Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 5

the closed loop system obtaining the digital controller by the conversion of an
analog to digital controller. In (Wittenmark 1989 ) the development of different anti
windup controllers are explained such as PID and cascade control for digital control
system with constrained input, where the back calculation is implemented similar to
the analog counterparts.
One of the common architectures for MIMO system with constrained inputs is the
design of an output feedback control law that stabilizes the system while reducing
the effects of windup, these control architectures can be applied in continuous and
discrete MIMO systems such as explained in (Rehan et al. 2013 ) where an output
feedback controller is implemented and the gains of the controller are found by
solving the LMI s for continuous time systems. Another anti windup controller

design technique is found in (Saeki and Wada 1996 ) where an output feedback
controller is found by solving the LMI

'

is for continuous MIMO systems with satu-
rated inputs, the controller gains are found by solving the H ∞ optimal LMI

'

s.
With this review about some commons anti windup architectures, in the fol-
lowing sections the development of this kind of novel con

'

guration is shown,

where in the first part of this chapter internal model anti windup architectures are

developed for the SISO continuous and discrete cases, and the second part of the
chapter, some anti windup techniques for MIMO continuous and discrete time
systems are shown with illustrative examples to evince the performance of these
control strategies.

3 Internal Model Anti Windup Control of Continuous
SISO Systems

In this section an anti windup control architecture is developed by implementing an
internal model controller (IMC). Internal model control is a technique that consists
in designing an appropriate controller according to the internal stability of the
system, therefore, as it is proved in this section, this control strategy is convenient
for the design of an antiwindup control architecture, reducing the unwanted effects
yielded by this phenomena and improving the system performance. The anti
windup control strategy shown in this section is developed by feedback the satu-
rated input to the internal model controller so the effects of windup are minimized.
The IMC PID controller synthesis is done by the minimization of the H ∞ norm of
the error signal as explained in (Morari and Za

riou 1989 ; Lee et al. 1998 ; Tu and
Ho 2011 ) when a unit step input is implemented as a reference signal (Cockbum
and Bailey 1991 ; Doyle III 1999 ). With this control technique, the resulting PID
controller has anti windup properties while maintaining its robustness, so this
control strategy is ideal to avoid the unwanted effects yielded by windup. In this
section the derivation of an IMC PID anti windup controller is shown step by step
ensuring the internal stability of the system while reducing the unwanted effects
yielded by the integral action of the PID controller.