzzy logic quantification of the expert™s linguistic description of how to achieve good control.
INFERENCE MECHANISM
This emulates the expertâ„¢s decision making in interpreting and applying knowledge about how best to control the plant.
FUZZIFICATION INTERFACE
This converts controller inputs into information that the inference mechanism can easily use to activate and apply rules.
DEFUZZIFICATION INTERFACE
It converts controller inputs into information that the inference mechanism into actual inputs for the process.
SELECTION OF INPUTS AND OUTPUTS
It should be made sure that the controller will have the proper information available to be able to make good decisions and have proper control inputs to be able to steer the system in the directions needed to be able to achieve high-performance operation.
The fuzzy controller is to be designed to automate how a human expert who is successful at this task would control the system. Such a fuzzy controller can be successfully developed using high-level languages like C, Fortran, etc. Packages like MATLAB® also support Fuzzy Logic.
CRISP SETS Vs FUZZY SETS
CRISP SETS
The word Ëœcrisp setsâ„¢ denote ordinary sets or classical sets. Examples for crisp sets are set of natural numbers ËœNâ„¢, set of all real numbers ËœRâ„¢, etc.
FUZZY SETS AND MEMBERSHIP FUNCTIONS
Given a linguistic variable Ui with a linguistic value Aij and membership function µ Aij(Ui) that maps Ui to [0,1], a ˜fuzzy set is defined as
Aij= {(Ui, µ Aij (Ui)); Ui e i}
The above written concept can be clearly understood by going through the following example. Suppose we assign Ui=temperature and linguistic value A11=hot, then A11 is a fuzzy set whose membership function describes the degree of certainty that the numeric value of the temperature, Ui e i, possesses the property characterized by A11. This is made even clearer by the figure 2.
Figure 2: Membership Function of Temperature.
In the above example, the membership function chosen is triangular. There are some other membership functions lime Gaussian, Trapezoidal, Sharp peak, Skewed triangle, etc. Depending on the application and choice of the designer, the required one can be chosen.
Figure 3: 1)Triangular, 2)Trapezoidal, 3)Skewed triangular, 4)Sharp peak
PH CONTROL
To illustrate the application of fuzzy logic, the remaining section of the paper is directed towards the design and working of a pH control system using fuzzy logic.
PH is an important variable in the field of production especially in chemical plants, sugar industries, etc. PH of a solution is defined as the negative of the logarithm of the hydrogen ion concentration, to the base 10. I.e., PH= -log 10 [H+]
Figure 4: Block Diagram of pH Control System
Let us consider the stages of operation of a sugar industry, where PH control is required. The main area of concern is the clarification of raw juice of sugarcane. The raw juice will be having a PH of 5.1 to 5.5. The clarified juice should ideally be neutral. I.e., the set point should be a PH of 7. The process involves addition of lime and SO2 gas for clarifying the raw juice. The addition of these two are called liming and sulphitation respectively. Since the process involves continuous addition of lime and SO2 ; lime has a property of increasing the PH of the clarified juice. This is the principle used for PH control in sugar industries. The PH of the raw juice is measured and this value is compared to the set point and this is further used for changing the diameter of the lime flow pipe as per the requirement. The block diagram of the process is given in figure 1.
The whole process can be summarised as follows. The PH sensor measures the PH. This reading is amplified and recorded. The output of the amplifier is also fed to the PH indicator and interface. The output of this block is fed to the fuzzy controller. The output of fuzzy controller is given to the stepper motor drive. This inturn adjusts the diameter of lime flow pipe as per the requirement. Thus, the input to the fuzzy controller is the PH reading of the raw juice. The output of the fuzzy controller is the diameter of the lime flow pipe valve or a quantity that controls the diameter of the lime flow pipe valve like a DC current, voltage, etc. The output obtained from the fuzzy controller is used to drive a stepper motor which inturn controls the diameter of the value opening of the lime flow pipe. This output tends to maintain the pH value of sugar juice to a target value. A detailed description of the design and functioning of the fuzzy controller is given in the following section.
The different sections in the fuzzy controller used in this PH controller are
¢ Fuzzification Section
¢ Rule Base
¢ Inference Mechanism
¢ Defuzzification Section
FUZZIFICATION SECTION
The variables ËœPHâ„¢ and ËœLFPDâ„¢ or Lime-flow-pipe-diameter are selected for Fuzzification. In this section, the action performed is obtaining a value of the input variable and finding the numerical values of the membership function defined for that variable. As a result of Fuzzification, the situation currently sensed (input) is converted into such a form that, it can be used by the inference mechanism to trigger the rules in the rule base.
As explained earlier, the set point for the process is normally 7. Let the diameter set point be 15mm and this corresponds to a pH of 7. Let the input range be taken from 4 to 10 and other variable, ie.output range from 1 to 18mm.
After fuzzification, the fuzzy sets obtained are labelled using the following term set, T={LAD, MAD, SAD, SP, SAL, MAL, LAL, LDD, MDD, SDD, SD, SID, MID, LID}
LAD = large acidic
MAD = medium acidic
SAD = small acidic
SP = set point pH
SAL = small alkaline
MAL = medium alkaline
LAL = large alkaline
LDD = large decrease diameter
MDD = medium decrease diameter
SDD = small decrease diameter
SD = set diameter
SID = small increase diameter
MID = medium increase diameter
LID = large increase diameter
The membership functions of input variable PH and output variable LFPD is shown in figures 5 and 6 respectively. µi is the membership function of output. Here, we use triangular membership functions.
Figure 5: Membership Function of pH
Figure 6: Membership Function of LFPD
As a result of Fuzzification, we get the names of fuzzy sets to which the input belongs and to what extend they belong to these sets i.e., their membership functions.
RULE BASE
Rule base stores the different rules that are to be fired or used according to the input. These rules are either gathered from experienced human operator or from careful study of existing pH control systems. The rule base thus represents the control strategy employed in the pH control. Table 1 gives the set of fuzzy action rules in our particular application.
Table 1: The Rule Base
The incoming pH value from sensor fires the rules from rule-base. This is done by the inference mechanism.
INFERENCE MECHANISM
The inference mechanism employed in pH control is based on individual rule firing. In this scheme, contribution of each rule is evaluated and overall decision is derived.
During inference process, each rule that is fired by a crisp value pf pH is summed up after giving the weightages decided by the fuzzification unit. This weightage is called degree of satisfaction (DoS). DoS is decided by the fuzzification module. The process of inference is illustrated in figure below.
Figure 7: Inference Mechanism and Defuzzification
In the above drawn case, the input pH is 6.25. The set point pH is 7. After fuzzification, we understand that the input belongs to the fuzzy set SAD with a degree of membership DoM=0.7 and at the same time, it belongs to SP with a DoM=0.3. Since the membership function chosen is symmetric (triangular), the DoS=DoM. The work until now was done by the fuzzification module. Now, the control switches to the inference mechanism.
In the inference mechanism, depending on which all fuzzy sets the input belongs to, the corresponding rules are fired. This describes the functioning of the three out of four blocks in the fuzzy controller. Now comes the defuzzification section.
DEFUZZIFICATION SECTION
This section performs the task of converting the output of inference mechanism, i.e., the rules that are fired, and the DoS given by the fuzzification module into a crisp value of LFPD. For this, it uses height defuzzification which is computationally simple and fast. The crisp rate of lime flow depends on the crisp value of lime flow pipe diameter LFPD, which is given by the formula
LFPD=(P1H1+P2H2) / (H1+H2)
In our example, a maximum of two sets are clipped simultaneously. The resulting LFPD will be LFPD=(15X0.3 +16X0.7)/ (0.3+0.7)
= 15.7 mm
PRACTICAL CONTROL CHARACTERISTICS
Practically, the above-described method is an iterative method. After a certain period of damped oscillations, the pH tends to maintain the desired value.
SUGAR PLANT WITH AND WITHOUT AUTOMATIC pH CONTROL
In sugar plants, pH control is achieved either manually or automatically. A comparative study is given below.
MANUAL CONTROL
These are many strategies used in manual pH control, out of which a couple are explained below. One of them is that the operator keeps the juice flow and SO2 gas flow rates constant and adjusts the lime control value to get the desired value of pH. The lime flow rate is adjusted by changing the diameter of an outlet pipe of lime milk tank. This adjustment is based on the operatorâ„¢s experience. In such a control, the pH of clear juice obtained is in the range 6.9 to 7.2. This is observed using pH indicator paper.
In another method, the lime is added to heated raw juice until the pH is 9.5 to 10.5. By maintaining the juice flow constant. Here, lime flow rate is varied manually. By adjusting the airflow to the Sulphur burner, SO2 gas is passed through limed juice and pH is maintained in the range 6.9 to 7.1. Here also, pH is observed using pH indicator paper.
AUTOMATIC CONTROL
The earlier discussed fuzzy logic pH control technique can be used for sugar factory automatic. To implement this controller, many methods can be adopted. It may be implemented using a PC, a microprocessor, or a micro controller. The first two methods are discussed in brief and we focus on the third method in detail. In the first two methods, a program is written down based on the fuzzy algorithm. If we are using a PC, any high level language can be used. If we are using a microprocessor, we have to either write the program in a high level language provided, we have a compiler to convert this program into the assembly language of the microprocessor or the program has to be written down in the assembly language itself. In these two methods, the input values and output values are taken in and given out through the ports of the µp or pc.
In the third method, we are using a microcontroller of PIC series. We are using the µc PIC 16F73 chip, to be specific. In addition to this µc, we are using an USART, input buffer, output latches, etc. A block diagram of the whole system is given below.
HARDWARE BLOCK DIAGRAM
Figure 8: Hardware Block Diagram
PIC MICROCONTROLLER
The PIC Microcontroller that is used here to realize the fuzzy controller is a general-purpose eight-bit microcontroller developed by the MICROCHIP INC. The programming of this microcontroller can be done in two ways. One is by assembly language programming of the micro controller. The other is by using a compiler MPLAB for converting the high-level language program written by the programmer into the assembly language of the microcontroller.
INPUT UNITS
The inputs to the microcontroller are crisp values of pH measured by the sensors. This input can be either digital or analog. Separate units are provided for analog and digital inputs. Buffer is used for holding the input for sampling. Buffer holds the input only for a small period. According to the required accuracy, the inputs are taken i.e., sampled from the input terminal continuously since the buffer can hold only for a fraction of time. If less accuracy is needed, sampling rate is decreased.
OUTPUT UNITS
The output of our fuzzy logic controller is crisp value of lime flow pipe diameter. This output is obtained through the output latch. The latch used here is 74373.
USART AND MAX232
USART or universal synchronous receiver transmitter is used for communicating with the computer. MAX232 is used for converting TTL level data to RS232 level.
OTHER APPLICATIONS OF FUZZY LOGIC
¢ Modern consumer goods like washing machine, owen, etc.
¢ Expert systems
¢ Fault tolerant aircraft control
¢ Genetic engineering
Fuzzy logic also finds application in the fields of Robotics, civil engineering, industrial engineering, mechanical engineering, economics, medicine, etc.
MERITS OF FUZZY LOGIC CONTROLLER
¢ The main advantage of a fuzzy controller is that a model is not required to develop such a controller.
¢ The method of using rule base is more lucid and natural t o people.
¢ Fussy logic methods can be used for tuning of conventional PID controllers.
DEMERITS OF FUZZY LOGIC CONTROLLER
¢ Since the fuzzy controllers have no mathematical model, it is difficult to analyse the system.
¢ The working of the controller heavily depends on the judgement of the human expert who formulated the rules.
CONCLUSION
Fuzzy logic is a relatively new technology, which is increasingly finding applications in the present scenario. With its ability to simulate a human decision making process, the technology seems to be lucid and natural to the human. In short, fuzzy logic is a car with an engineer in its driverâ„¢s seat. With proper design of its four components along with a wisely chosen set of rules, fuzzy control is all set to crack the most complex of control problems- thanks to Lotfi A. Zedah who is regarded as the father of Fuzzy logic.
BIBLIOGRAPHY
1. B. T. JADHAV, R.R. MUDHOLKAR & S.R. SAWANT,
FUZZY LOGIC pH CONTROL TECHNIQUE,
INDUSTRIAL AUTOMATION- APRIL 2003, pp 42-46.
2. KEVIN M. PASINO & STEPHEN YURKOVICH,
FUZZY CONTROL
ADDISON WESLEY, pp 21-65
3. GEORGE J. KLIR & BO YUAN,
FUZZY SETS AND FUZZY LOGIC-THEORY AND APPLICATION,
PHI, pp 1-32.
ACKNOWLEDGEMENT
I extend my sincere gratitude towards Prof . P.Sukumaran Head of Department for giving us his invaluable knowledge and wonderful technical guidance
I express my thanks to Mr. Muhammed kutty our group tutor and also to our staff advisor Ms. Biji Paul for their kind co-operation and guidance for preparing and presenting this seminars.
I also thank all the other faculty members of AEI department and my friends for their help and support.
CONTENTS
1. INTRODUCTION 1
2. FUZZY CONTROL - The Basics 2
RULE BASE
INFERENCE MECHANISM
FUZZIFICATION INTERFACE
DEFUZZIFICATION INTERFACE
SELECTION OF INPUTS AND OUTPUTS
3. CRISP SETS Vs FUZZY SETS 4
CRISP SETS
FUZZY SETS AND MEMBERSHIP FUNCTIONS
4. PH CONTROL 6
FUZZIFICATION SECTION
RULE BASE
INFERENCE MECHANISM
DEFUZZIFICATION SECTION
PRACTICAL CONTROL CHARACTERISTICS
5. SUGAR PLANT WITH AND WITHOUT
AUTOMATIC pH CONTROL 13
MANUAL CONTROL
AUTOMATIC CONTROL
6. HARDWARE BLOCK DIAGRAM 15
PIC MICROCONTROLLER
INPUT UNITS
OUTPUT UNITS
USART AND MAX232
7. OTHER APPLICATIONS OF FUZZY LOGIC 16
8. MERITS OF FUZZY LOGIC CONTROLLER 17
9. DEMERITS OF FUZZY LOGIC CONTROLLER 17
10. CONCLUSION 18
11. BIBLIOGRAPHY 19
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