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Design and Modeling of Anti Wind Up
PID Controllers
Ahmad Taher Azar and Fernando E. Serrano
Abstract In this chapter several anti windup control strategies for SISO and
MIMO systems are proposed to diminish or eliminate the unwanted effects pro-
duced by this phenomena, when it occurs in PI or PID controllers. Windup is a
phenomena found in PI and PID controllers due to the increase in the integral action
when the input of the system is saturated according to the actuator limits. As it is
known, the actuators have physical limits, for this reason, the input of the controller
must be saturated in order to avoid damages. When a PI or PID controller saturates,
the integral part of the controller increases its magnitude producing performance
deterioration or even instability. In this chapter several anti windup controllers are
proposed to eliminate the effects yielded by this phenomena. The
first part of the
chapter is devoted to explain classical anti windup architectures implemented in
SISO and MIMO systems. Then in the second part of the chapter, the development
of an anti windup controller for SISO systems is shown based on the approximation
of the saturation model. The derivation of PID SISO (single input single output)
anti windup controllers for continuous and discrete time systems is implemented
adding an anti windup compensator in the feedback loop, so the unwanted effects
are eliminated and the system performance is improved. Some illustrative examples
are shown to test and compare the performance of the proposed techniques. In the
third part of this chapter, the derivation of a suitable anti windup PID control
architecture is shown for MIMO (multiple input multiple output) continuous and
discrete time systems. These strategies consist in
finding the controller parameters
by static output feedback (SOF) solving the necessary linear matrix inequalities
(LMI
s) by an appropriate anti windup control scheme. In order to obtain the
control gains and parameters, the saturation is modeled with describing functions
for the continuous time case and a suitable model to deal with this nonlinearity in
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