Design and Real Time Implementation of Integrated 2009

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International Journal of Electronic Engineering Research

Volume 1 Number 1 (2009) pp. 1325

Research India Publications

http://www.ripublication.com/ijeer.htm

Design and Real Time Implementation of Integrated

Fuzzy Logic Controller for a High

Speed PMDC Motor

S.S. Patil and P. Bhaskar*

Department of Instrumentation Technology, Gulbarga University P. G. Centre,Raichur - 584 133, KA, INDIA

*Corresponding author Email: [email protected]

Abstract

This paper presents the design and implementation of an integrated fuzzy

logic controller (IFLC) for a high-speed permanent magnet DC (PMDC)

motor speed control system. The proposed strategy is intended to improve the

performance of the conventional controller by use of IFLC. The system is

studied for step input with and without load (magnetic) conditions and for

various standard input test commands such as square, triangular, sinusoidal,

and ramp. The experimental implementation demonstrates that IFLC is

particularly effective in speed control of PMDC motor under the above-

mentioned conditions. The graphical results of the proposed controller are

presented and are compared with conventional controllers.

Keywords: Integrated fuzzy logic controller, high speed control, PMDC

motor, analog interface card.

IntroductionThe PMDC motor is one of the most widely used prime movers in industry today.

PMDC motors used in many applications such as steel rolling mills, electric tracking

systems, textile mills -including weaving and spinning, robotic manipulators, defense

etc., require precise speed controllers to perform these tasks. The major problems in

applying the conventional control algorithms in a speed controller are the effects of

non-linearity in a DC motor. The nonlinear characteristics of a DC motor such as

saturation and friction could degrade the performance of conventional controllers [1].

Many advanced model-based control methods such as variable structure control and

model reference adaptive control have been developed to reduce these effects.


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14 S.S. Patil and P. Bhaskar

However, the performance of these methods depends on the accuracy of system

models and parameters. Generally, an accurate nonlinear model of an actual DC

motor is difficult to find, and parameter values obtained from system identification

may be only approximated values.

Emerging intelligent techniques have been developed and extensively used to

improve or to replace conventional control techniques, because these techniques do

not require a precise model. One of the intelligent techniques, fuzzy logic developed

by Lotfi A. Zadeh [2], is applied for controller design in many applications. A fuzzy

logic controller (FLC) was proved analytically to be equivalent to a nonlinear PI

controller, when a nonlinear defuzzification method is used [3].

There are many reports [4-12] on implementation of FLC and IFLC on PC, DSP,

and microcontroller for DC motor speed control. These platforms have their own

advantages and disadvantages. In the proposed work we have implemented integratedfuzzy logic controller, which is a combination of both fuzzy logic and PID controllers

(PIDC) [13], on a PC with a new high-resolution, high-speed 16-bit analog interface

card (AIC) designed for parallel port of PC. This approach is novice and makes the

hardware portable. The performance of the proposed controller is studied at high

speed of 5000 rpm and for various linear and nonlinear input test signals. The linear

input commands include triangular and sinusoidal, the non-linear input includes step

and square, and semi-linear input i.e., ramp.

In this paper, the real time implementation of IFLC for high-speed PMDC motor

is discussed. Heuristic knowledge is applied to define fuzzy membership functions

and rules. The membership functions and rules are modified after initially barrowing

the knowledge from PID controller developed from simple linear model. The processof fuzzification is done based on min-max (MOM) method. The defuzzification is

done using centre of gravity (COG) method.

Integrated Fuzzy Logic ControllerThe basic IFLC configuration is shown in Fig. 1, where FLC is used in a

supplementary role to enhance the conventional PIDC. When the control conditions

change, FLCs are easy to realize and the system behavior can be easily redesigned by

modifying the fuzzy logic rules. One does not have to redesign the existing control

system hardware in order to acquire satisfactory response during the change of load

conditions and appearance of disturbances [14].

r(t)y (t)

e(t)

ce(t)

-cu(t)

++ +

-

u(t)

IFLC

FLC PIDC PMDC

Motor

Figure 1: The block diagram of integrated fuzzy logic controller.


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Design and Real Time Implementation of Integrated Fuzzy 15

Design of PIDC

The block diagram of PIDC is shown in Fig. 2. The PID controller algorithm is

implemented with the following well-known PID difference equation given by:

Vn = Kp (en - en-1) + Ki en T+ Kd/T [(en - 2en-1 + en-2)] (1)

where, Vn is the control action,

en, en-1, and en-2 are the present, previous, and previous to previous

errors respectively,

and Kp, Ki, and Kd are proportional, integral, and derivative constants

respectively and T is the cycle time.

In the present application, the best-tuned Kp, Ki, and Kd values are found to

be equal to 150.0, 352.0, and 11.0 respectively and T is equal to 10ms.

Reference

signal r

-

uPIDC

PIDCPMDC

Motor

Speed y(t)

Figure 2: The block diagram of PID controller.

Design of FLC

Fuzzy logic uses membership functions to define the degree to which crisp physical

values belong to terms in a linguistic variable set [15-18]. The block diagram of a

basic FLC is shown in Fig. 3. The FL controller consists of mainly three basic

components namely the fuzzification interface, fuzzy inference engine (rule base) and

defuzzification stage. The fuzzification stage converts real number input values into

fuzzy values, the fuzzy inference engine processes the input data and computes the

control outputs using IF and THEN rules. These outputs, which are fuzzy values, are

converted into real numbers in the defuzzification stage.

FLC

Fuzzification

Inference

Rule

Base

Defuzzification

Z-1PMDCMotor

r +

+

-

-

e=r-y

yy

ce

uFLC

Figure 3: Block diagram of fuzzy logic controller.


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The two-input-one-output FLC is designed for the present application. The inputs

to the FLC are error e(k) = (set-point speed measured speed)/set-point speed, and

change-in-error ce(k) = (present error previous error) [19]. These two inputs are

defined on a universe of discourse with the nine membership functions (NL, NM, NS,

NZ, ZE, PZ, PS, PM, and PL). The output of the FLC is CU is given as input to the

PMDC motor. The inputs and controlled output of the FLC are described by,

E = e(k) = r(k) y(k) (2)

CE = ce(k) = e(k) e(k-1) (3)

CU = cu(k) (4)

The triangular membership function is used to fuzzify the error and change-in-

error. The error and change-in-errors are mapped between -1.0 and +1.0 on the

universe of discourse. The membership boundaries for error, change-in-error and

control output are shown in Fig. 4. The fuzzy inference engine is the heart of the FLCcomprises both the knowledge base and decision-making logic. The knowledge base

consists of a data base with necessary linguistic variables (rule set) and decision-

making logic used to decide what control action to be taken. The inference process of

the FLC relates the fuzzy state variables e(k) and ce(k) to the fuzzy controlled action

cu(k) with the help of linguistic rules. The decision-making logic uses IF and THEN

rules to pick up appropriate control action for the process. As an example, the

following is a possible control rule for a FLC

IF e(k) is PM and ce(k) is NS, THEN cu(k) is PS

A control rule can be regarded as an implication, Ei, CEi, Ui

The implementation of the inference mechanism in the present study is using

Mamdanis minimum operation Rc, which is given asRc : Ui=1 , nii (5)

Where i, the weighing factor, is the measure of the contribution of the ith

rule to

the fuzzy control action and is expressed as

i = CiCEi (6)

The output of the fuzzy inference engine is a fuzzy set on the output universe of

discourse, so this needs to convert into non-fuzzy (crisp value).

The centre of gravity (COG) method is used for defuzzification. The defuzzified

output for the process is calculated from the equation

i=1, nU (wi).wi

CU = (7)

i=1, nU (wi)Where, n is the number of elements in control output fuzzy set.

wi is the support member value for the ith element

U (wi) is the value of grade of membership function for ith element


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Grade of membership ( )

NL NM NS ZE PS PM PL

0.0 0.1 0.3 0.6 0.8-0.1-0.3-0.6-1.0

1.0

0.5

1.0

PZNZ

-0.8

Grade of membership ( )


0.0 0.1 0.3 0.6 0.8-0.1-0.3-0.6-1.0

1.0

0.5

1.0

PZNZ

-0.8

Grade of membership (

)


0.0 0.05 0.25 0.5 0.75-0.05-0.25-0.5-1.0

1.0

0.5

1.0

PZNZ

-0.75

Figure 4. Triangular membership functions of error, change-in error, and control output.


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Fuzzification stage

The fuzzification stage converts a crisp number (e(k) and ce(k)) into the fuzzy values

within a universe of discourse U. The U is quantified and normalized to [-1, +1] by

scaling factors Ge and Gce. We use the triangle-shaped membership function with

seven terms as shown in Fig. 4. Unlike the traditional digital logic the fuzzy logic

extends the ranges in degree of truth from 0 to100 percent.

Decision logic stage

Basically, the decision logic stage is similar to a rule base, consisting of the fuzzy

control rules, which decide how the FLC works. This stage is the core of the FLC and

is constructed from expert knowledge and experience. With specific reference to the

characteristics of the PMDC motor, we construct the decision-making logic based on

Min-Max operations.

Defuzzification stage

Defuzzification is a mapping from a space of fuzzy control actions defined over an

output universe of discourse into a space of non-fuzzy (crisp) control actions.

Experimental PMDC motor control systemThe block diagram of experimental PMDC motor control system is illustrated in Fig.

5. We have used PMDC motor unit from LUNAR Motors Pvt. Ltd. India. The motor

details are presented in Table I. The system consists of PMDC motor, speed sensor,

analog interface card, personal computer, and driver. An indigenous 16-bit analoginterface card (AIC), designed by the authors [20], is used as the interface for

implementation of digital controller. The card is designed for multi purposes i.e., it

can be used both for measurement, and control. The card mainly consists of a high-

speed four channel 16-bit serial A/D converter AD974 from Analog Devices [21],

and a 16-bit serial D/A converter MAX542 from Maxim [22]. The D/A converter is

operated in bipolar mode in order to drive the motor in both clockwise and anti-clock

wise directions. The control output from PC is a digital data, which is converted into

equivalent analog voltage by D/A converter. The D/A converter is provided with

onboard four channels using analog multiplexer CD4051 to control multiple

parameters. The card is interfaced to PC through parallel port. The AIC is shown in

Fig. 6. The photograph of AIC is shown in Fig. 7. In the present study a PC -IntelPentium-IV processor with 1.7GHz clock frequency, 128MB RAM, 40GB HDD, one

parallel port, and two serial ports is employed for controlling the speed of a PMDC

motor. The PC receives input signals and transmits output control signals through the

AIC. The proposed real-time control algorithms such as PID, FL, and IFL controllers

and other control schemes are implemented on this platform.

The hardware configuration of the experimental system is shown in Fig. 8. The

driver circuit is built with the power transistors to provide enough current to drive the

motor. The control signal from PC does not directly drive the motor. A pre-amplifier

increases the strength of output analog signal to the motor voltage level. It is followed

by a driver circuit consisting of an op-amp (LM356), and Darlington pair (CL100 and


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2N3055) in closed loop. The amplifier included in the closed loop will provide the

compensation for voltage drop across the Darlington pair.

The load is applied in the form of magnetic brake. The magnetic brake works by

means of an aluminum disc, which is mounted on the motor shaft. The aluminum disc

serves two purposes, one as a speed sensor and other as a speed brake. When disc is

rotated between the poles of a magnet, eddy currents form on the disc producing the

effect of frictional load, which in turn retards speed of the motor.

The optical encoder is used as a speed sensor. It converts the speed of the motor

into corresponding frequency with the help of the disc attached to the shaft. The

optical encoder used in this application produces 12 TTL compatible pulses for one

revolution. The frequency of these pulses is further converted into proportional

voltage by a F/V converter, which is constructed using LM2907. Hence, the output

voltage of F/V converter is directly proportional to the speed of the DC motor. Thisproportional voltage is acquired by PC through AIC. The picture of the complete

system is shown in Fig. 9.

PC

AIC

Buffer/

Driver

F/V

Converter

PMDC

Motor

Optical

Encoder

P

arallelPort

IFLC

Algorithms

Figure 5: Block diagram of IFLC based PMDC motor speed control system.

AIC

ADC

DAC MUX

From /ToAnalog Signal

Conditioners10

pinF

RC

Connector

4

4

PC

ParallelPortConnect

or

Figure 6: Block diagram of analog interface card.


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Figure 7: Photographs of analog interface card.

Figure 8: Circuit schematic of PC based PMDC motor speed control system.


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Figure 9: Photographs of experimental setup.

Table I: Specifications of PMDC Motor.

Parameter Unit

Size 35.7mm outer diameter, & 57.0mm

length with 2.3mm shaft diameter

Normal voltage 12 VDC

Power 46.7 Watts

No load speed (Max) 10500 rpm

No load current (Max) 0.270 Amp

Commutation Carbon Brush

Housing material SteelWeight 205 gms

Torque 83.0 gm-cm

Part Number No: CR-505-BS-2835

Experimental results and discussionsThe experimental results of PMDC motor are discussed here for a desired speed (of

5000 RPM), for load (magnetic) conditions, and for various standard input test

commands such as step, square, triangular, sinusoidal, and ramp.


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For desired speed

Fig. 10 shows the step response of PMDC motor for PID, FL, and IFL controllers for

a desired speed of 5000 rpm. The rise time of IFLC is observed to be 0.8 sec and is

better than the FLC, and PIDC.

Response for Step Input without Load

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8

Time in Sec

SpeedinRPM

PIDC

FLC

IFLC

Response for Step Input without Load

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8

Time in Sec

SpeedinRPM

PIDC

FLC

IFLC

Figure 10: Comparison of PIDC, FLC, and IFLC for step input.

Under load condition

Fig. 10 also shows the response of PMDC motor for PID, FL, and IFL controllers for

step input with load variations. The experimental results depict that during the load

conditions the speed corresponding to undershoot and overshoot are less than 2% in

case of PID and 5-6% in case of FLC and IFLC and the settling times are less than 2sec for PIDC and less than 2.6 sec for IFLC and FLC. Therefore the PIDC is the best

controller for load variations. Where as the responses of FL and IFL controllers are

almost similar for load variations.

For various standard input test commands Square

A square input command is applied to all the controllers. Fig. 11 shows the response

of PMDC motor for PID, FL, and IFL controllers for square input command. The rise

time of IFLC is observed to be better than the FLC, and PIDC. It is clear from the plot

that IFLCs trail is close to the input command than the other two.

Triangular and Sinusoidal

Triangular and sinusoidal input commands are applied to all the controllers. Fig. 12

shows the response of PMDC motor for PID, FL, and IFL controllers for triangular

and sinusoidal input commands respectively. In both the cases it is found that PIDC

and IFLCs trails are closer to the input command than the FLC.

Ramp

The performance of the controllers is also studied for a semi-linear input command

such as ramp. The responses of all three controllers are presented in Fig. 13. Here,

PID and IFLC follow the input command in the linear incrementing region of the


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input. But during the trailing region of the waveform FLC and IFLC follow the input

closely than the PIDC.

Response for Square Input

0

1000

2000

3000

4000

5000

6000

0 5 10 15 20 25 30

Time in Sec

Spe

edinRPM

PIDC

FLC

IFLC

Figure 11. Comparison of PIDC, FLC, and IFLC for square input.

Response for Triangular Input

0

1000

2000

3000

4000

5000

6000

0 20 40 60

Time in Sec

SpeedinRPM

PIDC

FLC

IFLC

Response for Sine Input

0

1000

2000

3000

4000

5000

0 10 20 30 40

Time in Sec

SpeedinRPM

PIDC

FLC

IFLC

Figure 12: Responses of PIDC, FLC, and IFLC for (a) triangular input, (b) sine input.


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Response for Ramp Input

0

1000

2000

3000

4000

5000

6000

0 5 10 15 20 25 30

Time in Sec

SpeedinRPM

PIDC

FLC

IFLC

Figure 13: Comparison of PIDC, FLC, and IFLC for ramp input.

Conclusions

By studying the response of PID, FL, and IFL controllers for various inputs, it isconcluded that for non-linear inputs (step and square) the FL and IFL controllers

perform better than the conventional PID controller. Where as for linear inputs

(triangular and sine) PID and IFL controllers are better than FLC. The above

statements can be confirmed by observing the response of ramp input (raising part of

the wave linear and trailing part is non-linear). PIDC response is best for linear

portion of the wave where as it has poor response for non-linear portion of the wave

(changing from max to zero). But for both the cases IFL responds quicker than the

other controller as it contains both the controllers.

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Design and Real Time Implementation of Integrated 2009

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