1 (160)

Prévia do material em texto

Problem 5.24PP
Suppose the unity feedback system of Fig. has an open-loop plant given by G(s) = 1/s2. Design e 
lead compensation Dc(s) = to be added in set 
of the closed-loop system are located at s = -2 ± 2j.
Figure Unity feedback system
- • a»)
Step-by-step solution
_
Step 1 of 2
The loop transfer function of the system with lead compensation is.
G W £ > , W - A r ( ^ ) ( l )
The characteristic equation of the system is,
l + G ( j)D c W = 0 
„ j f f i ± £ ¥ ' l = o
5* (5 + p ) + ( 5 + z ) » 0 
s * * p s * * K s * K z ^ 0
Step 2 of 2 ^
The dominant poles are at s = - 2 ± J 2 .
Assume a real pole at j s —2-
The characteristic equation of the system with dominant poles at s = —2 ± j2 and a real pole at 
5 = - 2 is.
( i + 2 ) [ ( i+ 2 ) ' + 2’ ] = 0
(j + 2)(j *+45 + 8) = 0 
j ’ + 6 s ‘ + I f a + I6 = 0
Compare the characteristic equation of the system with the desired characteristic equation.
p = 6
K ^ 1 6
Kz = 16
So.
Z »1
s designed lead compensator