Page 90 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

Basic Co1cepts i1 Process AIIIJsis 65

Anlwlr By setting dS/dt = 0 we have specified that 5 has been and forever will
be constant. On the other hand, by specifying that 5 is a step change at time zero
we have created an entirely different disturbance to our controlled process, hence
the appearance of the different numerator in Eq. (3-40).

3-3-5 More Block Diagram Algebra and Some
Useful Transfer Functions
The transfer function GP(s) for the process in Eq. (3-33) was

Y=-g-ii=G ii
-rs+l P

G =-g-
P -rs+l

The transfer function for the control algorithm, G c' can be devel-
oped as follows

t
U(t) = ke(t)+ I J due(u)
0
li(s)= kE(s)+ /~•) = (k+~)E(s)

£= ks+l =G
E s c

where G c is the transfer function for the PI controller. The block dia-
gram for a controlled system can be quickly modified from Fig. 3-3, as
in Fig. 3-11.
The overall transfer function relating 5 to Y under closed-loop
control can be derived using the following block diagram algebra:

Eliminate ii to get