me352_hw5 - (b Which system would have the smallest...

1
ME 352
System Dynamics and Control
Homework #5
Due: Fri 15.04.2011
[1]. Determine the type of the following unity-feedback systems for which the forward-path transfer functions are
given.
(a)
) 8 1 )( 4 1 )( 1 (
) (
s s s
K
s G
+ + +
=
(b)
) 3 )( 2 (
) 1 ( 10
) (
+ +
+
=
s s s
s
s G
(c)
) 5 5 (
) 1 ( 10
) (
2 3
+ +
+
=
s s s
s
s G
(d)
) 20 1 )( 10 1 )( 1 (
10
) (
2 . 0
s s s
e
s G
s
+ + +
=
-
[2]. For the unity-feedback control systems described in Problem 1, determine the steady-state error for a unit-step
input, a unit-ramp input and a parabolic input
) ( 1 ) 2 (
2
t t
.
[3]. Consider a system with the plant transfer function
[ ]
) 1 ( 1 ) ( + = s s s G
. You wish to add a dynamic controller so
that ω
n
=2 rad/s and ζ≥ 0.5. The following dynamic controllers have been proposed:
(i)
8
3
5 ) (
+
+
=
s
s
s D
(ii)
) 01 . 0 )( 8 (
) 1 . 0 )( 3 (
5 ) (
+ +
+ +
=
s s
s s
s D
(a) Using MATLAB, compare the resulting transient and steady-state responses to reference step inputs for each
controller choice. Which controller is best for the smallest rise time and smallest overshoot?