46
Chapter 4
Modeling and Simulation of Fuzzy Logic Variable Speed
Drive Controller
4.1 Introduction
Fuzzy logic is an important part of artificial intelligence. In recent times, artificial intelligence techniques are becoming a significant branch in electrical engineering, predominantly in the area of power electronics and motor drives.
Artificial intelligence is principally computer emulation of human thinking. The goal of AI is to imitate human intellect so that a computer can think like a human being.
Looking at the complexity of human thinking process, it is possible that the computers may help to solve problems that are difficult to solve by conventional methods.
Categorization of Artificial intelligence is, 1, Expert System 2, Fuzzy logic 3, Artificial Neural Network and 4, Genetic Algorithms.
Fuzzy Logic is another class of AI, but its history and applications are more recent. In 1965, Lofty Zadeh, a computer scientist, propounds the hypothesis of Fuzzy Logic. He said that thinking of a human being is often fuzzy, vague, or imprecise in nature and, therefore, cannot be expressed by 1 (yes) or 0 (no) type precision as this logic is used in ES. FL mainly based on multi-valued logic between 0 & 1. In 1975, First-time fuzzy logic control was applied for steam generation plant by Manmdani and Assilian in London Queen Mary College.
Fuzzy logic is a superset of conventional (Boolean) logic that has been
extended to handle the concept of partial truth—truth values between
“completely true” and” completely false”.
47
Fuzzy expert system:
A fuzzy expert system is an expert system that uses a collection of fuzzy membership functions and rules, instead of Boolean logic, to reason about data. The rules in a fuzzy expert system are usually of a form similar to the following:
If x is low and y is high then z = medium
where x and y are input variables (names for know data values),z is an output variable (a name for a data value to be computed),low is a membership function (fuzzy subset) defined on x, high is a membership function defined on y, and medium is a membership function defined on z.
The antecedent (the rule's premise) describes to what degree the rule applies, while the conclusion (the rule's consequent) assigns a membership function to each of one or more output variables. Most tools for working with fuzzy expert systems allow more than one conclusion per rule. The set of rules in a fuzzy expert system is known as the rule base or knowledge base.
The general inference process proceeds in three (or four) steps.
1. Under FUZZIFICATION, the membership functions defined on the input variables are applied to their actual values, to determine the degree of truth for each rule premise.
2. Under INFERENCE, the truth value for the premise of each rule is computed, and applied to the conclusion part of each rule. This results in one fuzzy subset to be assigned to each output variable for each rule. Usually only MIN or PRODUCT is used as inference rules. In MIN inferencing, the output membership function is clipped off at a height corresponding to the rule premise's computed degree of truth (fuzzy logic AND). In PRODUCT inferencing, the output membership function is scaled by the rule premise's computed degree of truth.
3. Under COMPOSITION, all of the fuzzy subsets assigned to each output variable are combined together to form a single fuzzy subset for each output variable. Again,
48 usually MAX or SUM are used. In MAX composition, the combined output fuzzy subset is constructed by taking the point wise maximum over all of the fuzzy subsets assigned to variable by the inference rule (fuzzy logic OR). In SUM composition, the combined output fuzzy subset is constructed by taking the point wise sum over all of the fuzzy subsets assigned to the output variable by the inference rule.
4. Finally is the (optional) DEFUZZIFICATION, which is used when it is useful to convert the fuzzy output set to a crisp number. There are more defuzzification methods than we can shake a stick at (at least 30). Two of the more common techniques are the CENTROID and MAXIMUM methods. In the CENTROID method, the crisp value of the output variable is computed by finding the variable value of the center of gravity of the membership function for the fuzzy value. In the MAXIMUM method, one of the variable values at which the fuzzy subset has its maximum truth values chosen as the crisp value for the output variable.
Implication methods:
Mamdani type:
Mamdani’s fuzzy inference method is the most commonly seen fuzzy methodology. Mamdani’s method was among the first control systems built using fuzzy set theory. It was proposed in 1975 by Ebrahim Mamdani as an attempt to control a steam engine and boiler combination by synthesizing a set of linguistic control rules obtained from experienced human operators.
Lusing Larson type:
In this method output MF is scaled instead of being truncated.
Sugeno type:
The sugeno method of implication was first introduced in 1985. The difference here is that unlike the mamdani and lusing Larson methods, the output MFS are only constants or have linear relations with inputs. With a constant output MF (singleton), it is defined as zero order sugeno method, whereas with a linear relation, it is known as first order sugeno method.
49
Defuzzification methods
:Conversion of fuzzy output to crisp output is defined as defuzzification.
There are various types of defuzzification methods. Some of them are
Centre of area method:
In the COA method of defuzzification the crisp output z of the z variable is o taken to be the geometric centre of the output fuzzy valueout
z area, where
zout is formed by taking the union of all contribution of rules ,whose DOF>0.the general expression for COA defuzzification is
dz z
z z
z
out out
.0 (4.1)
With a discretized universe of discourse, the expression is
n
i out n
i
i out i
i
z z z
z
1
1
0
(4.2)
COA method is a well known method and it is often used in spite of some amount of complexity in calculation.
Height method:
In the height method of defuzzification, the COA method is simplified to consider only the height of each contributing MF at the midpoint of base.
Mean of maximum method:
The height method of defuzzification is further simplified in MOM method, where only the highest membership function in the output is considered. The general expression for MOM is
M
m m
M z Z
1
0 (4.3) Where, zm mth element in the universe of discourse, where the output MF
is at the maximum value, and M = number of such elements.
50
4.2 Fuzzy logic control algorithm
A fuzzy algorithm consists of situation and action pairs. Conditional rules expressed in IF and THEN statements are generally used. For example, the control rule might be: if the output is lower than the requirement and the output is dropping moderately then the input to the system shall be increased greatly. Such a rule has to be converted into a more generally statement for application to fuzzy algorithms. To achieve this the following terms are defined: error equals the set point minus the process output, error change equals the error from the process output minus the error from last output: and control input applied to the process. In addition, it is necessary to quantize the qualitative statements and the following linguistic sets are assigned 1. Large Positive (LP) 2. Medium Positive (MP)
3. Small Positive (SP) 4. Zero (ZZ)
5. Small Negative (SN) 6. Medium Negative (MN) 7. Large Negative (LN)
Thus the statement of the example control will be: if the error is large positive and the error change is small positive then the input to the system is large positive.
Fuzzy control action
1. Specify and store the minimum and the maximum ranges of the error signal E=er(k) , the error change dE= der(k)and the control input change df.
2. If the minimum and maximum ranges of step one are different then quantize then into a common universe of discourse using scaling factors such that the maximum and minimum of the quantized error signal E, the quantized error change dE, and the quantized control input changed f are all the same.
3. Define the symmetrical linguistic fuzzy subsets of E, dE, and df.
4. Calculate the error er and the error change der for the current sampling period and find their quantized values E and dE respectively in the common universe of discourse.
51 5. From the E and dE the contribution of each rule given in Table 4.2 in the
fuzzy subsets of control input df and scaling of its membership grades using the rule can be found.
6. The result of application of all rules is membership function grades of control input df through the universe of its discourse. To calculate the crisp or numerical value of df the COA Criteria is used as follows:
(4.4)
Where n is the number of quantization levels of the output.
7. Add the control input change dF(k) to the previous value F(k-l) to calculate the new control action to be taken for the kth sample: F(k)=F(k-l)+dF(k).
Fuzzy logic tool box:
The Fuzzy Logic Toolbox is a collection of functions built on the MATLAB®
numeric computing environment. It provides tools for you to create and edit fuzzy inference systems within the framework of MATLAB, or if you prefer you can integrate your fuzzy systems into simulations with Simulink®, or you can even build stand-alone C programs that call on fuzzy systems you build with MATLAB. This toolbox relies heavily on graphical user interface (GUI) tools to help you accomplish your work, although you can work entirely from the command line if you prefer.
There are five primary graphical tools for building, editing and observing fuzzy inference systems in the fuzzy logic tool box.
They are
Fuzzy inference system (Fig. 4.1)
(FIS) editor
Membership function (MF) editor
Rule editor
Rule viewer
Surface viewer
52 Fig. 4.1 Fuzzy inference system
4.3 Design of PI Speed Controller
Considerable attention has to be paid in the selection of the controller as this not only decides the type of optimization but also determines the performance and behaviour of the system. Following factors can be considered in the selection of the type of controller: 1. Accuracy; 2. Time constants in the system; 3. Response of the controller; and noise.
Accuracy: The type of the controller to be chosen- depends on the accuracy required by the system. As we know that with a P-controller, there remains a permanent error in the regulating circuit which is however small and tolerable if T and hence under such circumstances a P or a PD controller, depending upon the number and magnitude of delay elements present in the system, can be used.
53 Time Constants Present in the System: The presence of delay elements (time constants) in the system affects its response. Thus it is advisable to cancel as many time constants as possible. Since in a system number of small and big time constants are present, attempts should be made to neutralize bigger time constants. With PID- controller two time constants and with PD and P1 one time constant each can be neutralized. PID-controller is especially suitable for field circuits having larger time constants.
Response of the Controller: P-controller has the fastest response while a I-controller has the slowest response. Thus, under the circumstances, where T , fast response property of a P-controller can be used without the risk of permanent control error.
Noise: Derivative controllers give an extremely fast response. They anticipate what is going to happen and apply corrective action. Noise which is always present in any system is intensified because of the derivative action. In thyristor converter application, output from regulating system determines the firing angle. The slightest noise will create considerable trouble and hence such type of regulators is never used in thyristor control circuit and other similar applications.
4.3.1 Different types of conventional controllers
We have the different types of controllers. some of them are
I-Controller
:Integral control adjusts the output of the controller so that it is proportional to the integral of the error signal. The output of an integral controller is given by:
Output = u(t) =k e
t dtt i
0
(4.5)
s k s es
Gc u i (4.6)
Due to the introduction of a time constant R this controller is sluggish in response as compared to a P-controller. The integral element helps the controller to have a finite output value even when its input is zero and thus it eliminates permanent control error.
54
Proportional controller
:A P-controller has got a fast response .this is because of the absence of any time constant in the regulator circuit. The output voltage is at all times proportional to input voltage.
Advantages of proportional controller:
- Very fast
- Simple to design - Good performance Disadvantages of proportional controller:
- Performance may not be good enough - High gain may cause instability
In general proportional controller is effective in reducing feedback error and tends to give good system performance. However this is not always the case. For example- motor velocity control.
Derivative controller
:Like a D-controller it is impossible to get an ideal PD controller because of the presence of input and source resistances. These resistances introduce a time constant into the system which is responsible for the slow decrease of output voltage. On account of the presence of D element the input voltage and the variation has to be limited to a value so that output voltage remains within the permissible limit. Like PI controller here also proportional gain and the time constant can be chosen and the time constant can be used to compensate one of the time constants of the system.
A proportional-plus –derivative PD control has the transfer function:
s k k sc p d (4.7)
s k
T S
c p 1 D (4.8) Where KPTD = KD and TD is the Derivative Time
Advantages of PD controller:
- Allows greater damping for no change in ɷn - Allows shorter settling time for no change in ɷn
- Rate of change of error is taken into account - Introduces positive phase (stabilization)
55 Disadvantages of PD controller:
- Susceptible to noise
PI Controller:
A P1-controller contains properties of both P- and I-controller and as such finds large application. Presence of I element makes the permanent control deviation Zero, and the proportional element helps in faster response. The proportional gain and the time constant can both be chosen to meet system requirements and thus it offers better adaptability as compared to P- or I-controller.
A PI control has the transfer function of form
S
K K
S
C
P
I (4.9) Where KP / TI = KI, and TI = Integral/ResetAdvantages of PI control:
- High accuracy achieved
- Steady-state error eliminated for step input Disadvantages of PI control
- Introduces negative phase-changes C.L.T.F to higher order - Need to design for two controller parameters
The basic block diagram of PI controller is shown in Fig. 4.2.
Fig. 4.2 Basic block diagram of PI controller
In continuous time domain a PI controller output represented by
C
t Kpr
t Ki
r
t (4.10) The reference torque is generated by speed error processed through the PI controller,Teref Kpe
t Ki
e
t (4.11)K
p+ K
i/s
error
signal C(t)
reference signal + +
56 Where e
t
ref
r (4.12)In a digital computer system, the speed sampling is in discrete time and so a discrete time model is desired taking the sampling interval to bet
Teref
n Teref
n1
KP
esn esni
Kiesn1t (4.13)Similarly the reference source current is generated by the dc link voltage error which is processed another PI controller
PID controller
:This controller consists of all the three elements and thus offers possibility to choose proportional gain and two time constants present in the controller. The two time constants of the controller can be used to compensate two time constants of the system.
Like D and PD controllers, it is also impossible in a PID controller to get ideal D performance.
A PID controller can be used to reduce the time constant and thus is preferable when thyristor converter is to be used for field control.
4.4 Comparisons between PI and fuzzy logic speed controllers
A standard approach for speed control in industrial drives is to use a PI controller.
Recent developments in artificial intelligence based control have brought into focus a possibility of replacing a PI speed controller with a fuzzy logic (FL) equivalent. Fuzzy logic speed control is sometimes seen as the ultimate solution for high performance drives of the next generation.
Operation of a drive with speed control by PI and FL techniques has been compared on a number of occasions. The comparison results show that summarized as follows:
The only transient in which FL speed control is superior to PI speed control in all the operating conditions is the load rejection transient. However, it has to be noted that even this is valid only if the controllers are designed for zero overshoot. If a small
57 overshoot is allowed in the design, load rejection capability of the PI speed control may be better than with FL control at certain speed settings.
Robustness of the drive to an increase in inertia is universally claimed as one of the main advantages of the FL speed control. Experimental results show that this is not necessarily the case. The robustness depends on the setting of the speed reference.
Speed response to small reference speed change depends on how close the speed responses of the two controllers are for the design point (rated step speed reference with rated inertia here). PI speed controller has much better response to all the reference speed changes, primarily because its response for the design point was slightly slower.
Compared to FL, PI speed controller shows better results with reversing transients.
4.5 Simulation Results
A block diagram of an indirect-vector-controlled (IVC) induction motor drive is shown in Fig. 4.4 and PI controller is shown in Fig. 4.3. Incorporating the proposed fuzzy speed controller, the feedback speed control loop generates the active or torque current command iqs*, as indicated. The vector rotator receives the torque and excitation current commands iqs*and ids*, respectively. The induction motor is fed by a hysteresis current-controlled pulse width modulated (PWM) inverter. The motor currents are decomposed into i and d iq, components which are respectively flux and torque components in the d-q reference frame rotating with the stator frequency s The inputs to the fuzzy logic speed controller have been selected as the speed error and its time variation. The output of the FLC is the variation of command current. The two inputs variablese
k andCe
k , are calculated at every sampling instant as e
k r
k r
k (4.14)ce
k e
k e
k1
(4.15) Where, r
k the reference is speed and r
k is the actual rotor speed.58 FLC consists of three stages Fuzzification, rule execution, and defuzzification.
In the first stage, the crisp variables e
k and Ce
k converted into fuzzy variables
e and Ce. Membership functions associated to the control variables have been chosen with triangular shapes. The universes of discourse of the input variables e and Ce are established after many simulations as (-180, 180) rad/s and (-0.8 0.8) rad/s respectively. The universe of discourse of the output variableciqs is (-2, 2).
Each universe of discourse is divided in to seven fuzzy sets: NL (Negative Large), NM (Negative Medium), NS (Negative Small), ZE (Zero), PL (Positive Large), PM (Positive Medium), PS (Positive Small). Each fuzzy variable is a member of the subsets with a degree of membership varying between 0 (non-member) and 1 (full member).
In the second stage of the FLC, the variablese andce are processed by an inference engine that executes 49 rules (7x7). These rules are established using the knowledge of the system behaviour and the experience of the control engineers. Each rule is expressed in the form as in the following example:
IF e is Negative Medium) AND ( ce is Positive Small) THEN ( ciqs is Negative Small). Different inference methods can be used to produce the fuzzy set values for the output fuzzy variableciqs , in this paper, the Max-Product inference method is used to calculate the final fuzzy value ciqs of the output.
In the defuzzification stage, a crisp value of the output variable ciqs(k) is obtained by using the centre of area defuzzification method.
The reference current iqs
k that is applied to the vector control system is computed by integrating ciqs(k)iqs
k iqs
k1
ciqs
k (4.16) The control performance of the described FLC is evaluated by Simulink. A trapezoidal trajectory for the speed reference has been selected, which is characterized by an initial constant acceleration period, a constant speed period, and finally a constant deceleration.59
The various components of the proposed simulation project
1. Three phase IGBT fed Squirrel cage Induction motor.
2. Indirect vector control block 3. Fuzzy controller block 4. PI controller block
Fig. 4.3 Main circuit diagram of PI speed controller
60
Demux Discrete,
Ts = 2e-006 s.
Phir
Te*
Iq*
Phir* Id*
Teta Id* Iq*
Iabc*
v + - +v
VDC -
z 1
z 1
z 1
z 1 Iq Phir wm Teta Step
Signal 3
Signal Builder
Scope9
Scope7
Scope6
Scope5
Scope4 Scope3 Scope2
Scope15 Scope13
Scope10
Scope1
Product1
1.15 Phir*
InMean m
is_abc
is_qd
v s_qd
wm
Te
1 s Integrator
Tm
m A
B
C Induction Motor g
A
B
C +
-
IGBT Inverter
-K- Gain4 1
Gain2 0.4 Gain1
Fuzzy Logic Controller with Ruleviewer
Id Phir + i
-
Iabc Iabc*
Pulses
Fig. 4.4 Main circuit diagram of proposed fuzzy logic speed controller
Three phase IGBT fed Squirrel cage Induction motor
In this thesis a 3-phase hysteresis current controlled pulse width modulated inverter is used and it is used to control a 3-phase squirrel cage induction motor of parameters 2.2KVA, 50HZ (Table 4.1). On the basis of the parameters inverter ratings are selected. It is basically a 4-pole motor with synchronous speed of 1500 rpm. The rated speed of the motor as per its characteristics is 1470 rpm.
61 Table 4.1 parameters of three phase induction motor used
Rotor Type Squirrel cage
Reference frame Synchronous
Nominal Power 2.2 KVA
Voltage Line to Line 208 Vrms
Frequency 50 Hz
Stator resistance 0.59 ohm
Stator inductance 0.06472 H
Rotor resistance 0.37 ohm
Rotor inductance 0.06472 H
Mutual inductance 0.06191 H
Inertia 0.056
Friction factor 0.000479
Number of poles 4
4.5.1 Indirect vector control block
The induction motor is fed by a current-controlled PWM inverter, which operates as a three-phase sinusoidal current source. The motor speed is compared to the reference * and the error is processed by the speed controller to produce a torque command Te*. The stator quadrature-axis current reference iqs* is calculated from torque reference Te* as
r est e
m qs
T L Lr i p
2
3
2 (4.17)
Where, Lr is the rotor inductance, Lm is the mutual inductance, and |r|est is the estimated rotor flux linkage given by
s i
L
r ds m
r est
1 (4.18) Where, r = Lr / Rr is the rotor time constant. The stator direct-axis current reference
ids* is obtained from rotor flux reference input |r|*
m r
ds L
i
(4.19)
62 The rotor flux position e required for coordinates transformation is
generated from the rotor speed m and slip frequency sl:
e
m sl
dt (4.20) The slip frequency is calculated from the stator reference current iqs* and the motor parameters. qs
r r
r est m
sl i
L R L
(4.21)
The iqs* and ids* current references are converted into phase current references ia*, ib*, ic* for the current regulators. The regulators process the measured and reference currents to produce the inverter gating signals. The role of the speed controller is to keep the motor speed equal to the speed reference input in steady state and to provide a good dynamic during transients. It can be of proportional-integral type.
The current-controlled PWM inverter circuit is used. The IGBT inverter is modeled by a Universal Bridge block in which the Power Electronic device and Port configuration options are selected as IGBT/Diode and ABC as output terminals respectively. The DC link input voltage is represented by a 780 V DC voltage source the current regulator, which consists of three hysteresis controllers, is built with Simulink blocks (Fig. 4.5). The motor currents are provided by the measurement output of the Asynchronous Machine block.
1 Pulses Mux
NOT NOT NOT
Demux Demux
boolean boolean
double double double boolean
2 Iabc*
1 Iabc
Fig. 4.5 Hysteresis current control block
63 The conversions between abc and dq reference frames are executed by the abc to dq0 transformation as shown in Fig. 4.6.
1 Iabc*
ic f(u)
ib f(u) ia
Mux Mux
-K- -K- -K- cos(u)
sin(u)
3 Iq*
2 Id*
1 T eta
Fig. 4.6 abc to dqo transformation
The rotor flux is calculated by the Flux Calculation block (Fig. 4.7).
Phi r = Lm *Id / (1 +T r .s) Lr = 64.72
mH
Rr = 0.37 ohms 1
Phi r
-K-
Lm H=1/(1+T .s)
T = 0.1749 s
Di screte T ranfer Functi on
1 Id
Fig. 4.7 Rotor flux calculation block
The rotor flux position ( e) is calculated by the Theta Calculation block as shown in Fig. 4.8.
T eta= Electrical angle= integ ( wr + wm)
wr = Rotor frequency (rad/s) = Lm *Iq / ( T r * Phir)
Lm = 61.91 mH
Rr= 0.37 ohms Lr = 64.72 mH
wm= Rotor mechanical speed (rad/s)
T r = Lr / Rr = 0.1749 s
1 T eta Mux
Mux
1 s Integrator 2
1 61.91e-3* u[1]/(u[2]*0.1749+1e-3)
3 wm 2
Phir 1 Iq
Fig. 4.8 Theta calculation block
64 The stator quadrature-axis current reference (iqs*) is calculated by the iqs*
Calculation block (Fig. 4.9 and Fig. 4.10).
Iq= ( 2/3) * (2/p) * ( Lr/Lm) * (T e / Phir) Lm = 61.91mH Lr = 64.72mH
p= nb of poles = 4 Iq= 0.348 * (T e / Phir)
1 Iq*
Mux u[1]*0.348/(u[2]+1e-3) 2
T e*
1 Phir
Fig. 4.9 iqs* calculation block
Id* = Phi r*/ Lm Lm= 61.91 mH
1 Id*
-K-
KF 1
Phi r*
Fig. 4.10 id* calculation block
4.5.2 PI controller block:
A PI controller contains properties of both p and I controller and as such finds large applications. Presence of I element makes the permanent control zero, and the proportional element helps in faster response. The inputs to the PI controller is
*(reference speed) and (actual speed) as shown in Fig. 4.11.
Fig. 4.11 PI controller
65
4.5.3 Fuzzy controller block
:The inputs to the fuzzy logic speed controller are the speed error and its time variation. The output of the FLC is the variation of command current. The two inputs variablese
k andCe
k , are calculated at every sampling instant. A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1 (Fig. 4.12). The input space is sometimes referred to as the universe of discourse, a fancy name for a simple concept. The characteristic of one FLC can be more intuitive represented in the three- dimensional space.
Fig. 4.12 Membership function of the fuzzy variables ew, cew and ciqs*
Table 4.2: Rule base for speed control EW
WEW
NL NM NS ZE PS PM PL
NL NL NL NL NL NM NS ZE
NM NL NL NL NM NS ZE PS
NS NL NL NM NS ZE PS PM
ZE NL NM NS ZE PS PM PL
PS NM NS ZE PS PM PL PL
PM NS ZE PS PM PL PL PL
66
4.5
.4 Fuzzy Logic Program for Development of Fuzzy Rules
R
[System]
Name='change1'
Type='mamdani'
Version=2.0
NumInputs=2
NumOutputs=1
NumRules=49
AndMethod='min'
OrMethod='max'
ImpMethod='prod'
AggMethod='max'
DefuzzMethod='centroid'
[Input1]
Name='input1'
Range=[-180 180]
NumMFs=7
MF1='NL':'trapmf',[-180 -180 -130 -50]
MF2='NM':'trimf',[-130 -50 -20]
MF3='NS':'trimf',[-50 -20 0]
MF4='ZE':'trimf',[-20 0 20]
MF5='PS':'trimf',[0 20 50]
MF6='PM':'trimf',[20 50 130]
MF7='PL':'trapmf',[50 130 180 180]
[Input2]
Name='input2'
Range=[-0.8 0.8]
NumMFs=7
67
MF1='NL':'trapmf',[-0.8 -0.8 -0.5 -0.2]
MF2='NM':'trimf',[-0.5 -0.2 -0.1]
MF3='NS':'trimf',[-0.2 -0.1 0]
MF4='ZE':'trimf',[-0.1 0 0.1]
MF5='PS':'trimf',[0 0.1 0.2]
MF6='PM':'trimf',[0.1 0.2 0.5]
MF7='PL':'trapmf',[0.2 0.5 0.8 0.8]
[Output1]
Name='output1'
Range=[-2 2]
NumMFs=7
MF1='NL':'trapmf',[-2 -2 -1 -0.5]
MF2='NM':'trimf',[-1 -0.5 -0.2]
MF3='NS':'trimf',[-0.5 -0.2 0]
MF4='ZE':'trimf',[-0.2 0 0.2]
MF5='PS':'trimf',[0 0.2 0.5]
MF6='PM':'trimf',[0.2 0.5 1]
MF7='PL':'trapmf',[0.5 1 2 2]
[Rules]
1 1, 1 (1) : 1
1 2, 1 (1) : 1
1 3, 1 (1) : 1
1 4, 1 (1) : 1
1 5, 2 (1) : 1
1 6, 3 (1) : 1
1 7, 4 (1) : 1
2 1, 1 (1) : 1
2 2, 1 (1) : 1
2 3, 1 (1) : 1
68
2 4, 1 (1) : 1
2 5, 3 (1) : 1
2 6, 4 (1) : 1
2 7, 5 (1) : 1
3 1, 1 (1) : 1
3 2, 1 (1) : 1
3 3, 2 (1) : 1
3 4, 3 (1) : 1
3 5, 4 (1) : 1
3 6, 5 (1) : 1
3 7, 6 (1) : 1
4 1, 1 (1) : 1
4 2, 2 (1) : 1
4 3, 3 (1) : 1
4 4, 4 (1) : 1
4 5, 5 (1) : 1
4 6, 6 (1) : 1
4 7, 7 (1) : 1
5 1, 2 (1) : 1
5 2, 3 (1) : 1
5 3, 4 (1) : 1
5 4, 5 (1) : 1
5 5, 6 (1) : 1
5 6, 7 (1) : 1
5 7, 7 (1) : 1
6 1, 3 (1) : 1
6 2, 4 (1) : 1
6 3, 5 (1) : 1
6 4, 6 (1) : 1
69
6 5, 7 (1) : 1
6 6, 7 (1) : 1
6 7, 7 (1) : 1
7 1, 4 (1) : 1
7 2, 5 (1) : 1
7 3, 6 (1) : 1
7 4, 7 (1) : 1
7 5, 7 (1) : 1
7 6, 7 (1) : 1
7 7, 7 (1) : 1
4.5.5 Fuzzy Rules
1. If (input1 is NL) and (input2 is NL) then (output1 is NL) (1) 2. If (input1 is NL) and (input2 is NM) then (output1 is NL) (1) 3. If (input1 is NL) and (input2 is NS) then (output1 is NL) (1) 4. If (input1 is NL) and (input2 is ZE) then (output1 is NL) (1) 5. If (input1 is NL) and (input2 is PS) then (output1 is NM) (1) 6. If (input1 is NL) and (input2 is PM) then (output1 is NS) (1) 7. If (input1 is NL) and (input2 is PL) then (output1 is ZE) (1) 8. If (input1 is NM) and (input2 is NL) then (output1 is NL) (1) 9. If (input1 is NM) and (input2 is NM) then (output1 is NL) (1) 10. If (input1 is NM) and (input2 is NS) then (output1 is NL) (1) 11. If (input1 is NM) and (input2 is ZE) then (output1 is NL) (1)
70 12. If (input1 is NM) and (input2 is PS) then (output1 is NS) (1)
13. If (input1 is NM) and (input2 is PM) then (output1 is ZE) (1) 14. If (input1 is NM) and (input2 is PL) then (output1 is PS) (1) 15. If (input1 is NS) and (input2 is NL) then (output1 is NL) (1) 16. If (input1 is NS) and (input2 is NM) then (output1 is NL) (1) 17. If (input1 is NS) and (input2 is NS) then (output1 is NM) (1) 18. If (input1 is NS) and (input2 is ZE) then (output1 is NS) (1) 19. If (input1 is NS) and (input2 is PS) then (output1 is ZE) (1) 20. If (input1 is NS) and (input2 is PM) then (output1 is PS) (1) 21. If (input1 is NS) and (input2 is PL) then (output1 is PM) (1) 22. If (input1 is ZE) and (input2 is NL) then (output1 is NL) (1) 23. If (input1 is ZE) and (input2 is NM) then (output1 is NM) (1) 24. If (input1 is ZE) and (input2 is NS) then (output1 is NS) (1) 25. If (input1 is ZE) and (input2 is ZE) then (output1 is ZE) (1) 26. If (input1 is ZE) and (input2 is PS) then (output1 is PS) (1) 27. If (input1 is ZE) and (input2 is PM) then (output1 is PM) (1) 28. If (input1 is ZE) and (input2 is PL) then (output1 is PL) (1) 29. If (input1 is PS) and (input2 is NL) then (output1 is NM) (1) 30. If (input1 is PS) and (input2 is NM) then (output1 is NS) (1) 31. If (input1 is PS) and (input2 is NS) then (output1 is ZE) (1)
71 32. If (input1 is PS) and (input2 is ZE) then (output1 is PS) (1)
33. If (input1 is PS) and (input2 is PS) then (output1 is PM) (1) 34. If (input1 is PS) and (input2 is PM) then (output1 is PL) (1) 35. If (input1 is PS) and (input2 is PL) then (output1 is PL) (1) 36. If (input1 is PM) and (input2 is NL) then (output1 is NS) (1) 37. If (input1 is PM) and (input2 is NM) then (output1 is ZE) (1) 38. If (input1 is PM) and (input2 is NS) then (output1 is PS) (1) 39. If (input1 is PM) and (input2 is ZE) then (output1 is PM) (1) 40. If (input1 is PM) and (input2 is PS) then (output1 is PL) (1) 41. If (input1 is PM) and (input2 is PM) then (output1 is PL) (1) 42. If (input1 is PM) and (input2 is PL) then (output1 is PL) (1) 43. If (input1 is PL) and (input2 is NL) then (output1 is ZE) (1) 44. If (input1 is PL) and (input2 is NM) then (output1 is PS) (1) 45. If (input1 is PL) and (input2 is NS) then (output1 is PM) (1) 46. If (input1 is PL) and (input2 is ZE) then (output1 is PL) (1) 47. If (input1 is PL) and (input2 is PS) then (output1 is PL) (1) 48. If (input1 is PL) and (input2 is PM) then (output1 is PL) (1) 49. If (input1 is PL) and (input2 is PL) then (output1 is PL) (1)
72
4.5.6 Comparison of result between PI and Fuzzy Logic controller
Fig. 4.13 Speed of Step input without load (PI controller)
Fig. 4.14 Speed of Step input without load (Fuzzy controller)
73 Fig. 4.15 Motor torque of Step input without load (PI controller)
Fig. 4.16 Motor torque of Step input without load (Fuzzy controller)
74 Fig. 4.17 Current of step input without load (PI controller)
Fig. 4.18 Current of step input without load (Fuzzy controller)
75 Fig. 4.19 Error in speed of step input without load (PI controller)
Fig. 4.20 Error in speed of step input without load (fuzzy controller)
76 Fig. 4.21 Speed of step input with load (PI controller)
Fig. 4.22 Speed of step input with load (fuzzy controller)
77 Fig. 4.23 Motor torque of step input with load (PI controller)
Fig. 4.24 Motor torque of step input with load (Fuzzy controller)
78 Fig. 4.25 Current of step input with load (PI controller)
Fig. 4.26 Current of step input with load (Fuzzy controller)
79 Fig. 4.27 Error in speed of step input with load (PI controller)
Fig. 4.28 Error in speed of step input with load (Fuzzy controller)
80 Fig. 4.29 Speed of Non step without load (PI controller)
Fig. 4.30 Speed of Non step without load (Fuzzy controller)
81 Fig. 4.31 Motor torque of non-step input without load (PI controller)
Fig. 4.32 Motor torque of non-step input without load (Fuzzy controller)
82 Fig. 4.33 Current of non-step input without load (PI controller)
Fig. 4.34 Current of non-step input without load (Fuzzy controller)
83 Fig. 4.35 Error of speed in non-step input without load (PI controller)
Fig. 4.36 Error of speed in non-step input without load (Fuzzy controller)
84 Fig. 4.37 Speed of Non step input with load (PI controller)
Fig. 4.38 Speed of Non step input with load (Fuzzy controller)
85 Fig. 4.39 Motor torque of non-step input with load (PI controller)
Fig. 4.40 Motor torque of non-step input with load (Fuzzy controller)
86 Fig. 4.41 Current of non-step input with load (PI controller)
Fig. 4.42 Current of non-step input with load (Fuzzy controller)
87 Fig. 4.43 Error of speed of non-step input with load (PI controller)
Fig. 4.44 Error of speed of non-step input with load (Fuzzy controller)
88
4.6 Conclusion
A fuzzy logic controller based indirect vector control of induction motor has been presented. Fuzzy logic controller has been designed for speed control loop. The simulation has been carried out using Simulink Fuzzy Logic toolbox user guide (Fig. 4.13 to 4.44). In order to minimize the real-time computational burden simple membership functions and rules have been used (Table 4.2). Since exact system parameters are not required in the implementation of the proposed controller, the performance of the drive system is robust, stable and sensitive to parameters and operating condition variations. In order to prove the superiority of the FLC, a conventional PI controller based IM drive system has also been simulated and the performance has been investigated at different dynamic operating conditions. It is concluded that the proposed fuzzy logic controller has shown superior performances over the PI controller and form the wave form of the stator current, we can say that under all the conditions the fuzzy logic controller optimize the stator current that is input to the motor drive and give considerable saving in energy required.
