Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 27

4 : 08250 00

10 8 F ¼ ð 58 Þ

0 4 : 0825 0 0

and the following gain matrices for the H ∞ anti windup controllers are given by:

4 : 0825 0

10 8 F 1 ¼

0 4 : 0825

2000 0

F 2 ¼ ð 59 Þ

0 2000

1000 0

F 3 ¼

0 1000

and the compensator gain ʔ is given by:

20
02

D ¼ ð 60 Þ

The main idea of this example is to keep the nominal angular velocity(1,750
RPM) or (183.26 rad/s) while applying a disturbance torque of (100 Nm) at 0 s, so
the anti windup PID controller must be able to keep this velocity even when an
external disturbance is applied on the model.
In Fig. 18 the angular velocity of the DC motor in three cases; with anti windup,
no anti windup and H ∞ anti windup PID controllers are shown; where in the H ∞
and standard static feedback anti windup controller better results were obtained with
smaller settling time, smaller steady state error and smaller overshoot in comparison
when there is not anti windup compensation. For these reasons, the anti windup
controllers and compensator are better than the uncompensated controller version.

Fig. 18 Angular velocities with AWC, H ∞ and no AWC