Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 28

Fig. 19 Armature current i a

It is clear when an anti windup compensator is implemented the performances is
improved signi cantly, this means, that the settling time, steady state error and

overshoot are smaller than the performance indexes of the uncompensated system.
In Fig. 19 the armature current i a is depicted for the three cases of static output
feedback (SOF) controller. It can be noticed that even than in the standard and H ∞
SOF the armature current is greater in comparison when no compensation is
implemented in the SOF controller. These results are obtained due to the better
performance of the standard and H ∞ SOF in comparison with the uncompensated
controller, so more control effort is necessary in order to obtain an acceptable
performance.
In Fig. 20 the input voltage of the DC motor (

(field voltage) is depicted where the
input voltage of the non compensated systems increases to higher values than the
compensated control systems. The input voltage for the uncompensated controller
raises to higher values due to the windup effects that increases the integral action,
similar to the SISO case, deteriorating the system performance.
The anti windup PID compensator by SOF improves the system response and
performance signi cantly due to the compensator added to the MIMO PID con-

troller, The windup effects are suppressed by the compensator action, reducing the
integral action when the input of the system is saturated.
Finally, in Fig. 21 the mechanical torque of the DC motor is depicted where this
variable reaches the

final value of 100 Nm, which is the value of the disturbance
input applied to the motor at 0 s while keeping the desired nominal velocity.
In this section the design of an anti windup PID controller for MIMO system by
standard and H ∞ SOF is explained in order to obtain a suitable controller that
eliminates the unwanted effects yielded by windup. As it occurs in the SISO case,
the windup phenomena occurs when the input of the system is saturated increasing
the integrator action, this effects damage the system performance, specially, it yields
higher overshoot and longer settling times.