ECE 6740 Nonlinear Control Systems

Fall 2021
version 11 October 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 A-240, 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, 2nd 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, Springer-Verlag, 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, 2nd 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, Prentice-Hall, 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://www-inst.eecs.berkeley.edu/~ee129/fa09/handouts/GenesisChuasCircuit.pdf

4.      K. Bryan, “Taylor’s Theorem in One and Several Variables.” Available at https://www.rose-hulman.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/multivariable-calculus

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 Gender-Based 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 in-depth exploration of plagiarism, see http://libguides.wmich.edu/plagiarism

 

COVID-19 Statement

 

Safety requirements are in place to minimize exposure to the Western Michigan University community. These guidelines apply to all in-person 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/facial-covering-mask

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: 0-60 E | 60-65 D | 65-70 DC | 70-75 C | 75-80 CB | 80-85 B | 85-90 BA | 90-100 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 pseudo-code;

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 pseudo-code 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
Tue

Syllabus

Class moved to M W noon-1:15PM C-141

Read syllabus
Read Prefaces (1st and 2nd edition)
Read CH 1 Overview

Read CH 2 Flows on the Line

 

Project 1: DUE 9/15
CH 2: 2.1 (all parts), 2.2.1-2.2.6 (OK to use mathematics software), 2.2.8, 2.2.10, 2.2.12 (verify solution with LTspice®), 2.3.1, 2.4.1-6, 2.4.9, 2.5.1,2.5.4, 2.6.1, 2.7.1-4, 2.8.3, 2.8.5, 2.8.7

WEEK 2

 

9/6

 

LABOR DAY: NO CLASS

Read Numerical Recipes in C:
16.0, 16.1, 16.2 (From Integration of Ordinary Differential Equations Chapter)

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
Due 10/8 to instructor mailbox

Investigate
dy/dt = -t y^2, y(2)=1
Discuss solution existence and uniqueness. Compare the error between numeric solutions using Euler (for at least two step sizes) and RK4 and the actual solution over the interval t
[2,3]. Based on example in [Maron 1982].

 

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

Tour of Dr. John Jellies Lab

 

8 

9/29

3 Bifurcations

 

WEEK 6

9 

10/4

3 Bifurcations

Electronic Circuit with Hysteresis



 

10 

10/6

3 Bifurcations
Bifurcations in Neural Systems [Izhikevich]

 

 

10/8

 

Project 2 DUE

WEEK 7

11 

10/11

4 Flows on the Circle

Project 3: DUE 10/25
Text: 4.1.1, 4.1.2—4.1.7, 4.1.8, 4.2.1, 4.2.2, 4.3.2, 4.3.3, 4.3.8, 4.4.4, 4.5.3

12 

10/13

5 Linear Systems

6 Phase Plane

 

WEEK 8

13 

10/18

6 Phase Plane

Project 3 DUE

 

10/20

FALL BREAK

 

WEEK 9

14 

10/25

7 Limit Cycles

 

15 

10/27

7 Limit Cycles

 

WEEK 10

16 

11/1

LAST DAY TO WITHDRAW
7 Limit Cycles

 

17 

11/3

7 Limit Cycles

 

WEEK 11

 

11/8

7 Limit Cycles

 

18 

11/10

 

 

WEEK 12

19 

11/15

8 Bifurcations Revisited

 

20 

11/17

8 Bifurcations Revisited

 

WEEK 13

21 

11/22

9 Lorenz Equations

 

 

11/24

THANKSGIVING BREAK

 

WEEK 14

22 

11/29

Control of Inverted Pendulum

 

23 

12/1

TBD

 

WEEK 15

24 

12/6

TBD

 

25 

12/8

TBD

 

WEEK 16

26 

???

FINAL EXAM

 

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