Fundamentals of Control Systems (ELEC 372)
List of the formulas that will be provided in the final exam:
p
2
PO = 100 e 1
Ts =
4
n
Tp =
p
n 1 2
Tr1 =
Mp =
2.16 + 0.6
n
1
p
2 1 2
r = n
p
1 2 2
(0.3 0.8)
2
)
2
2
)
(0 < <
2
(0 < <
B = (1.196 + 1.85)n
=
(0.
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
Fundamentals of Control Systems
ELEC372
Fall 2016
Solutions for Assignment 1
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.
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2016
S. Hashtrudi Zad
Assignment 3
Due: Wednesday, October 5, 2016 (in class or in instructors mailbox in EV5175)
1. Problem E2.22.
Note
Fundamentals of Control Systems
ELEC372
Fall 2016
Solutions for Assignment 5
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.
Fundamentals of Control Systems
ELEC372
Fall 2016
Solutions for Assignment 4
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.
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2016
S. Hashtrudi Zad
Assignment 9
Do not submit this assignment.
1. Problem E9.19.
2. Problem E10.15.
3. Problem P10.5 (Change in a spec
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2016
S. Hashtrudi Zad
Assignment 7
Due: Wednesday, November 23, 2016 (in class or in instructors mailbox in EV5175)
1. Problem E8.6.
Not
Fundamentals of Control Systems
ELEC372
Fall 2016
Solutions for Assignment 2
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.
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC372)
Fall 2016
S. Hashtrudi Zad
Assignment 8
Due: Wednesday, November 30, 2016 (in class or in instructors mailbox in EV5175)
1. Consider a unity
Control Systems Example History Block Diagrams
Introduction to Feedback Control Systems
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
September 2016
c Copyright by Shahin Hashtrudi Zad 20152016
1 / 16
Control Systems
Fundamentals of Control Systems
ELEC372
Fall 2016
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.
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
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 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
Concordia University
Department of Electrical and Computer Engineering
ELEC 372 : Fundamentals of Control Systems
Section R
Fall 2015
General Information
Lecturer: Shahin Hashtrudi Zad
Room EV5151
[email protected]
Office hours: Wednesdays 14:0015:00
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 9
Stability in the Frequency Domain
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be produc
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 6
The Stability of Linear Feedback Systems
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 8
Frequency Response Methods
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be produced or r
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 10
The Design of Feedback Control Systems
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be
Fundamentals of Control Systems
ELEC372
Fall 2015
Supplementary Notes for Chapter 7
The Root Locus Method
S. Hashtrudi Zad
Dept. of Electrical and Computer Engineering
Concordia University
These notes, or any part thereof, are not to be produced or reprod
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
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC 37 2)
S. Hashtrudi Zad
Final Exam
7 Questions, 10 pages
December 5, 2008
Family name:
Given name:
Student ID:
Time allotted: Three hours.
Instruct
Concordia University
Department of Electrical and Computer Engineering
Fundamentals of Control Systems (ELEC 372)
S. Hashtrudi Zad
Term Test 2
3 Questions, 5 pages
November 4, 2008
Family name:
Given name:
Student ID:
Time allotted: 60 minutes.
In