16.413 Linear Feedback Systems
Instructor:
Charles Thompson, Professor and Co-Director CACT
Office: Kitson 312
Phone: 508-934-3360
Email: charles_thompson2@uml.edu
Web: http:/morse.uml.edu/~thompson
FTP: ftp:/morse.uml.edu/pub/16.413
Textbooks:
Modern Co
16.413 Problem Selected problems
B-4.1. A thermometer requires 1 min to indicate 98% of the response to a step input. Assuming
the thermometer to be a rst-order system
(a) Find the time constant.
1
1
Y (s)
= H(s) =
; X(s) =
Ts + 1
s
X(s)
y(t) = (1 et/T )u
-1-
Department of Electrical and Computer Engineering
University of Massachusetts Lowell
16.413 SOLUTION Problem Set #3
1. The steady-state error in the velocity of a system is dened as
dx dy
t dt
dt
limit
where x is the input and y is the output. Find
University of Massachusetts Lowell
Department of Electrical and Computer Engineering
16.413 Linear Feedback
Problem set 3
Posted: 10-18-2002
Due: 10-23-2002
1. The steady-state error in the velocity of a system is dened as
dx dy
t dt
dt
limit
where x i
University of Massachusetts Lowell
Department of Electrical and Computer Engineering
16.413 Linear Feedback
Problem set 2
Posted: 9-25-2002
Due: 10-2-2002
FIGURE 1
FIGURE 2
(A)
(B)
M
B0
U0
U0
U
B0
V
K0
FIGURE 3
M
M
UI
U1
K
U1
b
K1
M
L
U0
M
U1
1.In Figure
University of Massachusetts Lowell
Department of Electrical and Computer Engineering
16.413 Linear Feedback
Posted: 9-11-2002
Due: 9-18-2002
1. Find the Laplace transform of the following functions. Please denote their regions of
convergence.
a.
x(t) = 3(
16.413 Problem Set #2
Due: 2-23-2000
I. Consider the signal ow graphs below. Determine C(s)/R(s).
(a)
G.
(8) Dene .5
0) Dene a
(c)Findthematrix AandthematrixB 3. Consider the system
Find Y(s)/U(s).
4. Verify that 1&sz and x3 can be determined using a si
_ 16.413
PS #4
1. For a unit step input a unity gain feedback control system whose openloop transfer
function is
G(s)=1r'cfw_s(s+1) .
(a) Determine the rise time
(b) Determine the peak-time
(c) The maximum overshoot
(d) Settling time
2. Obtain the impulse
StlI-q,
16.413
PS #5
l. The open loop transfer functions for three unity feedback control systems are given.
Compare the unit step, unit-impulse and ramp responses. Which of systems is the best
with respect to the speed of response and maximum overshoot i
16-413 Problem set two
Date: 2f9f00
Due: 2f16f00
Problem one:
Examine the following arrangements of the mechanical elements and obtain the electrical
network model. The mass is given by M, the mechanical compliance is given by C. The
losses are given by f
Department of Electrical and Computer Engineering
University of Massachusetts Lowell
16.413 Problem Set #2
Posted: 2-24-2001
Due: 2-28-2001
1. Consider the mechanical system. The displacement of the masses are given by x and applied
force by the variable
University of Massachusetts Lowell
Department of Electrical and Computer Engineering
16.413 Linear Feedback
Posted: 2-17-2001
Due: 2-21-2001
1. Find the Laplace transform of the following functions. Please denote their regions of convergence.
a. x(t) = t
University of Massachusetts Lowell
Department of Electrical and Computer Engineering
16.413 Linear Feedback
Posted: 2-17-2001
Due: 2-21-2001
1. Find the Laplace transform of the following functions. Please denote their regions of convergence.
a. x(t) = t
-1-
Department of Electrical and Computer Engineering
University of Massachusetts Lowell
16.413 Problem Set #5
Date: 11-1-2006
1. The steady-state error in the velocity of a system is dened as
dx dy
t dt
dt
limit
where x is the input and y is the outpu
Department of Electrical and Computer Engineering
University of Massachusetts Lowell
16.413 Problem Set #4
Posted:10-5-2006
Due: 10-11-2006
1. Consider the block diagram below.
H3(s)
X(s)
G1(s)
G2(s)
Y (s)
H1(s)
H2(s)
(a) Evaluate the signal ow graph
(b)
Department of Electrical and Computer Engineering
University of Massachusetts Lowell
16.413 Problem Set #2
Posted: 9-20-2006
Due: 9-27-2006
1. Consider the mechanical system. The displacement of the masses are given by x and applied
force by the variable
University of Massachusetts Lowell
Department of Electrical and Computer Engineering
16.413 Linear Feedback
Due: 9-19-2006
1. Find the Laplace transform of the following functions. Please denote their regions of
convergence.
a. x(t) = t 3 e6t u(t) + tu(t)
,m_
/ MASS, Lowell ECE 16.364 Engineering Mathematics Fall, 2011
Exam "-3
Name:
In every problem, you must show work to get full (or any) credits.
Problem One:
a) Using the Ratio Test Prove whether the series converges or diverges.
Sax-2r)"
= (11-1)! (NU
ECE 16.413 Linear Feedback Systems
Instructor: Ahmed Abu-Hajar, Ph.D.
Office: ENB 118-B
Phone: 978-934-3572
Email: Ahmed_AbuHajar@uml.edu
Web: TBA
Office Hours: M & W 12:00-1:00 pm
T & TH 12:00-2:00 pm.
Friday: By appointment.
Textbooks:
Modern Control E
ASS, Lowell ECE 16.364 Engineering Mathematics Fall, 2011
Exam ll-A
Name: (6
1-
In every problem, you must show work to get full (or any) credits.
Problem One:
3) Using the Ratio Test Prove whether the series converges or diverges.
n4 \ Q n 4< A .
EMU (M
UMASS,LowellECE16.413LinearFeedbackSystemFall,2011
PracticeExam#2
Time:75Minutes
Name:_
Problem#1
ForthefollowingTransferfunction:
a) FindtheFrequencyResponseG(j)
b) Find|G(j)|andphaseofG(j).
c) WhatistheDCgain
d) Iftheinputsignalis10cos(100t),solvefort
UMASS,LowellECE16.413LinearFeedbackSystemFall,2011
Quiz#4
Time10Minutes
R2
Name:_Key_
a) Ananalogcontrollerisshown,findthetransferfunctionG(s)
R1
+
Vi
C
+
+
Vo
b) Findthedifferentialequationthatdescribestheoutputasafunctionoftheinput.
c) Whatistheimpulser