FUZZYLOGI
With this fast changing world everything changes to be faster, smarter and automatic. Man orders machines and now machines mimic humans in all aspects. This all happens just with a push of button. We are witnessing a miracle in technology. How does this happened? and how is it happening? The answer to this question is “FUZZY”.
This paper describes the procedures required in designing fuzzy logic machines starting with the basic, fuzzy rules moving on to FUZZY CONTROLLER used in the “speed control of DC motor”.
Also a comparison between the conventional PID controller and fuzzy logic controller produces the satisfactory speed control of DC motor than the conventional controllers in such a way that it reduces the transient, peak overshoot and steady state error and also it accepts the rapid change in load variations. From simulation, it is clear that under various load distributions FLC provides the better performance than the conventional controller.
INTRODUCTION:-
Due to excellent speed control characteristics, DC motor has widely used in industrial applications such as mining, steel mills, paper industries even though its maintenance costs are higher than the induction machines. Facing the problem of nonlinear process investigators realized that speed control of DC motor has attracted considerable research and several methods have evolved.
Mostly conventional controllers like Proportional-Integral-Derivative(PID) have been widely used for this purpose. But these controllers are generally designed on the basis of nonlinear one. As a result it produces speed regulation with many overshoots, steady state error and more transient time with less time accuracy.
To overcome the above difficulties, now a days intelligent controllers like “fuzzy logic controller” is used for implementation of human intelligence.
Fuzzy logic is the one which makes the machine to understand the vague concepts such as load disturbances and produces the control output correspondingly. The obtained results shows that the proposed fuzzy logic controller can significantly improve the dynamic performance of the machine over a wide range of operating points.
DESIGN OF PID CONTROLLER:-
This is a commonly used analog control technique. In this controller, the control output is proportional to the speed error, the integral of the error and the derivative of the error. All these terms are summed to achieve the controller output.
PID controller is designed as,
U(t)=[Kpe(t)+Ki∫e(t)+Kd(de(t)/dt)]
Kp-Proportional gain;
Ki-Integral gain;
Kd-Derivative gain.
SPEED CONTROL BY PID CONTROLLER:-
The transfer functions which regulates the output is given by,
U(s) = 0.55
4.8×10-3s3+6.632×10-3s2+0.3049s
The simulated result using the PID controller shows fluctuations to the rapid change in the load variations. The overshoot and the variations of response in using the PID controller are the main drawbacks that led to the development of fuzzy logic controller.
FUZZY LOGIC:-
Fuzzy logic refers to the modeling of complex system using knowledge and experience of an operation. It provides a simple way to arrive a definite conclusion from vague or imprecise information and resembles human decision making in its ability to work with approximate data.
Fuzzy logic uses the following concepts. They are,
(i) Fuzzy sets
(ii) Membership functions
(iii) Fuzzy rules
(iv) Fuzzy patches
FUZZY SETS:-
They are range of values, which form basis of fuzzy logic. They are the
set of labels such as slow, medium, moderate, small, large, positive, negative which
define the range.
MEMBERSHIP FUNCTIONS:-
The membership function is a graphical representation of magnitude of participation of each input.
Figure 1.Fuzzy Membership
a- very slow b- some what medium c- little fas
FUZZY RULES:-
Fuzzy logic uses a set of rules to define its behaviour. Rules associate ideas and relate one event to another. The rules control a system. FUZZY RULES are simple IF- THEN statements. These rules define the condition expected and outcomes desired with if / then statement. Fuzzy rules cover control requirements during certain ranges of operation.
Eg: IF the motor is too slow THEN speed it up.
slow is a linguistic variable which denotes a range.
FUZZY PATCHES:-
Fuzzy rules define fuzzy patches, which is the key idea in fuzzy logic. In fuzzy system all our rules can be seen as patches and input and output of machine are associated together using these patches.
Figure 2.Fuzzy patches.
The more the patches we have over the control range, better the control.
FUZZY CONTROL:-
Fuzzy control which directly uses of fuzzy rules is the most important application of fuzzy theory. Fuzzy control follows 3 main steps namely,
I fuzzification [using membership functions to describe a situation]
II Rules evaluvation [Application of fuzzy rules]
III Defuzzification [obtaining crisp results]
SPEED CONTROL OF DC MOTOR:-
The fuzzy control method applied in speed control of DC motor is explained.
Fuzzy logic controller Motor Power Amplifier DC motor
Vdesired Verror Verror Vactual
+
The speed of DC motor can be controlled by taking out proportional voltage with help of generator. The voltage from generator is fed to fuzzy logic controller, programmed with some set of rules. Appropriate decisions according to the error voltage are taken by FLC and fedback to input controlling speed.
Steps in building the system controller:
Figure 4.Fuzzy logic design
(i)Determine a control input:-
The actual motor voltage is compared with desired voltage and difference in voltage (error) is supplied as input to FLC . Other input is the rate of change of error. Inputs are Verror, d/dt(Verror)
(ii) Determine a control system output:-
The speed proportional voltage ,motor voltage is output. Output is Vmotor.
Ø FUZZIFICATION:
(iii) Linguistic variable:
The linguistic variable which define fuzzy sets are
Large Negative (LN);
Large positive (LP);
Small Negative (SN) ;
Small positive (SP);
Zero (ZE).
(iv) Determine rules:-
Rules for the FLC are
1. Verror is LPand d/dt (Verror) is any then Vmotor is LP
2. Verror is SP and d/dt (Verror) is SP or ZE then Vmotor is SP
3. Verror is ZE and d/dt (Verror) is SP then Vmotor is ZE
4. Verror is ZE and d/dt (Verror) is SN then Vmotor is SN
5. Verror is SN and d/dt( Verror)is SN then Vmotor is SN
6. Verror is SP and d/dt (Verror) is SP then Vmotor is LN
(v)Determination of membership functions:
Ø RULE EVALUVATION:-
rps/s 3 0 -3 -6 6
OR evaluates the highest of two memberships
Vmotor
AND evaluates the lowest of two memberships
Consider the case where , Verror = 30 rps and d/dtVerror = 1rps/s
According to rules:-
If Verror is LP and d/dt (Verror) is any then Vmotor is LP.
1 24 18 12 6 0 v SPN ZEN SNN LN LPN
Figure 5
Membership Functions
Ø RULE EVALUVATION:-
OR evaluates the highest of two memberships
AND evaluates the lowest of two memberships
Consider the case where , Verror = 30 rps and d/dtVerror = 1rps/s
According to rules:-
If Verror is LP and d/dt(Verror) is any then Vmotor is LP
Figure 6
Graphs
Ø DEFUZZIFICATION:
The result obtained by evaluation of the rules of the FLC is a fuzzy set. To obtain Defuzzification is the process which converts the fuzzy set output to crisp value.
The most common method used in obtaining crisp output by defuzzification is center of gravity method.
It uses,
V motor = ∑ ni=1 (Vmotor i) (membershipi)
(membership i)
For the given example,the output will be,
V motor = 0.6 (17v) + 0.4 (14v) = 15.8v
Result: 0.6 + 0.4
Thus the final, motor control voltage calculated for the given set of FUZZY rules is 15.8v .
NEED FOR USING FUZZY CONTROL:-
(i) FLC process user defined rules governing target control system.
(ii) Because of rule based operation any number of reasonable input can be processed.
(iii) FLC can control non-linear system that would be difficult or impossible to model mathematically.
(iv) Any sensor data that provides some indications of a system action and reaction is sufficient. Not necessarily the rate of change of parameters is to be measured.
(v) During debugging and tuning cycle we can change our system by simply modifying rules instead of redesigning the control
APPLICATIONS:-
v Fuzzy technology are used in automotive industries to improve quality
v Fuzzy in aerospace enables to solve very complex real time problems.
v Fuzzy is used in consumer electronics to improve the time to market the product.
v They are used in industrial controls, transportation systems, video equipments, washing machines and so on.
CONCLUSION:-
A new approach based on fuzzy set theory has been presented for controlling the speed of DC motor which is capable of providing good speed regulation with stability. The experimental results show that the fuzzy logic controller produces the satisfactory speed control of DC motor than the conventional controls in such a way that it reduces the transient and steady state error and also accepts the rapid change in load variations. Thus the fuzzy logic controller provides the better performance than the conventional controllers.
ABSTRACT
With this fast changing world everything changes to be faster, smarter and automatic. Man orders machines and now machines mimic humans in all aspects. This all happens just with a push of button. We are witnessing a miracle in technology. How does this happened? and how is it happening? The answer to this question is “FUZZY”.
This paper describes the procedures required in designing fuzzy logic machines starting with the basic, fuzzy rules moving on to FUZZY CONTROLLER used in the “speed control of DC motor”.
Also a comparison between the conventional PID controller and fuzzy logic controller produces the satisfactory speed control of DC motor than the conventional controllers in such a way that it reduces the transient, peak overshoot and steady state error and also it accepts the rapid change in load variations. From simulation, it is clear that under various load distributions FLC provides the better performance than the conventional controller.
INTRODUCTION:-
Due to excellent speed control characteristics, DC motor has widely used in industrial applications such as mining, steel mills, paper industries even though its maintenance costs are higher than the induction machines. Facing the problem of nonlinear process investigators realized that speed control of DC motor has attracted considerable research and several methods have evolved.
Mostly conventional controllers like Proportional-Integral-Derivative(PID) have been widely used for this purpose. But these controllers are generally designed on the basis of nonlinear one. As a result it produces speed regulation with many overshoots, steady state error and more transient time with less time accuracy.
To overcome the above difficulties, now a days intelligent controllers like “fuzzy logic controller” is used for implementation of human intelligence.
Fuzzy logic is the one which makes the machine to understand the vague concepts such as load disturbances and produces the control output correspondingly. The obtained results shows that the proposed fuzzy logic controller can significantly improve the dynamic performance of the machine over a wide range of operating points.
DESIGN OF PID CONTROLLER:-
This is a commonly used analog control technique. In this controller, the control output is proportional to the speed error, the integral of the error and the derivative of the error. All these terms are summed to achieve the controller output.
PID controller is designed as,
U(t)=[Kpe(t)+Ki∫e(t)+Kd(de(t)/dt)]
Kp-Proportional gain;
Ki-Integral gain;
Kd-Derivative gain.
SPEED CONTROL BY PID CONTROLLER:-
The transfer functions which regulates the output is given by,
U(s) = 0.55
4.8×10-3s3+6.632×10-3s2+0.3049s
The simulated result using the PID controller shows fluctuations to the rapid change in the load variations. The overshoot and the variations of response in using the PID controller are the main drawbacks that led to the development of fuzzy logic controller.
FUZZY LOGIC:-
Fuzzy logic refers to the modeling of complex system using knowledge and experience of an operation. It provides a simple way to arrive a definite conclusion from vague or imprecise information and resembles human decision making in its ability to work with approximate data.
Fuzzy logic uses the following concepts. They are,
(i) Fuzzy sets
(ii) Membership functions
(iii) Fuzzy rules
(iv) Fuzzy patches
FUZZY SETS:-
They are range of values, which form basis of fuzzy logic. They are the
set of labels such as slow, medium, moderate, small, large, positive, negative which
define the range.
MEMBERSHIP FUNCTIONS:-
The membership function is a graphical representation of magnitude of participation of each input.
Figure 1.Fuzzy Membership
a- very slow b- some what medium c- little fas
FUZZY RULES:-
Fuzzy logic uses a set of rules to define its behaviour. Rules associate ideas and relate one event to another. The rules control a system. FUZZY RULES are simple IF- THEN statements. These rules define the condition expected and outcomes desired with if / then statement. Fuzzy rules cover control requirements during certain ranges of operation.
Eg: IF the motor is too slow THEN speed it up.
slow is a linguistic variable which denotes a range.
FUZZY PATCHES:-
Fuzzy rules define fuzzy patches, which is the key idea in fuzzy logic. In fuzzy system all our rules can be seen as patches and input and output of machine are associated together using these patches.
Figure 2.Fuzzy patches.
The more the patches we have over the control range, better the control.
FUZZY CONTROL:-
Fuzzy control which directly uses of fuzzy rules is the most important application of fuzzy theory. Fuzzy control follows 3 main steps namely,
I fuzzification [using membership functions to describe a situation]
II Rules evaluvation [Application of fuzzy rules]
III Defuzzification [obtaining crisp results]
SPEED CONTROL OF DC MOTOR:-
The fuzzy control method applied in speed control of DC motor is explained.
Fuzzy logic controller Motor Power Amplifier DC motor
Vdesired Verror Verror Vactual
+
The speed of DC motor can be controlled by taking out proportional voltage with help of generator. The voltage from generator is fed to fuzzy logic controller, programmed with some set of rules. Appropriate decisions according to the error voltage are taken by FLC and fedback to input controlling speed.
Steps in building the system controller:
Figure 4.Fuzzy logic design
(i)Determine a control input:-
The actual motor voltage is compared with desired voltage and difference in voltage (error) is supplied as input to FLC . Other input is the rate of change of error. Inputs are Verror, d/dt(Verror)
(ii) Determine a control system output:-
The speed proportional voltage ,motor voltage is output. Output is Vmotor.
Ø FUZZIFICATION:
(iii) Linguistic variable:
The linguistic variable which define fuzzy sets are
Large Negative (LN);
Large positive (LP);
Small Negative (SN) ;
Small positive (SP);
Zero (ZE).
(iv) Determine rules:-
Rules for the FLC are
1. Verror is LPand d/dt (Verror) is any then Vmotor is LP
2. Verror is SP and d/dt (Verror) is SP or ZE then Vmotor is SP
3. Verror is ZE and d/dt (Verror) is SP then Vmotor is ZE
4. Verror is ZE and d/dt (Verror) is SN then Vmotor is SN
5. Verror is SN and d/dt( Verror)is SN then Vmotor is SN
6. Verror is SP and d/dt (Verror) is SP then Vmotor is LN
(v)Determination of membership functions:
Ø RULE EVALUVATION:-
rps/s 3 0 -3 -6 6
OR evaluates the highest of two memberships
Vmotor
AND evaluates the lowest of two memberships
Consider the case where , Verror = 30 rps and d/dtVerror = 1rps/s
According to rules:-
If Verror is LP and d/dt (Verror) is any then Vmotor is LP.
1 24 18 12 6 0 v SPN ZEN SNN LN LPN
Figure 5
Membership Functions
Ø RULE EVALUVATION:-
OR evaluates the highest of two memberships
AND evaluates the lowest of two memberships
Consider the case where , Verror = 30 rps and d/dtVerror = 1rps/s
According to rules:-
If Verror is LP and d/dt(Verror) is any then Vmotor is LP
Figure 6
Graphs
Ø DEFUZZIFICATION:
The result obtained by evaluation of the rules of the FLC is a fuzzy set. To obtain Defuzzification is the process which converts the fuzzy set output to crisp value.
The most common method used in obtaining crisp output by defuzzification is center of gravity method.
It uses,
V motor = ∑ ni=1 (Vmotor i) (membershipi)
(membership i)
For the given example,the output will be,
V motor = 0.6 (17v) + 0.4 (14v) = 15.8v
Result: 0.6 + 0.4
Thus the final, motor control voltage calculated for the given set of FUZZY rules is 15.8v .
NEED FOR USING FUZZY CONTROL:-
(i) FLC process user defined rules governing target control system.
(ii) Because of rule based operation any number of reasonable input can be processed.
(iii) FLC can control non-linear system that would be difficult or impossible to model mathematically.
(iv) Any sensor data that provides some indications of a system action and reaction is sufficient. Not necessarily the rate of change of parameters is to be measured.
(v) During debugging and tuning cycle we can change our system by simply modifying rules instead of redesigning the control
APPLICATIONS:-
v Fuzzy technology are used in automotive industries to improve quality
v Fuzzy in aerospace enables to solve very complex real time problems.
v Fuzzy is used in consumer electronics to improve the time to market the product.
v They are used in industrial controls, transportation systems, video equipments, washing machines and so on.
CONCLUSION:-
A new approach based on fuzzy set theory has been presented for controlling the speed of DC motor which is capable of providing good speed regulation with stability. The experimental results show that the fuzzy logic controller produces the satisfactory speed control of DC motor than the conventional controls in such a way that it reduces the transient and steady state error and also accepts the rapid change in load variations. Thus the fuzzy logic controller provides the better performance than the conventional controllers.
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