Design and Modeling of Anti Wind Up PID Controllers - Complex System Modelling and Control Through Intelligent Soft Computations - page 31

first part the design of a
PID anti windup controller is derived by adding a back calculation signal to the
controller and converting the anti windup PID controller in a static output feedback
problem and then this problem is solved by LMI

This section is divided in two subsections, where in the

is Another anti windup PID
controller is designed by a H ∞ synthesis where the stability and robustness of the
system is considered, then the closed loop system is robust when unmodeled
dynamics and disturbances are found in the system. Finally, an illustrative example
is explained in the last subsection where the PID anti windup controller for a DC
motor is shown, where the main objective is to maintain a constant nominal angular
velocity by following a desired pro

'

le torque. With the theoretical background and
the illustrative example shown in this section a complete demonstration of a PID
anti windup control strategy for discrete time system is shown where the stability
and robustness condition are met by selecting an appropriate static output feedback
controller.

6.1 PID Anti Windup Controller Design for MIMO Discrete
Time Systems

Consider the PID antiwindup controller shown in Fig. 22 .
Where G(z) is the discrete time transfer matrix, and v is the back calculation
input signal of the anti windup PID controller. Consider the transfer matrix G(z)in
state space form

xk ð þ 1 Þ ¼ Ax ð k Þ B rð u ð k ÞÞ

ð 61 Þ

y ð k Þ ¼ Cx ð k Þ

m
matrix. m > 0 denotes the number of states, n > 0 is the number of inputs, l is the
number of outputs and

m , A is a m m matrix x is a m vector, B is a n m and C is a l

where x 2< < < < <

) is the saturation input. Consider the following anti
windup PID controller given by:

˃ ( ·

Fig. 22 Anti windup PID
controller

+
-

r

G ( z )

+

-

v

PID

Saturation