Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 9

series expansion as shown in (Shamsuzzoha and Lee 2007 ). The IMC gain and
constants are obtained as follow (Lee et al. 1998 ):

K c ¼ f ð 0 Þ

f

ð 0 Þ

s i ¼

ð Þ ð 15 Þ

f 0

f

ð 0 Þ

s d ¼

2f ð 0 Þ

The IMC anti windup controller gains are given in detail in Appendix 1, so the
reader can refer to this section for detailed information. The function f and its deriv-
atives are de

ned in this section according to the formulas given in (Lee et al. 1998 ).
With the derivation and design of an IMC anti windup controller for SISO
system, the internal stability of the system while suppressing the unwanted effects
of windup is ensured with the addition of a feedback loop which includes the
saturated input signal through a filter that improves the system performance when

the input is saturated and windup occurs in the PID controller. As it is veri

ed later

this control strategy is ef cient when saturation occurs in the model, as it is noticed,

this strategy is based on the implementation of a saturation model that includes all
the properties of this nonlinearity. In the following section an illustrative and
comparative example is done in order to test the performance of the IMC anti
windup controller, the conclusions of this section are shown in order to compare the
system performance with anti windup compensation and no compensation.

3.2 Example 1

In this subsection an illustrative example of the internal model anti windup con-
troller for SISO continuous time system is shown. Consider the following FOPTD
system:

e 0 : 0000001s
0

G p ð s Þ ¼ ð 16 Þ

: 001s þ 1

and the following parameters for the anti windup filter and saturation model as

shown in Table 1 .
Now implementing the formulae found in Appendix 1, the following IMC
parameters are found for the IMC PID controller with anti windup compensation
and when there is no anti windup compensation. These parameters are shown in
Table 2 .
The system response of the IMC anti windup controller is depicted in Fig. 4 .
It can be noticed that when the AWC is implemented the system response has
almost no overshoot and a small settling time in comparison when no AWC is