modeling ward leonard speed control...
TRANSCRIPT
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