Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 39

the system performances are improved due to the filter included in the additional

loop reduces the integral action when the input of the system saturates. Similar to
the continuous time counterpart, an internal model controller (IMC) is implemented
with an additional loop which includes a

filter as a compensator while the internal
stability and robustness of the system are ensured to guarantee an appropriate
system performance.
In the case of the design of an anti windup controller for continuous and discrete
time MIMO systems, an anti windup compensation approach is implemented where
the saturated and non saturated signals are added by a feedback loop to the PID
controller to eliminate the windup phenomena when the input of the system is
saturated, as occurs in SISO systems. For continuous and discrete time systems, an
anti windup PID controller by static output feedback was implemented, converting
the PID controller into an static output feedback law and adding the difference of
the saturated and non saturated input to compensate the windup effects. The
advantages of the PID anti windup controller for continuous time systems, is that
the system performance is not deteriorated by the in uence of windup when the

input is constrained or saturated, improving the controller action and preventing a
high overshoot, settling time and other performance properties. In the case of the
anti windup control of discrete time systems, the same advantages and properties
are proved theoretically similar as the continuous time case; the system perfor-
mance is improved by the addition of the difference of the saturated and no satu-
rated signal that improves the system performance avoiding the deterioration of the
system output by decreasing the integral action when the input of the system are
constrained or saturated.

fl

8 Conclusions

In this chapter some anti windup control strategies for SISO and MIMO system for
discrete and continuous time models are shown. In the SISO cases an internal
model anti windup PID controller is implemented by a back calculation algorithm
in order to suppress the unwanted effects yielded by windup, when the system input
is saturated and the integral action of the PID controller is increased. It was proved
that the system performance is improved by the implementation of the back cal-
culation loop that includes a compensator

filter. The performance of the system with
anti windup and no anti windup compensation was tested, and it was proved that in
the first case the system performance is not deteriorated producing a smaller

overshoot and settling time reducing the integral action in the discrete and con-
tinuous time SISO systems.
In the MIMO cases, a continuous and discrete time anti windup PID controllers
are implemented in order to eliminates the performance deterioration caused by the
integral action of the controller when the input of the system is saturated. It is
proved that in the discrete and continuous time cases, the PID controllers can be
achieved by a static output feedback control law (SOF) and by a H ∞ controller