1 (377)

Prévia do material em texto

Problem 10.07PP
(a) Using root-locus techniques, design a compensator Dc(s) that will place the dominant roots e 
s = -5 ± 5) {corresponding to ojn = 7 rad/sec, ^ = 0.707).
A stick balancer and its corresponding control block diagram are shown in Fig. The control is a
torque applied about the pivot.
(b) Use Bode plotting techniques to design a compensator Dc(s) to meet the following 
specifications;
• Steady-state 6 displacement of less than 0.001 for a constant input torque Td=
• Phase margin > 50°. and
• Closed-loop bandwidth~= 7 rad/sec.
Figure Servomechanism
• Closed-loop bandwidth~= 7 rad/sec.
Figure Servomechanism
1
(j2 -6 4 )
Step-by-step solution
step 1 of 2
To have the cotnpens ated plant root locus go through the pole location 
S = - S ± ^ ; we employ a led con^ensator
Using the angle criterion 
= - 1 8 0
At the closed - loop pole location S = - S + ^ we can write an expression 
for the angle contribution. From the lead network zero, and lead network 
pole 4î . We have.
To fmd the compensator gain, k, we can utilize the magnitude criterion at the 
desired dominant closed - loop pole locations. We find that 
\D ^ { S ) a [S ) \ ^ = - S ± ^ = 'i=t^ k = A7\
Therefore, we have the compensator
' S + 451
Step 2 of 2
We need a lag network in addition to a lead network to get the required .
Let Dcz[S) = '■ ' U o + v 
U - o i + i j U o o o + i j
This compensator will meet our design specifications. The bode plot of
D X s ) a ( s )