ECE
6740 Nonlinear Control Systems
Fall 2021
version
17 November 2021
The online
version of this syllabus at http://homepages.wmich.edu/~miller/ECE6740.html has hyperlinks and will be updated
as needed.
Instructor
Dr. Damon A. Miller, Associate Professor of Electrical and Computer
Engineering, Western Michigan University, College of Engineering and Applied
Sciences, Floyd Hall, Room A240, 269.276.3158, 269.276.3151 (fax), damon.miller@wmich.edu, www.homepages.wmich.edu/~miller/.
Office Hours
Guaranteed office hours are posted on Dr. Miller’s door and at http://homepages.wmich.edu/~miller/. Please respect my office
hours. Other times are available by
appointment.
Description (WMU Graduate Catalog)
ECE 6740 Nonlinear Control Systems, 3 hrs.
This is a first course in nonlinear systems. Students will learn to
characterize nonlinear phenomena such as limit cycles and chaotic behavior,
both analytically and numerically. Students will also delve into the world of
strange attractors and fractals. All this will be applied to a number of
engineering, mechanical, biological and chemical problems. Specifically,
students will consider the family nonlinear control problems (such as the
inverted pendulum) and chaotic communication systems (such as the Cummo and Chua circuits).
Prerequisites: ECE 5710 State Space Control Systems.
Note: Instructor will consider students outside ECE based on their background.
Acknowledgment
Adapted/adopted in part from syllabi by J. Gesink and
J. Kelemen.
Textbook and Materials
Required:
1.
S.
H. Strogatz, Nonlinear
Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering,
Westview Press, 2^{nd} ed., 2015.
2.
Mathematics
software suite. Any relatively recent release will suffice. Examples include:
a.
MATLAB
by The
MathWorks, MATLAB. The CAE center provides access
to this software; however, students are strongly encouraged to have access on
their personal computer.
b.
Mathematica
by Wolfram.
3.
LTspice®, Linear Technology SPICE
Simulator, available at http://www.linear.com/designtools/software/
References:
Texts:
1.
T.
S. Parker and L. O. Chua, Practical
Numerical Algorithms for Chaotic Systems, SpringerVerlag, 1989.
2.
E.
M. Izhikevich, Dynamical
Systems in Neuroscience: The Geometry of
Excitability and Bursting, The MIT Press, Cambridge, Massachusetts, 2007.
3.
Press
et al., Numerical Recipes in C,
Cambridge University Press, 2^{nd} ed., 1992. Available at http://apps.nrbook.com/c/index.html. Versions of this book for other
computer languages are acceptable, but this edition will be used in class.
Recommend a paper copy of this invaluable reference.
4.
J.
A. Cadzow and H. F. Van Landingham,
Signals, Systems, and Transforms,
PrenticeHall, Inc., New Jersey, 1985.
5.
M.
J. Maron, Numerical Analysis A Practical
Approach, Macmillan, New York, 1982.
6.
E.
Scheinerman, Invitation
to Dynamical Systems, Prentice Hall, 1996.
7.
A.
Sedra K. C. Smith, T. C. Carusone,
and V. Gaudet, Microelectronic Circuits,
Oxford University Press, 8th edition, 2019.
Online:
1.
Steven
Strogatz, MAE5790 Nonlinear Dynamics and Chaos Spring
2014 lectures, available at this YouTube Channel.
2.
https://www.wolframalpha.com/
3.
L. O. Chua, “The Genesis of Chua’s Circuit,” AEO,
vol. 64, no. 4, 1992. Available at http://wwwinst.eecs.berkeley.edu/~ee129/fa09/handouts/GenesisChuasCircuit.pdf
4.
K. Bryan, “Taylor’s Theorem in One and Several
Variables.” Available at https://www.rosehulman.edu/~bryan/lottamath/mtaylor.pdf
5.
The Khan Academy has an extensive list of excellent education videos, a
good source to brush up on calculus topics, etc., e.g. https://www.khanacademy.org/math/multivariablecalculus
Course
Policies
Academic Honesty
General:
“Students
are responsible for making themselves aware of and understanding the University
policies and procedures that pertain to Academic Honesty. These policies
include cheating, fabrication, falsification and forgery, multiple submission,
plagiarism, complicity and computer misuse. The academic policies addressing
Student Rights and Responsibilities can be found in the Undergraduate Catalog
at http://catalog.wmich.edu/content.php?catoid=32&navoid=1350 and the Graduate Catalog at http://catalog.wmich.edu/content.php?catoid=33&navoid=1404. If there is reason to believe you
have been involved in academic dishonesty, you will be referred to the Office
of Student Conduct. You will be given the opportunity to review the charge(s)
and if you believe you are not responsible, you will have the opportunity for a
hearing. You should consult with your instructor if you are uncertain about an
issue of academic honesty prior to the submission of an assignment or test.
Students
and instructors are responsible for making themselves aware of and abiding by
the “Western Michigan University Sexual and GenderBased Harassment and
Violence, Intimate Partner Violence, and Stalking Policy and Procedures”
related to prohibited sexual misconduct under Title IX, the Clery
Act and the Violence Against Women Act (VAWA)and Campus Safe. Under this
policy, responsible employees (including instructors) are required to report
claims of sexual misconduct to the Title IX
Coordinator
or designee (located in the Office of Institutional Equity). Responsible
employees are not confidential resources. For a complete list of resources and
more information about the policy see www.wmich.edu/sexualmisconduct.
In
addition, students are encouraged to access the Code of Conduct, as well as
resources and general academic policies on such issues as diversity, religious
observance, and student disabilities:
·
Office
of Student Conduct www.wmich.edu/conduct
·
Division
of Student Affairs www.wmich.edu/students/diversity
·
Registrar’s
Office http://www.wmich.edu/registrar/calendars/interfaith
·
Disability
Services for Students https://wmich.edu/disabilityservices.”
—
provided by the WMU Faculty Senate Professional Concerns Committee
Plagiarism: For an indepth exploration of plagiarism,
see http://libguides.wmich.edu/plagiarism
COVID19
Statement
Safety requirements are in place to
minimize exposure to the Western Michigan University community. These
guidelines apply to all inperson and hybrid classes held inside a WMU building
to ensure the safety of all students, faculty, and staff during the pandemic.
Noncompliance is a violation of the class requirements and the Student Code. https://wmich.edu/conduct/code
Facial coverings (masks), over
both the nose and mouth, are required for all students while in class, no
matter the size of the space. Following this recommendation can minimize the
transmission of the virus, which is spread between people interacting in close
proximity through speaking, coughing, or sneezing. During specified classes in
which facial coverings (masks) would prevent required class elements, students
may remove facial coverings (masks) with instructor permission, in accordance
with the exceptions in the Facial Covering (mask) Policy ("such as playing
an instrument, acting, singing, etc."). https://wmich.edu/policies/facialcoveringmask
Facial
coverings (masks) must remain in place throughout the class. Any student who
removes the mandatory facial covering (mask) during class will be required to
leave the classroom immediately.
Students who are unable to wear a
facial covering (mask) for medical/disability reasons must contact Disability
Services for Students before they attend class. https://wmich.edu/disabilityservices
—
section provided by the WMU Faculty Senate, highlight added
NO FOOD OR DRINK IN LECTURE OR LAB.
ONLY STUDENTS WITH A GREEN BADGE STATUS
ARE PERMITTED IN LECTURE
Grading
Basis
Grade is based completely on
projects. LATE
PROJECTS WILL NOT BE ACCEPTED AND ARE DUE AT THE BEGINNING OF CLASS.
All projects are to be completed individually.
Projects may include/consist of a series of homework style problems. Use
the prescribed homework format for those problems. Be sure to follow the
guidelines for computer assignments.
OUTSTANDING
WORK might earn extra credit.
Scale:
060 E  6065 D  6570 DC  7075 C  7580 CB  8085 B  8590 BA  90100
A 
HOMEWORK contributes to the
project grade category. Each homework problem must be worked on separate
page(s). LATE HOMEWORK will not be
accepted, except under extraordinary circumstances. Homework is to be completed individually.
Homework
should normally be done on 8 1/2'' by 11'' sheets. “Engineer's Pad” sheets are
preferred. Solutions must be done in a
neat, structured, logical, and orderly manner with frequent brief notations
enabling the grader to readily verify the author's source of information, steps
taken, sources of formulas, equations, and methods used. USE THE PARTIAL CHECK
LIST FOR SUBMITTED HOMEWORK BELOW.
Papers failing to meet these guidelines may not be graded and may be
returned, with or without an opportunity for resubmission with a penalty.
PARTIAL CHECK LIST
FOR SUBMITTED HOMEWORK
1. Each problem must
include: (a) author's name, (b) name/title of the assignment, and (c) date of
completion.
2. Use only one side
of the paper and include a brief and concise statement of the problem prior to
its solution. Begin each problem on a new page.
3. Number the pages
and DOUBLE SPACE the text.
4. Staple each
problem in the upper left corner as needed.
5. Entitle graphs,
label and include axes, include key symbols for multiple curve graphs, and give
brief notes of explanation where appropriate.
6. Briefly but clearly
annotate your document in a way which will provide the document reader with
information such as
a.
which
part of the assignment is this?
b.
what
is being done and why?
c.
how
was it done and what are the results?
d.
how
was this equation obtained and how was it used?
e.
sample
calculations and definitions of symbols/parameters where appropriate; and
f.
BOX AND LABEL
ANSWERS.
COMPUTER ASSIGNMENTS must include
1.
a
problem statement;
2.
description
of techniques utilized including pseudocode;
3.
results;
4.
discussion
of results; and
5.
computer
code listing(s) attached as an appendix. Computer code must include explanatory
comments. Some of those comments should relate computer code to the pseudocode
of item 2 above. Use modular
programming.
Course
Schedule
A tentative
schedule for the semester was provided in class; the online schedule will be
frequently updated as the semester progresses.
# 
date 
topic 
assignments 
WEEK 1 

1 
9/2 
Syllabus Class moved to M W noon1:15PM C141 
Read
syllabus Read
CH 2 Flows on the Line Project
1: DUE 9/15 
WEEK 2 


9/6 
LABOR DAY: NO CLASS 
Read
Numerical Recipes in C: 
2 
9/8 
Linear
Systems: definition, impulse response, frequency response 1 Overview 2 Flows on the Line 

3 
9/10 FRI 
SPECIAL MAKEUP CLASS 2 Flows on the Line 

WEEK 3 

4 
9/13 
2 Flows on the Line 
Read
CH 3 Bifurcations 
5 
9/15 
Numerical
Methods (solving ODEs) 3 Bifurcations 
Project
1 DUE Project
2 Investigate Text:
3.1 (all parts), 3.2.1, 3.2.4, 3.3.1, 3.4.1, 3.4.11, 3.4.13, 3.4.16 (all), 3.5.2,
3.6.7, 3.7.3 
WEEK 4 

6 
9/20 
3 Bifurcations 


9/22 
NO LECTURE: Engineering Expo 2021 
Read
CH 4 Flows on a Circle 
WEEK 5 

7 
9/27 


8 
9/29 
3 Bifurcations 

WEEK 6 

9 
10/4 
3 Bifurcations Electronic
Circuit with Hysteresis


10 
10/6 
3 Bifurcations 


10/8 

Project
2 DUE 
WEEK 7 

11 
10/11 
4 Flows on the Circle 
Read
CH 5 Linear Systems Project
3: DUE 10/25 
12 
10/13 
5 Linear Systems 
Read
CH 6 Phase Plane Project
4 DUE 11/5 to instructor mailbox 
WEEK 8 

13 
10/18 
6 Phase Plane 
Project
5 DUE 11/12 to instructor mailbox Text:
6.1.2, 6.1.4, 6.1.7, 6.1.8, 6.1.12, 6.2.1, 6.3.1, 6.3.3, 6.3.5, 6.3.8, 6.3.9,
6.3.10, 6.3.11, 6.4.2, 6.5.1, 6.5.7, 6.5.8, 6.5.20, 6.6.4, 6.7.2, 6.8.1,
6.8.9 

10/20 
FALL BREAK 

WEEK 9 

14 
10/25 
6 Phase Plane 
Project
3 DUE 
15 
10/27 
6 Phase Plane 

WEEK 10 

16 
11/1 
LAST DAY TO WITHDRAW 
Read
CH 7 Limit Cycles Project
6 DUE 11/19 to instructor mailbox Text:
7.1.6, 7.2.1, 7.2.5, 7.2.6, 7.2.10, 7.2.14, 7.2.18, 7.3.1, 7.3.2, 7.3.9,
7.4.1, 7.6.1, 7.6.2, 7.6.26 
17 
11/3 
7 Limit Cycles 


11/5 

Project
4 DUE 
WEEK 11 

18 
11/8 
7 Limit Cycles 
Read
CH 8 Bifurcations Revisited 
19 
11/10 
8 Bifurcations Revisited 


11/12 

Project
5 DUE 
WEEK 12 

20 
11/15 
8 Bifurcations Revisited 
Read
CH 9 Lorenz Equations Project
7 DUE 11/29 
21 
11/17 
8 Bifurcations Revisited 


11/19 

Project
6 DUE 
WEEK 13 

22 
11/22 
9 Lorenz Equations 


11/24 
THANKSGIVING BREAK 

WEEK 14 

23 
11/29 
9 Lorenz Equations 
Project
7 DUE Project
8 DUE 12/9 Text:
9: 9.3.2 to 9.3.7 10:
Reproduce Figure 10.2.7 of the text Final
exam project: formal report due at final exam period: Introduction; Methods;
Results; Discussion; References. Present results during final exam period. 
24 
12/1 
10
OneDimensional Maps Discuss
final exam project 

WEEK 15 

25 
12/6 
Inclass
work session 

26 
12/8 
Inclass
work session 


12/9 

Project
8 DUE 
WEEK 16 

27 
WED 12/15 2:45PM4:45PM 
FINAL EXAM 

© 2021
Damon A. Miller. All rights reserved. 