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PID Controller
System & Control Engineering Lab.
School of Mechanical Engineering
PID Controller
2
PID Controller via ZN step response
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PID Controller via Ziegler-Nichol(ZN) step response
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PID Controller via ZN frequency response
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PID Controller design
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PID Controller designOpen-loop TF-Bode diagram
7
-150
-100
-50
0
50
Magnitu
de (
dB
)
System: sys
Gain Margin (dB): 26
At frequency (rad/sec): 2
Closed Loop Stable? Yes
10-2
10-1
100
101
102
-270
-225
-180
-135
-90
System: sys
Frequency (rad/sec): 2
Phase (deg): -180
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
26
200 020log 26 dB 10 19.95K K= → = =
0 0
2 at 2 rad/secT T
= = → =
PID Controller design
8
0
0
0
0.6 9.976
0.5 =1.57
0.125 0.3927
p
i
d
K K
T T
T T
= =
=
= =
9.976
6.354
9.976(0.3927) 3.917
P
P
i
P d
P K
KI
T
D K T
= =
= =
= = =
PID parameters for Simulink/MATLAB
PID Controller design
90 2 4 6 8 10 12 14 16 18 20
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Time,(sec)
c(t
), O
utp
ut
response
P Controller
10
PI Controller
11
PD Controller
12
13
DC motorSpeed control
Armature Controlled DC motor
Field Controlled DC motor
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DC motorPosition control
Armature Controlled DC motor
Field Controlled DC motor
Speed control for Armature controlled DC motor
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Speed control for Armature controlled DC motor
16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
2
4
6
8
10
12
14
16
18
Time, (sec)
Speed r
esponse,
RP
M
Unit-Step Response
System type = 0
PI-Speed control for Armature controlled DC motor
17
PI parameters for Simulink/MATLAB
0.05
0.055
0.01
P
P
i
P K
KI
T
= =
= = =
Speed control for Armature controlled DC motor
18
0 0.05 0.1 0.15 0.2 0.25 0.30
0.2
0.4
0.6
0.8
1
1.2
X: 0.05072
Y: 1.06
Time, (sec)
Speed r
esponse,
RP
M
Unit-Step Response
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.005
0.01
0.015
Time, (sec)
Err
or
sig
nal
%Overshoot = 6%, Steady state error for unit-ramp input = 0.012
Settling time = 0.08 sec
Position control for Armature controlled DC motor
19Td =0
System type = 1
Position control for Armature controlled DC motor
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Position control for Armature controlled DC motor
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
Time, (sec)
Positio
n r
esponse,
(degre
e)
Unit-Step Response
1; 0; 0PP P d
i
KP K I D K T
T= = = = = =
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.01
0.02
0.03
0.04
0.05
0.06
Time, (sec)
Err
or
sig
nal
Steady state error for unit-ramp input = 0.06
