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8/2/2019 Fuzzy Logic Speed Control of Dc Drive
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SESSION:
ANN, FUZZY LOGIC AND GENETIC ALGORITHMS APPLICATION
TO VARIABLE SPEED DRIVES.
FUZZY LOGIC SPEED CONTROL OF DC DRIVE
Presented By
Ch.kalyan chakrawarthi(1/4 c.s.e)
Y.pramodh kumar(1/4 E.CE)
Koneru lakshmaih engineering college, vijayawada
ABSTRACT:
DC motors are used widely in many industrial and domestic applications. For the
proper use of these motors, an efficient speed control system is required. Though there
are many conventional methods, speed control of DC motors using Fuzzy Logic is more
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advantageous and easy compared to all other systems. This paper presents the theory,
design and simulation of a fuzzy logic based controller used for speed control of
separately excited D.C. motor. The FLC algorithm has been simulated on Simulink
toolbox in Matlab. Here two mathematical models of a Dc drive (Linear and non-linear)
are investigated and two controllers (PI and Fuzzy) are used. The first model is build as
linear transfer function of converter and DC motor. The second model is build using
advanced blocks from Power System Block set (PSB) library. The advantages of using
fuzzy and PI controller are analyzed.
KEYWORDS:
Control systems, DC drive, Fuzzy control, MATLAB, Power System Block set.
INTRODUCTION:
Engineers, in general deal with problems that are more complex in nature
where the degree of automation is very important aspect. Though many technologies are
employed for development of sophisticated control systems, Fuzzy logic is one of the
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most successful technologies and at present is being extensively explored as a means to
develop controllers for plants with complex and often not precisely known models. In
many applications Fuzzy logic controllers perform better than conventional controllers.
Based on the nature of fuzzy human thinking, Professor Lotfi A Zadeh
originated the “Fuzzy logic”, in 1965, according to him: fuzzy logic is mathematical
imprecise description. Fuzzy logic is an innovative technology that enhances
conventional system design with engineering expertise. Using Fuzzy logic, we can avoid
the need for rigorous mathematical solution. Fuzzy logic enables computers to think more
like we do by endowing them with approximate reasoning capabilities. It provides
algorithmic and philosophical framework necessary to exploit the tolerance for
imprecision and arrive at answers to more complex problems.
LINEAR MODEL OF DC DRIVE:
The linear model consists of two parts: converter/rectifier and DC motor. A
linear model of DC motor as shown in fig. was build using Simulink blocks. There are
two inputs (voltage and load) and two outputs (angular motor velocity and current).
Its parameters are computed automatically from nominal catalogue data:
motor power, voltage, current, speed, etc). It is very convenient to use nominal motor
data as rotor inductance and resistance.
Converter/rectifier is described as first order inertia
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kp(s)
Gconv = --------------
Tmip·s +1
Where kp -gain of converter/rectifier, Tmip -mean dead time of converter/rectifier
The dead time Tmip may vary from zero to one-half the period of an AC
source (0.01s for 50 Hz). It is assumed that six-phase thyristor bridge with mean dead
time Tmip=1.67ms is used in the Converter.
Simple transfer function model of motor current vs. voltage was used
kia
Gmot = ------------Ta·s +1
Where: kia - gain of DC motor, Ta - armature circuit time constant
USING PSB TO MODEL THE DC DRIVE:
An advanced set of linear and nonlinear blocks can be found in Power System
Blockset . Three AC sources, three-phase six-pulse converter, pulse generator and DC
motor are taken from the library. They are used to prepare high quality model of three-
phase DC drive. The three-phase bridge converter is the most frequently used motor
control system. Two of six thyristors conduct at any time instant. Gating of each thyristor
initiates a pulse of load current; therefore this is a six pulse controlled rectifier. The three-
phase six-pulse rectifier is also capable of inverter operation in the fourth quadrant.
FUZZY LOGIC:
FUZZY SETS:
The fuzzy logic problem can be defined as an input/output, static, non-
linear mapping problem through a “black box “, as shown in the following fig.
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All the input information is defined n the input space, it is processed in the
black box, and the solution appears in the output space. In general, mapping can be static
and dynamic, and the mapping characteristics are determined by the black box‟s
characteristics. The black box cannot only be a fuzzy system, but also neural network,
general mathematical system such as differential equations, algebraic equations. If X is
the universe of discourse and its elements are denoted by x, then a fuzzy set A in X is
defined as a set of ordered pairs.
A = {( x, A( x)), | x
Where A( x) is called the membership function (or MF) of x in A. The
membership function maps each element of X to a membership value between 0 and 1.
3.4 IF-THEN RULES:
Fuzzy sets and fuzzy operators are the subjects and verbs of fuzzy logic.
These if-then rule statements are used to formulate the conditional statements that
comprise fuzzy logic. A single fuzzy if-then rule assumes the form
if x is A then y is B
Where A
and B
are linguistic values defined by fuzzy sets on the ranges X and Y. The if-
part of the rule “ x is A” is called the antecedent or premise, while the then-part of the rule
“ y is B” is called the consequent or conclusion.
MEMBERSHIP FUNCTIONS:
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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. A membership function can different shapes such as Triangular, Trapezoidal,
Gaussian, Two-sided Gaussian etc. The simple and most commonly used MF is the
Triangular type.
FUZZY INFERENCE SYSTEMS:
Fuzzy inference is the process of formulating the mapping from a given
input to an output using fuzzy logic. The mapping then provides a basis from which
decisions can be made, or patterns discerned. The process of FIS involves membership
functions, fuzzy logic operators, and if-then rules. There are two types of fuzzy inference
systems that can be implemented in the Fuzzy Logic
Mamdani-type
Sugeno-type
These two types of inference systems vary somewhat in the way outputs are
determined. Fuzzy inference systems have been successfully applied in fields such as
automatic control, data classification, decision analysis, expert systems, and computer
vision. Because of its multidisciplinary nature, fuzzy inference systems are associated
with a number of names, such as fuzzy-rule-based systems, fuzzy expert systems, fuzzy
modeling, fuzzy associative memory, fuzzy logic controllers, and simply fuzzy systems.
Mamdani‟s method was among the first control systems built using fuzzy set theory. It
was proposed in 1975 by Ebrahim Mamdani. Mamdani‟s effort was based on Lotfi
Zadeh‟s 1973 paper on fuzzy algorithms for complex sys tems and decision processes.
Mamdani-type inference expects the output membership functions to be fuzzy sets. After
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the aggregation process, there is a fuzzy set for each output variable that needs
defuzzification
In the Fuzzy Logic Toolbox, there are five parts of the fuzzy inference process:
Fuzzification of the input variables
Application of the fuzzy operator in the antecedent
Implication from the antecedent to the consequent
Aggregation of the consequents across the rules
Defuzzification.
Depending on these guidelines, both the inputs are fuzzified. Seven fuzzy variables
(Linguistic variables) are selected for the speed control of a separately excited DC Motor.
These variables are
Negative Big - NB
Negative Medium - NM
Negative Small - NS
Zero - ZE
Positive Small - PS
Positive Medium - PM
Positive Big - PB
The word „Negative‟ indicates that actual speed is greater than the reference
speed and so the error is negative. Similarly, the word „Positive‟ indicates that actual
speed is less than the reference speed and so the error is positive. The terms Big, Medium
and Small indicate the degree or range by which the Positive or Negative error varies
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from the actual value.
Depending on these IF-THEN rules, the fuzzy logic controller performs the
specified operation on the system giving required outputs. But writing of these rules
generally depends on the experience and commonsense of the person who is writing
those rules.
CHANGE IN ERROR
ERROR PB PM PS ZE NS NM NB
NB NB NB NB NM NS NS ZE
NM NB NM NM NM NS ZE PS
NS NB NM NS NS ZE PS PM
ZE NB NM NS ZE PS PM PMPS NM NS ZE PS PS PM PB
PM NS ZE PS PM PM PM PB
PB ZE PS PS PB PM PB PB
RULE BASE
DEFUZZIFICATION:
The conversion of fuzzy output to crisp output is defined as Defuzzification. There are
four methods of Defuzzification. They are
Center of area (COA) method
Height Method
Mean of maxima (MOM) method
Sugeno Method.
MODELLING AND SIMULATION RESULTS:
A classic DC drive with two PI controllers is presented on the following figure.
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Fig. DC drive with PI controllers in current and velocity loop. Linear transfer function
models are used
The simulation results (DC motor current and angular velocity vs. time) are
presented on the following figure. This is raw simulation as linear model has very low
granularity: AC component of current and switching of currents in Thyristor Bridge are
neglected. Only envelope of transients can be seen on simulation output.
Fig. Current and angular velocity of DC motor. Simulink and linear model
were used for simulation.
The following figure shows DC drive with PI controllers in current and velocity
loops. The Synchronized 6-Pulse Generator block can be used to fire the six thyristors of
a six-pulse converter. The output of the block is a vector of six pulses individually
synchronized on a three-phase commutation voltage. The pulses are generated alpha
degrees after the increasing zero crossings of the commutation voltages.
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Fig. DC drive with PI controllers in current and velocity loops. Power System Blockset isused to build advanced drive model.
The simulation results (current and angular velocity vs. time) are presented on figure.
Fig. Simulated current signal and angular velocity using Simulink and PSB
Linguistic variables and rules:
There are two fuzzy variables (error and INTEG error) and seven linguistic
variables (from big negative to big positive). The fuzzy controller attributes are:
Type: 'Mamdani'
And Method: 'prod'
Or Method: 'max'
DefuzzMethod: 'centroid'
Imp Method: 'prod'
AggMethod: 'max'
Input: [1x2 struct]
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Output: [1x1 struct]
Rule: [1x25 struct]
The membership functions (pimf and gausmf are used) and rules are design tools that
give opportunity to model a control surface and controller properties. It is obvious that
using this attributes one can more precisely fulfill a quality criterion in full operational
range. The control surface is defined with 25rules. The following figure shows DC drive
with Fuzzy controllers in current and velocity loops. The simulation results of the motor
current with PI controller and Fuzzy controller shown in the following fig.
Fig. DC drive with fuzzy controller in current loop. Power System Block set is used to
build advanced drive model
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CONCLUSION:
Both simple transfer function model and the advanced set of linear and
nonlinear blocks from Power System Blockset are useful for tuning the DC drive control
system. Advanced models build with Power System Blockset blocks are suitable for
preliminary verification of control system, as AC component of current and switching
phenomena of thyristor bridge are not neglected. The fuzzy controller is more difficult to
design comparing with PI controller but has more design parameters and is more suitable
to fulfill nonlinear quality criterion in all operational range. For real time operation a
discrete fuzzy algorithm can be implemented on microcomputer, or DSP chip, which is
more suitable for industrial application.
REFERENCES:
Fundamentals of Electrical Drives -Gopal K. Dubey
Modeling and Fuzzy Control of DC Drive
-Ghent, pp 186-190 ,Bogukila Mrozek, Zbigniew Mrozek,
Modern Power Electronics and AC Drives - Bimal K.Bose
Design and testing control system for DC-drive using Simulink and
Power System Blockset (in Polish), B. Mrozek, 2-nd National Conference
Methods and Computer System, pp 185-190, Krakow, Oct. 1999, Poland.
Fuzzy Logic – An introduction -Steven D.Kaehler
Fuzzy Logic Toolbox User‟s Guide-The Mathworks ,Inc. 1995-1998
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