Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 20

In the following sections, the design and analysis of anti windup techniques for
discrete and continuous time MIMO systems is shown, where different approaches
are implemented in order to improve the control system performance when satu-
ration or constrained inputs are present in the system. Generally, the design of anti
windup control strategies for MIMO systems are more dif

cult than the anti windup
control of SISO system, for this reason, the solution of this problem is done by
static output feedback control law design, where MIMO PID controllers are
designed in the continuous and discrete time cases.
It will be proved that as similar to the SISO system cases, the modeling and
design of effective anti windup control techniques is possible improving the system
performance when some kind of compensation is added to the controller.

5 Anti Windup Control of Continuous MIMO Systems
by Static Output Feedback (SOF)

In this subsection the design of an anti windup PID controller for continuous time
MIMO system is derived based on static output feedback (SOF) controller. This
work is based on the solution of the speci ed linear matrix inequalities (Cao et al.

2002 ;Wuetal. 2005 ; Rehan et al. 2013 ) where a static output feedback controller is
de

ned in order to improve the anti windup characteristics of this MIMO controller
(Neto and Kucera 1991 ; Henrion et al. 1999 ; Fujimori 2004 ; He and Wang 2006 ).
A PID control law is obtained by solving the required LMI nd the

PID controller gains. The controller gains are found by two static output feedback
solutions, by solving an standard LMI and a H ∞ problem. With these two control
strategies it is possible to

' is in order to

find appropriate controller gains for the PID anti windup
controller taking in count the saturation nonlinearity.
In order to design the anti windup PID controller it is necessary to model the
saturation nonlinearity by a describing function approach (Taylor and O

Donnell
1990 ) in order to deal with the nonlinearities added to the system by the actuators
saturation.
The intention of this control approach is to design an ef

'

cient anti windup
controller system for MIMO continuous time systems when the inputs are con-
strained or saturated. It is proved that solving the system constraints by LMI

sin
order to obtain a stable PID control law, the addition of anti windup compensation
similar as the SISO time systems, improves the system performance and avoids the
deterioration of the output signal. In the following subsections the design of an anti
windup controller is explained in detail, and in order to test the system performance
an illustrative example of the stabilization and control of a DC motor is evinced.

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