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Table 5 Parameters of the
DC motor
Parameter
Value
0.02215 kg m
2
J
m
0.01 kg m
2
J
L
B
L
0.002953 Nm s
R
11.2 Ohms
L
0.1215 H
K
m
0.5161 Nm/A
Nominal speed
1,750 RPM
and
Y
¼
Cx
ð
54
Þ
where x
1
is the angular velocity of the motor, x
2
is the armature current and C is a
2
×
2 identity matrix. The motor parameters are shown in Table
5
.
Solving the LMI (
48
) for P by an optimization algorithm, a matrix F can be
found from M in order to obtain the gain matrices for the PID controller. The gain
matrices of the PID anti windup controller can be obtained by (
55
).
800
0
1
0
F
¼
ð
55
Þ
0
800
0
1
From F the following PID anti windup controller parameters are found
200
0
F
1
¼
0
200
2000
0
F
2
¼
ð
56
Þ
0
2000
1000
0
F
3
¼
0
1000
The gain matrices when there is no anti windup compensation are the following:
100000
0
F
1
¼
0
100000
2000
0
F
2
¼
ð
57
Þ
0
2000
1000
0
F
3
¼
0
1000
The matrix F for the H
∞
controller are given by:
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