AME 455
Sample EXAM #1/Hwk 5
Due 2/22/02
Problem 1,For the system shown below
(a) Show the system has a zero on the right half plane (i.e,the system is non-minimum
phase) (10pts)
(b) Obtain the time response of the system )(tc due to a unit step input,(20pts)
(c) Sketch )(tc from part (b) versus the time t,(10pts)
Problem 2,For the following second order system
44)(
)(
2
++
+
=
ss
bs
sR
sC
(a) Find the value of b that gives the following system a 5% overshoot to a unit step input,
(15pts)
(b) What is the maximum value of the system output for the unit step input? (10pts)
Problem 3,
(a) Determine the transfer function Y(s)/F(s) between the input force F(t) and the output y(t) of
the following mass-spring system,(20pts)
(b) What is the order of this systems (how many poles does the Y(s)/F(s) have)? (5pts)
(c) What are the energy storage elements corresponding to these orders,(5pts)
Problem 4,You are asked to design a controller for the water level in a water tower of a small
city,Formulate at least one question you would ask from the city engineer,which will give you a
starting point in the design of the controller,(5pts)
2
6
+s
1
4
+s
+
_
)(sR )(sC
1
m
2
m
2
k
1
k
1
c
2
c
)(tF
)(ty
