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Speed Control Based on Adaptive Fuzzy Logic Controller For AC-DC

Converter Fed DC Motor Drives

E. E. El-kholy, H. Yousef, and A. M. Dabroom

General Organization for Technical Education and Vocational Training,

College of Telecomm. & Electronics, R & D Center, Jeddah, Saudi Arabia.

e-mail: [email protected]



Abstract:

This paper presents fuzzy logic control (FLC)

based speed control system for a DC Motor

drive through the use of Genetic optimization.

The control system design and implementationprocedures of DC motor drive using Digital

Signal Processor are described. Results of

simulation and experimental on the real

control system demonstrated that the proposed

FLC is able to overcome the disadvantage of

use PI controller. Also, the results obtained

have shown the feasibility and effectiveness of

the control system.

1. Introduction

High performance DC motor drives are used

extensively in industrial applications. The DC

motor drive is a highly controllable electrical

motor drive suitable for robotic manipulators,

guided vehicles, steel mills and electrical

traction [1-5]. Usually, precise, fast, effective

speed reference tracking with minimumovershoot/undershoot and small steady state

error are essential control objectives of such a

drive system [6-7].

There has been several conventional control

techniques in DC motor drives are presented

[8-12]. The conventional control strategies are

a fixed structure, fixed parameter design.

Hence the tuning and optimization of these

controllers is a challenging and difficult task,

particularly, under varying load conditions,

parameter changes, abnormal modes of

operation, etc. Attempts to overcome such

limitations using adaptive and variablestructure control have had limited success due

to complexity, requiring of estimation stages,

model structure changes due to discontinuous

drive mode of operation, parameter variations,

load excursions and noisy feedback speed and

current signals [13-17]. In the drive field,fuzzy logic has applied to various problems,

such as robust control of DC drive systems.

This paper presents.

In this paper, fuzzy logic controller is used

instead of the PI controller to overcome the

undesired undershoots coming from load

impact at some abnormal conditions. A

complete circuit for the system under

consideration has constructed. The proposed

controller is implemented using a high speed

DSP in order to verify the robustness of these

controllers.

2. FLC For Separately Excited DC Motor

Drive

In recent years many authors have reportedthat fuzzy control is a more robust control

method than usual PID-control to variation of

system parameters [15]. It must be so, becausethe fuzzy control is more flexible. As opposed

to the PID-control it allows to use nonlinear

relations between input and output values of

the controller. That is, before the fuzzy

controller design it is necessary to be clearly

aware of what type of nonlinearity has to be

introduced for the robust speed control of the

DC drive and what parameters of the fuzzy

controllers form its type of nonlinearity.

As mentioned above the fuzzy approach is aconvenient method to design a controller with

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a desired nonlinear dependence between the

input and the output of the controller. So, our

task is to properly choose the fuzzy controller

parameters that form the desired controller.

The fuzzy system need to get such a fuzzy

controller for which in the range of inputvalues close to zero the following conditions

are valid [12]: Value of the change-of-control

increment decreases when the error decreases.

And, value of the change-of-control increment

increases when the change-of-error decreases.

x System Configuration:

DC is considered one of the best electrical

motor drives used in traction and a fan type

loads that have quadratic torque-speedcharacteristics [12]. A high starting torque is

recommended in traction applications, which

can easily be met by a DC motor [13]. The

speed control drive system under consideration

is shown in Fig. 2. The speed control loop is to

provide fast transient response as well as to

limit the armature current. The speed

controller is designed in such a way to produce

a desired reference signal for the current

controller. The output of the current controller

is fed to generate the firing angle, which

controls the motor terminal voltage. Figure (1)

shows a schematic diagram for the proposed

speed control system. It consists of a cascade

combination of a diode bridge rectifier and a

symmetrical angle control converter,

connected to a single-phase AC supply. The

motor voltage is regulated by the control

voltage (Vc) from zero to the maximum value

(A) of the timing voltage (Za) as shown in Fig.

(2). The inductance Lf and capacitance Cf areused as an output DC filter. One IGBT is used,

and controlled by an impulse generator. The

parameter values of this system are given in

Appendix (1).

The system under investigation has two modes

of operation. These modes are represented by

the equivalent circuits of Fig. (2). The

mathematical model can be obtained as

follows:

Fig. 1 System configuration

x Modeling of The Power Circuit andMotor:

Mode (1):

In this mode, the IGBT is ON. The differential

equations describing this mode are given as

follows:

mVfR

fisV

dtf

di

fL

(1)

mmKmrmimV

dt

mdimL Z

(2)

LTmBmim

Kdt

mdJ

Z

Z

(3)

mifidtmdvfC

(4)

fisi (5)

t)(sinVsV Z (6)

Mode (2):

In this mode, the IGBT is OFF as shown in

Fig. (2). The differential equations describing

this mode are given:

Pulse

generatorscheme

Lf imRf

ACSupply

Rectifier

Vs

LimiterZ ref

Z m

Cf

V Vm

if

Encoder

Vc(k)

DSP-ds1102 controller board (ds1102)

ew

Load

is

v

Drive circuit

d/dt

d/dt

FuzzyPI

speed

FuzzyPI

current

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fR

fimV

dt

fdi

fL

(7)

mmK

mr

mi

mV

dt

mdi

mL Z

(8)

LTmBmim

Kdt

mdJ

Z

Z

(9)

mifi

dt

mdv

fC

(10)

0si (11)

Mode (1) IGBT is ON

Mode (2) IGBT is OFF

Fig. 2 Modes of operation for the system

x Modeling of The Impulse Generator:

From Fig. (2) the equation that represents the

timing voltage (Za) is given by:

t)(sinAZZ

a (12)

The IGBT is turned ON when:

Vc < Za (13)

The IGBT is turned OFF when:

Vc > Za(14)

x Modeling of FLC:

The motor variables to be controlled are the

speed and the armature current. In the

proposed fuzzy logic control scheme, the

motor speed error and the error change are

used as input variables to Fuzzy speed

controller. However, the armature current errorand the error change are the input variables to

fuzzy current controller. The error and error

change for both speed and current are scaled

using appropriate scaling factors. These scaled

input data are then converted into linguistic

variables, which may be viewed as labels of

fuzzy sets. The linguistic variables, which are

used for the input variables, are shown in Fig.

(3). Also, the choice of membership function

shape is mainly dependent on the designerpreference. For simplicity, the triangular-

shaped functions are used in this application.

In the universe of discourse, the numbers for

the aforementioned linguistic variables are

selected. The membership functions for the

error and the error change are shown in Fig.3.

a. Error

b. Change in error

Lf

Cf

VsVm

if imRf

Motor and

Load

is

Lf

Cf

V=VsVm

if imRf

Motor and

Load

NB NM NS ZE PS PM PB

Universe of

discourse (e)

-3/4 -1 -2/3 -1/3 0 1/3 2/3 1

Universe of

discourse ( e)


-3/4 -1 -2/3 -1/3 0 1/3 2/3 1

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c. Change in control

Fig. 3. Membership functions for speed and

current controllers

The fuzzy control rules are selected. Since

both the speed and current loops must satisfy

the needs of fast transient response with

minimum overshoot and they have essentially

first order characteristics, consequently thesame fuzzy control rules should be valid for

both loops. These rules are given in Table 1.

Where, PVB: positive very big, and NVB:

negative very big.

The final stage of FLC, which called

defuzzification, is a mapping from a space of

fuzzy control actions defined over an output

universe of discourse into a space of crisp

control actions. The widely used strategy for

defuzzification is the center-of-gravity

method, which is adopted in this scheme.

Table 1. Fuzzy control rules for speed and

current controllers

3. Adaptive Fuzzy Logic Controller

Certain inherent difficulties of the approach

are restricting its success in control

applications. The following are some of the

difficulties, which face its application

development:

x Difficulties in developing fuzzy rules byhand for large systems.

x Difficulties in selecting appropriatemembership function shapes.

x Difficulties in fine tuning fuzzy solutionsfor specific levels of accuracy, andguaranteeing the reliability/robustness of

solutions. The trial and error method is still

the basic method in improving the expert

knowledge towards developing tuned and

stable fuzzy controllers.

The most important task in fuzzy control

engineering is to build advanced tools for

automated knowledge-base generation and

tuning fuzzy controllers. Moreover, an

improved approximate reasoning mechanismto speed up the on-line controller response is

required. The tools for auto-generation of the

knowledge-base will decrease the cost and

time of fuzzy controller application

developments. The tools for tuning the

controller knowledge will provide the stability

requirements for the operation of the controller

[14].

The conventional method to optimize the FLCis the steepest cell descent. Nevertheless, this

method required some prerequisites, such as

fixing the number of rules, which has been

obtained through trials of success and failure,

been the method tedious and bored because it

requires a lot of time. The Genetic Algorithm

(GA) driven by fuzzy reasoning is the

advanced method for learning the FLC

systems.

x FLC Learning Using GA

The GA is one of the most up-to-date artificial

intelligence techniques [8]. GA have been

applied successfully to many engineering

applications and optimization problems. The

GA is an optimization method developed by

biological evolution, which was used to find

the shapes and places of membership

functions, getting the inference rules and

output memberships. They presume that the

potential solution of a problem is an individualand can be represented by a set of parameters.


NB NVB NVB NVB NB NM NS ZE

NM NVB NVB NB NM NS ZE PS

NS NVB NB NM NS ZE PS PM

ZE NB NM NS ZE PS PM PB

PS NM NS ZE PS PM PB PVB

PM NS ZE PS PM PB PVB PVB

PB ZE PS PM PB PVB PVB PVB

Universe of

discourse

( u)

NVB NB NM NS ZE PS PM PB PVB

-1.2 - 1 -0.8 -0.6 -0. -0.2 0 0.2 0 . 0.6 0.8 1 .0 1 .2

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These parameters are regarded as the gens of

chromosome and can be structured by a string

of values in binary form or real form.

Generally, a positive value know as fitness

value, is used to reflect the degree of goodness

of the chromosome for solving the problem.

This section considers the problem of

automatically learning a set of optimized fuzzy

rules and membership functions [13]. The

method applies evolutionary programs in a two

steps fashion to a rule-based fuzzy controller.

The type of fuzzy controller considered here

consists of triangular membership functions

for the fuzzy variables in the premises, and

singleton membership functions for the fuzzy

variables in the conclusions. Figure 4illustrates a block diagram of the overall

closed loop DC control system [13].

Fig. 4. GA-optimized FLC architecture

This membership places an upper bound on the

number of fuzzy rules, which is the product of

the number of membership functions for the

fuzzy variables in the premises. For the case of

the DC motor, there are two input variables,

and a single output variable of voltage. TheDefuzzification is performed by the discrete

center-of-gravity method [14].

The first step in the method produces the

singleton conclusions for a reduced set of rules

using fixed symmetric triangular membership

functions. The second step is then adjusts the

membership functions. We considered two

ways of performing the first step of rule

learning and reduction. In the first case, an

evolutionary program was used to select the

singleton values of the rules. The basic idea

was to maintain a population of chromosomes,

each of which represented a proposed rule-base. An individual chromosome consisted of

a string of integers, in the range {-6,6},

representing the singleton conclusions of the

rules. A zero in the string signified that the

corresponding rule was not used in the

calculation. The fitness function was chosen to

combine the error produced by the simulatedDC motor and the number of rules with

conclusions different from zero. The idea

being is to simultaneously reduce the number

of rules and the corresponding error.

After some experimentation with the genetic

parameters and operator, the following settings

were used throughout: Populations of 20

chromosomes run for 150 generations, the

roulette method for selection with normalized

fitness values, one point crossover was applied

to selected individuals, and mutation per genswas always applied. As the coding of the

chromosomes in this program was realized

directly with integers, uniform mutation was

used. For the second step of membership

function adjustment, another evolutionary

program was applied. The chromosomes

represented the positions of the triangles and

were coded directly as real numbers. A weight

was added to the error produced by the

simulated DC motor in the fitness function to

achieve a smoother curve.

4. Experimental Results

An algorithm is developed to simulate the

drive model with fuzzy logic speed ,and

current controller. A series of experimental

investigation has been carried out to verify thevalidity of the control scheme of the drive

system. The result were obtained at different

operating points, including transient, steadystate, and step changes in speed.

x Set-Up HardwareThe experimental of the proposed controller

was conducted using Digital Signal Processor

(DSP). The system is based on Texas

instrument TMS320C31 and TMS320P14. The

main processor implements the deadbeat

vector torque control algorithm, whereas the

second provides the vector modulation. The

configuration of the experimental system isshown in Fig. (5). The experimental system

Reference

speed

FLC

DC

motor

Armature

voltageMotor

speed

GA

1/s

+

-

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contains single phase rectifier circuit and one

insulated gate bipolar transistor (IGBT). A

personal computer is used for software

development and results visualization. The

sampling period of the control algorithm is 100

Ps. The incremental encoder of 2048 pulsesper revolution is attached to the motor shaft.

Two-phase output signals of the encoder are

preprocessed by hardware circuit and

multiplied by four. The basic sampling period

of speed detection is 0.1 ms. Analog signals

such as phase currents are converted to digital

values using two 12-bit A/D converters whose

conversion time is about 3 Ps. All internal dataof the DSP can be displayed through a four-

channel 12-bit D/A converter. The software is

written in high level language C.

Fig. 5 Experimental setup system

x Steady State Operation

Figure 6 shows samples of the steady state

experimental waveforms at a control voltage

equal to 2.5 volts, with duty ration of 0.5 with

uniform pulse width modulation. This figureshows the carrier voltage and switch gate

pulses.

Figure 7 shows the waveforms of the supply

voltage, supply current, motor voltage and

current during steady state with half load and

Zref= 1500 rpm.

Fig. 6 Run-up behavior for 0.5 of rated load

torque and ref= 1500 r.p.m.

Fig. 7 Steady state behavior for half rated load

torque and ref= 1500 rpm.

x The motor Run up

Figure 8 shows the experimental waveforms

of the motor speed, supply voltage, supply

current, the motor voltage and the motor

current during run up with half rated load

torque at Z ref =1500 rpm.

DCGenerat

or

DC

motor

Drive and protection

Incremental encoderDSP board

A/D

Converter

Incremental

Encoder

interface

D/A

Converter

RS-232C

Gate Pulse Generator

Motor voltage

and current

AC/DC converter

PC

Load

Oscilloscope

Time (msec)

Time (sec)

Time (sec)

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Fig. 8 Run-up behavior for half-rated load

torque and ref= 1500 r.p.m.

x Reference Speed Step ChangeFig 9 shows the speed and the current response

using the control strategy for step up in Z ref

from 1300 rpm to 1800 rpm. It is seen that the

fuzzy PI controller has shown accepted

performance as it eliminates the undesired

steady state error.

Fig. 9 Variation of motor speed and current

due to a step up in reference speed

5. CONCLUSIONS

In this paper, we realized the controller for a

DC motor, which is demanded increasingly

using the fuzzy logic. We present fuzzy

reasoning algorithm to control DC motor inorder to improve the PI controller, which is

hard to get optimum control under the unstable

driving situation or different condition of load

and speed. The simulation and experimental

study clearly indicates the superior

performance of fuzzy control, because it is

inherently adaptive in nature.

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APPENDICE:

The parameters of the designed system are as

follows:

Vs (max) =71 volt rf=2 ohm

Cf=1200 Pf Lf=0.222 HenryA=5 volt Fs=50 Hz.

The test motor is a separately excited DC

motor, 55 volt, 50 watt, 1 Ampere, 3000 rpm.

having the following measured parameters:

rm =10.5 ohm km=0.127volt/(rad/sec)

B=0.0001 N.m./(rad/sec) Rf=550 ohm

Lm=0.06 henery J=0.00015 kg.m2

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