Page 195 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

An Underdamped Process 169

u

u

F1auRE 6-27 Choose Ku• Ky. Ky to make the compensated and desired
models identical.

Note that this desired process has the same structure as the origi-
nal process but the parameters, g , { , and co are yet to be speci-
0 0 0
fied. We will specify the values and then find the values of
K:v, K:v,, and Ku that will make them happen (Fig. 6-27). As you
might expect, we would wantthedampingparameter { 0 to be greater
than that of the original process so that there is less ringing. Likewise,
we might want to make the natural frequency co greater than con so
0
that the response would be quicker. To make life simple, g is chosen
0
to be unity.
To find the values of K:v, K:v,, and Ku after having picked values
for , 0 , co , and g , one compares Eqs. (6-11) and (6-12), as in
0
0
2
s y = Kugco!U +(K:vgco! -co!}9+(K:v-gco! -2{corr)s9
(6-13)
s y(s)= g cof,U -cof,y(s)-2{ co sy(s)
2
0 0 0
Comparing the coefficients of U, y, and sy gives the following
expressions.

Kugco! = Korob
K gco -co =-ai
2
2
n
n
D
y