1 (108)

Prévia do material em texto

Problem 4.11 PP
Consider the system shown in Fig., which represents control of the angle of a pendulum that has 
no damping.
(a) What condition must Dc(s) satisfy so that the system can track a ramp reference input with 
constant steady-state error?
(b) For a transfer function Dc(s) that stabilizes the system and satisfies the condition in part(a), 
find the class of disturbances w(t) that the system can reject with zero steady-state error.
Figure Control system
c Control Of Dynamic Systems (7th Edition)
Problem
Consider the system shown in Fig., which represents control of the angle of a pendulum that has 
no damping.
(a) What condition must Dc(s) satisfy so that the system can track a ramp reference input with 
constant steady-state error?
(b) For a transfer function Dc(s) that stabilizes the system and satisfies the condition in part(a), 
find the class of disturbances w(t) that the system can reject with zero steady-state error. 
Figure Control system
j * + a:
(1)
step 2 of 6
The reduced block diagram is shown in Figure 1.
w
Step 3 of 6
From Figure 1, the closed loop transfer function is.
Substitute — !— for r ( s ) in the above equation.
A M _ ! _
W(s]
step 4 of 6
Determine the expression for error signal.
A M=*M- i ’ + A :+ o . ( j ) ' ' i '+ A : + z ) . ( j )
w ( , )