ECE 442/542
Homework 1
Spring 2014
Due Date: January 30, 2014
1. Derive a simplified transfer function model, G[s], of an armature controlled DC motor. A
discussion of this process is available in many locations, e.g., Problem 6.28 in (Sc), Example 2.5 in
ECE 442/542
Homework 3
Spring 2014
Due Date: February 27, 2014
1. For the given transfer function and the different regions of convergence (ROC), find the Inverse
z-Transform and state whether the time-domain sequence is bounded.
(a) [] =
(b)
(c)
2
(0.5)(
ECE 442/542
Homework 5
Spring 2014
Due Date: April 3, 2014
1. Create two-pole system transfer functions designed to meet the requirements indicated in each
part below.
(a) Assume a sample period of T = 0.02 seconds, a DC gain of 1, a zero at the origin, a
ECE 442/542
Homework 6
Due Date: April 10, 2014
1. Assume a system, [] =
4
,
0.75
Spring 2014
and a controller, [] = , connected in the conventional
negative unity, output feedback configuration.
(a) Find the range of gain, , for the system to be closed-l
ECE 442/542 Exam 2 March 08, 2017
Name: 3 Q i Mi" 2:3 3"er
l. (25 pts) (a) Find an exact statespace, ZeroOrder Hold (ZOH) equivalent of the given
system. Keep the system matrix, (I), and the input matrix, F, in terms of the sample
period, T:
(b) Find a re
ECE 442/542 Exam 3 April 12, 2017
Name:
1. (25 pts.) (a) Shade the region in the complex z-plane that satises the following
transient performance specications associated with a twopole system.
i) A peak time, tp, between 5 sample periods and 10 sample per
MATLAB Homework #2.
MATLAB Homework #2a: m-file, diary, figures.
% hmwk2a.m
%
% M-file to execute the commands needed for Homework #2 ECE 442/542.
%
zeta=[0.2,0.4,0.7]; % Define a vector containing the three damping ratios.
wn=[1.0,2.0,4.0]; % Define a ve
ECE 4421542
Name:
Exam 1
SO\,+;
February 1l,20 11
Code No:
0-3
5
K(s+a)(s+b)
.
1. (25 pts.) For the system G [s] = ; ;design a PID controller, D [s] =
;,
;
,i.e.,
S
find values for K, a, and b, to place closed-loop system poles that correspond to a peak
t
4. (25 pts) Find a second-order transfer function that has a finite zero at z = 0.4, a DC
gain of 0.5, and has poles that yield st 1% settling time of 5 seconds and a peak time of
0.7 seconds. Let the sample period be T = 0.1 second.
ECE 4421542
Name:
Exam 1
February 12,2010
s~(ut/oht
K(s+a)(s+b)
4
1. (25 pts.) For the system G[s] = ; ;i design a PID controller, D [s] =
i;
; ,
S
'
.
.
i.e., find values for K, a, b ,to place closed-loop system poles such that the 1% settling
time is ap
h,
1
n
3. (25 pts.) (a) Find y(k), if Y[z] =
0.252
z2 - 0.72 + 0.06 '
(b) Find W[z], if w(k) = 2(0.8)~ 3k2. (You may assume T=l. You do not need
+
to simplify your answer by combining individual terms.)
Amplitude
Exam 3
ECE 4421542
Name:
April 15,201 1
SoLk*t;o
ns
1. (25 pts.) Find a controller, D[s], and a sample period, T, in the first phases of an
emulation-based, digital controller design. However, do not And D[z] ! Assume
C [s] = -and D[s] is designed to stab
ECE 4421542
Name:
Exam 3
April 16,2010
S&~;OVLS
1. (25 pts.) Find a controller, D[s], and a sample period, T, in the first phases of an
emulation-based, digital controller design. However, do not find D[z]! Assume
(S 4,
,the time to peak is approximately
ECE 442/542
Homework 2
Spring 2014
Due Date: February 6, 2014
find [] =
[]
.
[]
1. (a) Find the transfer function description associated with the following difference equation, i.e.,
This difference equation could be associated with the dynamics of a
serv
ECE 442/542
Homework 4
Spring 2014
Due Date: March 6, 2014
1. Consider a normalized (frequency and gain) model of a DC motor, [ ]
. Suppose a
closed-loop bandwidth of = 10 radians/second is desired.
(a) Explain why a sample period of T = 0.02 seconds is a
ECE 442/542
Homework 7
Spring 2014
Due Date: May 1, 2014
1. Without finding exact values for the breakaway or re-entry points, produce a rough Root Locus
sketch of the following systems by computing the asymptote angles and the centroid of the
asymptote a