Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 2

the discrete time case. Finally a discussion and conclusions sections are shown in
this chapter to analyze the advantages and other characteristics of the proposed
control algorithms explained in this work.

1 Introduction

In this chapter several control architectures of anti windup controllers are shown for
the stabilization of SISO and MIMO systems in their discrete and continuous forms.
Windup is a phenomena found in different kind of systems, when a PI or PID
controller is implemented, produced by the integral action of the controller. This
phenomenon occurs when the input of the system saturates increasing the magni-
tude of the integrator producing unwanted effects on the system like high overshoot
and long settling time. There are several techniques and architectures found in
literature to deal with this problem, for the SISO and MIMO cases, usually by
suppressing the integral action of the PI or PID controller with input saturation.
For the SISO continuous case, different anti windup controller architectures are
found in literature such as the tracking anti windup, conditional integration and
limited integrator (Bohn and Atherton 1995 ), these are some of the classical anti
windup control architectures implemented to eliminate the unwanted effects of
windup. These classical techniques usually consist in adding an extra feedback loop
to the controller from the saturated output so the effects of windup can be cancelled
by implementing these control models. The back calculation techniques is a

common anti windup control architecture that ensures the system stability when the
input is saturated, improving the system performance by producing smaller over-
shoot and acceptable settling time (Tu and Ho 2011 ). One issue that makes it
dif

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cult to obtain a suitable anti windup control architecture is the nonlinearity
introduced by the actuator saturation, one way to design an appropriate control
system when this nonlinearity is found, is the introduction of a saturation model
which includes all the properties of this nonlinearity (Saeki and Wada 1996 ). This
consideration is very important in the design of anti windup controllers for SISO
and MIMO systems in the continuous and discrete time cases respectively, allowing
the development of appropriate controllers including a saturation model.
In the case of SISO discrete system, there are similar anti windup control
techniques as the continuous counterpart that can be implemented when a dis-
cretized model of the system is available. One of the control architectures that is
very popular in the control community is the back calculation model, where the
saturated signal is feedback to the controller integrator in order to suppress the
windup effects yielded by the integrator action (Wittenmark 1989 ). Apart from this
anti windup control architecture for discrete time SISO systems, the anti windup
controller design by the frequency response of the model is usually implemented