ECE 486 Assignment # 2
http://courses.ece.uiuc.edu/ece486/
Issued: January 30 Due: February 6, 2009
Problems:
3 Find all of the models for the mass-spring system shown at right, 40 pts
(a) Block-diagram model.
(b) State space model.
(c) Transfer function.
(d) Pole-zero plot.
k k
mbb
f(t)
y(t)
m
In part (d) take m= 1, b= 2, k= 1, and use a computer!
4 Consider the plant described by the state space model 40 pts
˙x=0 1
1−1x+0
1u , y = [1 0] x.
(a) Find the open-loop transfer function G=Y /U . Is the system BIBO stable?
(b) Consider the output feedback control law of the form u=Ke, with e=r−y,
where ris a reference input. Find the transfer function of the closed loop system,
H=Y/R.
(c) Design Kso that the overshoot to a step input is between 10 and 25% of the final
value. What is the resulting rise time? Settling time? DC gain?
5 Find the closed loop transfer function Y /R for each of the feedback configurations
below, in terms of the transfer functions Gand P.20 pts
(a) ∑YUR G(s) P(s)
+
-
Controller Plant
(b)
∑
YUR
G(s)
P(s)
+
-
Controller
Plant