MODELING WARD LEONARD SPEED CONTROL system

PROJECT CODE:PRJ103BY

SEBASTIAN M.MUTHUSIF17/8228/2004

SUPERVISOR: DR. M. K. MANG’OLIEXAMINER: DR MBUTHIA MWANGI

Introduction

• In Ward Leonard system, a prime mover drives a direct current (DC) generator at a constant speed.

• The armature of the (DC) generator is connected directly to the armature of a DC motor. The DC motor drives the load equipment at an adjustable speed.

• The motor a speed is adjusted by adjusting the output voltage of the generator using rheostat to adjust the excitation current in the field winding .

•To use a proportional action that will reduce steady state error and increase the step response overshoot as the proportional band Kp is reduced.

OBJECTIVES

•Integral action that will eliminate steady state error arising from most causes and as the integral action time T1 is reduced ,increase the step response overshoot

Schematic Diagram of a PID controller

Proportional term

Plot of PV vs time, for three values of Kp (Ki and Kd held constant)

INTEGRAL TERM

Plot of PV vs time for three values of Ki (Kp and Kd held constant)

DERIVATIVE TERM

Plot of and Ki held constant)PV vs time, for three values of Kd (Kp

Schematic diagram of Ward Leonard speed controller

ffff eiR

dtdi

Lf =+

CONSIDERING SECTION 0NE OF THE SCHEMATIC DIAGRAM

NOW CONSIDER SECTION 2

eb=ea -

+

dtLadiaiR aa

dttW )(0T = KTia = FW0(t)+Jd

++

++

=

T

ba

T

aa

T

aa

KKFR

KFLJRS

KJLsse

sW)(

1)()(

2

0

Combing the above equations we shall have

Transfer block diagram of simplified closed loop

G(s) =)1)(1( STST

KKK

mg

mgA

++

)1)(1(1

)1)(1()()(0

STSTKtKKK

STSTKKK

sesW

mg

mgA

mg

mgA

a

+++

++=

01)(2 =

++

++

gm

tgkA

gm

gm

TTkKKK

TTSTT

S

The closed loop transfer function

The open loop transfer function

The characteristic equation

( )gm

tmgA

gm

gm

gm

mgA

in

TTKKKK

TTsTT

S

TTKKK

sesW

++

++

= 1)()()(

2

0

Examination of natural frequency

220

2 nn wSwSK

++ ε=

)1)(1()(

1

1)(

)(

00

0

STSTsZKKKK

TsW

TsW

gm

tgmA

OLL

FBL

+++

=

Index of control

-100

-50

0

50

100

150

0 5 10 15 20 25 30 35 40Ge

ne

rato

r V

olt

ag

e

Field Voltage

DETERMINATION OF KG

y

Work motor input voltages vs. speed

-1500

-1000

-500

0

500

1000

1500

-100 -50 0 50 100 150Spee

d in

rpm

Voltage in volts

DETERMINATION OF KM

Series1Linear (Series1)

DERTERMINATION OF KT

020406080

100120140160

0 500 1000 1500

SPEED IN RPM

VOLT

AGE

IN V

OLTS

YLinear (Y)

DETERMINATIION OF RF

0

5

10

15

20

25

30

35

40

45

0 0.5 1 1.5

CURRENT IN AMPS

VO

LT

AG

E I

N V

OL

TS

YLinear (Y)

-0.015 -0.01 -0.005 0 0.005 0.01-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04Root Locus

Real Axis

Imag

inar

y Ax

is

ROOT LOCUS

-50

-40

-30

-20

-10

0

10

20

30

40

50Ma

gnitu

de (d

B)

Bode Diagram

Frequency (rad/sec)10

-410

-310

-210

-110

0-180

-135

-90

-45

0

System: HPhase Margin (deg): 16.5Delay Margin (sec): 5.42

At frequency (rad/sec): 0.0533Closed Loop Stable? Yes

Phas

e (de

g)

BODE PLOT

UNIT STEP RESPONSE

Step Response

Time (sec)

Ampl

itude

0 100 200 300 400 500 600 700 8000

2

4

6

8

10

12

14

16

System: GFinal Value: 13.9

System: GSettling Time (sec): 399

System: GPeak amplitude: 15.8Overshoot (%): 13.3At time (sec): 260

System: GRise Time (sec): 118

Nyquist Diagram

Real Axis

Imag

inary

Axis

-20 0 20 40 60 80 100 120 140 160-80

-60

-40

-20

0

20

40

60

800 dB

System: HPeak gain (dB): 43.2

Frequency (rad/sec): 2.86e-012

System: HPhase Margin (deg): 16.5Delay Margin (sec): 5.42At frequency (rad/sec): 0.0533Closed Loop Stable? Yes

NYQUIST DIAGRAM

NICHOLS DIAGRAM

Nichols Chart

Open-Loop Phase (deg)

Ope

n-Lo

op G

ain

(dB)

-360 -315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

System: GPeak gain (dB): 23.7

Frequency (rad/sec): 0.00853

System: GPhase Margin (deg): 17.1Delay Margin (sec): 5.42At frequency (rad/sec): 0.055Closed Loop Stable? Yes

CONCLUSION• The integral term in the PI Controller caused the steady state

error to be zero• By use of the PI controller it improved the damping and

reduced the maximum overshoot.

RECOMMENDATION• In this work, voltage control was done using the energy

wasting rheostat to provide a variable voltage.this instead could be done by the use of voltage choppers which uses chopper circuit to provide variable dc voltage from affixed dc supply.

MANY THANKS