Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 6

3.1 IMC PID Anti Windup Controller for Continuous Time
SISO Systems

The anti windup controller architecture implemented in this section is de ned in

Fig. 2 and it is based on the controller architecture explained in (Saeki and Wada
1996 ) where a compensator is added to the feedback loop from the saturation input
of the system. In Fig. 2 the description of each block is the following; G p is is the
plant transfer function that is represented by a first order plus time delay model

(FOPTD), G c is is the internal model PID controller and R(s) is the anti windup
compensator filter.

In order to obtain a simpli ed model of the saturation nonlinearity, it is nec-

essary to represent this model by the following equation (Saeki and Wada 1996 ):

¼ ða þ bD / Þ U
D /

U

\

1

ð 1 Þ

a þ b ¼ 1

a b ¼ a

Where the saturation nonlinearity is considered to be in the interval [a, 1]. The filter

R(s)isde ned by a first order system as described below:

1

R ð s Þ ¼ ð 2 Þ

a 1 s þ a 0

Then the equivalent transfer function of the nonlinearity ( 1 ) and the filter ( 2 ),

depicted in Fig. 2 , is given as G sat is as shown in Fig. 3

a þ bD /

G sat ð s Þ ¼ ð 3 Þ

1 R ð s Þða þ bD / Þ

d

~

r

u u

+ + +

G c ( s ) G p ( s )

+

- +

Saturation

R ( s )

Fig. 2 Anti windup controller architecture