MEM 459 Homework #2
1. Consider the following sampled-data system,
where
T
=06.sec
, Gs s
p() .
=
+
2
05 , Dz z
z
() . .
=+
−
11 002
1
(a) Find the corresponding discrete-time closed-loop transfer function, Yz Rz()/ ()
.
(b) Derive a discrete state model for the system based on the closed-loop transfer
function in (a).
(c) Find an analog state model for G
s
p( ) and then its corresponding discrete state
model.
(d) Find a discrete state model for
D
z()
.
(e) Derive a discrete state model for the discrete-time closed-loop system based on
the subsystem state models in (c) and (d).
(f) Calculate the transfer function from the state model of (e).
(g) How are the states of parts (b) and (e) related?
2. (a) Visit the following two web sites
http://www.engin.umich.edu/class/ctms/simulink/basic/basic.htm
http://www.engin.umich.edu/class/ctms/simulink/examples/motor/motorsim.htm
to gain experience in simulink model building and simulation.
(b) Write a report on what you have learned from the web sites and apply it to build a
simulink simulation diagram for the closed-loop system in Problem#1 and plot the
step response.
1−
−
e
s
Ts
G
s
p()
Dz
(
)
+
−
T
R
s
(
)
Y
s
(
)
004.