Page 89 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

&4 C~apter T~ree

where Eq. (F-19) or the fifth entry in the box was used for the integral. Using
the definition of e gives

fsY + ¥ = g(k+;)e = g( k+;)(s-¥)

Y(rs+ 1 + g~+~))= g~+~)s

If the set point is constant then

- 5
5=...£..
s
and
I)
g k+-
Y- ( s 5c _ gks+I 5c
2
-( ( I)~ s n +(1+ gk)s+ gi s
fs+1+g k+-
s

Questloa 3-8 What can the final value theorem tell us about proportional-only
control?

AniMir Start with
dY
f-+ Y = gk(5- Y)
dt

and apply the Laplace transform to get

fY + ¥ = gk(S- Y)

but

y gk5c 5
so and Y(oct =lim sY = gk c
s(fs+1+gk) •-tO 1+ gk

........_ 3-8 In the development of Eq. (3-22) we set d5/dt = 0 and then looked
at the dynamic behavior for the case of a constant set point. If we take the Laplace
transform of Eq. (3-21) we do not get the Eq. (3-40). Why?