Concordia University
ELEC372 Fundamentals of Control Systems
Homework #5
Professor Amir G. Aghdam
1. The unit step response of a LTI control system is shown in the following figure. Find
the transfer function of a second order prototype system to model th
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #6
Professor Amir G. Aghdam
1. The block diagram of a linear control system is shown in the following figure, where
r (t ) is the reference input and d (t ) is the disturbance.
D( s)
Pr
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #7
Professor Amir G. Aghdam
1. Problems E7.23 from the eighth, ninth, tenth, eleventh, and twelfth editions of the
main textbook.
2. The characteristic equation of a linear control syst
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #8
Professor Amir G. Aghdam
1. Design the controller GC (s ) for the following servomotor so that for all inside a
unit circle ( < 1 ) the settling time is less than 0.4 sec.
+
GC (s )
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #9
Professor Amir G. Aghdam
et 0 s
1. Plot the Nyquist diagram for the transfer function
for:
s ( s + 1) 2
a) t0 = 0
b) t0 = 0.1
c) t0 = 1
2. Sketch the Bode plots for the following tra
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #10
Professor Amir G. Aghdam
1. Problems P9.3 from the eighth, ninth, tenth, eleventh, and twelfth editions of the main
textbook.
2. The characteristic equation of a linear control syst
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #11
Professor Amir G. Aghdam
1.
a) Consider a stable closedloop system with an openloop transfer function G (s )
whose Nyquist diagram is given below:
Find the gain margin and phase m
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2013
S. Hashtrudi Zad
Assignment 1
Due: Monday, September 16, 2013 (in the instructors mailbox in EV5175)
1. Problem P1.3.
2. Problem P1
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2013
S. Hashtrudi Zad
Assignment 2
Due: Monday, September 23, 2013 (in the instructors mailbox in EV5175)
1. Problem P2.48.
(Note: Fig.
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2013
S. Hashtrudi Zad
Assignment 4
Due: October 15, 2013, 10:00am (in class or in the instructors mailbox in EV5175)
1. Problem E5.10.
2
Concordia University
ELEC372 Fundamentals of Control Systems (Lecture U)
Homework #1
Due: January 17,2007
Assigned: January 10,2007
1. Problem 1.1 1
2. Find the Laplace transforms of the following functions. Check if the initial value
theorem and the fina
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #3
Amir G. Aghdam
1. Problem E2.14 from eighth, ninth, tenth and eleventh editions, and E2.15 from the
twelfth edition of the main textbook.
2. Problem P2.2 from eighth, ninth, tenth, e
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #4
Amir G. Aghdam
1. Consider the standard first order system
H (s) =
K
.
s +1
a) Write the Laplace transform of the signal x(t ) in the following figure.
x(t )
1
0
1
2
3
t
b) What is
1
ELEC 372 LECTURE NOTES, WEEK 1
Dr. Amir G. Aghdam
Concordia University
Introduction

System: An integrated whole even though composed of diverse, interacting,
specialized structures and subjunctions. Notes: Any system has a number of
objectives and th
1
ELEC 372 LECTURE NOTES, WEEK 6
Dr. Amir G. Aghdam
Concordia University
Steadystate error in feedback systems

Consider the following unity feedback control system and assume that the overall
system is stable (this is the main assumption).
E (s )
R(s )
1
ELEC 372 LECTURE NOTES, WEEK 7
Dr. Amir G. Aghdam
Concordia University
Rootlocus technique

It is a method to investigate the trajectories of the roots of the characteristic
equation when a certain system parameter varies.

Example 7.1: Plot the root
1
ELEC 372 LECTURE NOTES, WEEK 8
Dr. Amir G. Aghdam
Concordia University
Rootlocus technique (contd)

The following tips can also be very helpful in plotting the RL and CRL in general.
o The root loci for all K are symmetrical with respect to the real a
1
ELEC 372 LECTURE NOTES, WEEK 9
Dr. Amir G. Aghdam
Concordia University
Controller design using the root locus method (contd)

The lead controller improves the transient response by adding positive phase to
the open loop transfer function.

One can imp
1
ELEC 372 LECTURE NOTES, WEEK 10
Dr. Amir G. Aghdam
Concordia University
Bode plot (contd)
1. G ( s ) = K (constant gain)
20 log G ( j ) = 20 log K
0
G ( j ) =
o
180
K >0
K <0
Lecture Notes Prepared by Amir G. Aghdam
2
Note that since the horizontal a
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 5
The Performance of Feedback Control Systems
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 2
Mathematical Models of Systems
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be produced
Concordia University
ELEC372 Fundamentals of Control Systems
Homework 1
Amir G. Aghdam
1. Problem P1.11 from eighth, ninth, tenth, eleventh and twelfth editions of the main
textbook.
2. Find the Laplace transforms of the following functions. Check if the
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #2
Amir G. Aghdam
1. The flow of traffic in a single lane can be described by the following equation:
dy
= V Ae y (t )
dt
where
y (t ) : relative distance between two cars,
V : constant
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2013
S. Hashtrudi Zad
Assignment 3
Due: Monday, September 30, 2013 (in the instructors mailbox in EV5175)
1. Problem E2.22.
Note: Make t
Fundamentals of Control Systems
ELEC372
Fall 2013
Solutions for Assignment 3
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be produced or reproduced for
commercial use.
1
ELEC 372 LECTURE NOTES, WEEK 11
Dr. Amir G. Aghdam
Concordia University
Stability analysis in frequency domain (contd)

For stability analysis it is very important to note that the closedloop poles are the
zeros of 1 + G ( s ) and the openloop poles
1
ELEC 372 LECTURE NOTES WEEK 12
Dr. Amir G. Aghdam
Concordia University

GM and PM in the Bode plot: Consider the following closedloop system:
+
G (s )

Assume that the Bode plot of the openloop transfer function G (s ) is given. The
frequency at whi
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC 37 2)
S. Hashtrudi Zad
Term Test 2
3 Questions, 5 pages
November 4, 2008
Family name:
Given name:
Student ID:
Time allotted: 60 minutes.
Instructi
Concordia University
Department of Electrical and Computer Engineering
“WW—WanlSﬁf—Gentml—Systems—(ELEG 372)
S. Hashtrudi Zad
————Temr=resc———————
3 Questions, 5 pages
October 7, 2008
Family name:
Given name:
Student ID:
Time allotted: 55 minutes.
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC 37 )
S. Hashtrudi Zad
erm Test 1
3 Questions, 5 pages
October 8, 2013
Family name: T
Given name:
Student ID:
M
Time allotted: 45 minutes.
In
1
ELEC 372 LECTURE NOTES, WEEK 1
Dr. Amir G. Aghdam
Concordia University
Introduction

System: An integrated whole even though composed of diverse, interacting,
specialized structures and subjunctions. Notes: Any system has a number of
objectives and th
ELEC 372  FUNDAMENTALS OF
CONTROL SYSTEMS
LABORATORY MANUAL
2016Winter, January
Department of Electrical & Computer Engineering
Concordia University
1515 St. Catherine West, SEV005.139,
Montreal, Quebec, Canada H3G 2W1
http:/www.ece.concordia.ca/~realt
1
ELEC 372 LECTURE NOTES, WEEK 6
Dr. Amir G. Aghdam
Concordia University
Parts of these notes are adapted from the materials in the following references:
Modern Control Systems by Richard C. Dorf and Robert H. Bishop, Prentice Hall.
Feedback Control of Dy
Concordia University
ELEC372 Fundamentals of Control Systems
Homework #5
Professor Amir G. Aghdam
1. (Automatic Control Systems by Farid Golnaraghi and Benjamin C. Kuo, Eighth
Edition, John Wiley & Sons, Inc., 2010) The unit step response of a LTI control