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M.SC. in Electrical and Electronics Engineering (With Thesis)
EEE 611 | Course Introduction and Application Information
| Course Name |
Nonlinear System Analysis
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
EEE 611
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
Third Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| National Occupation Classification | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| Course Objectives | The course aims the students: i) to get a solid mathematical background on nonlinear systems’ equilibrium points, limit cycle and other nonlinear behaviors together with their Liapunov and input-output stabilities, ii) to gain skills of determining the existence, qualitative properties and stability of certain nonlinear behaviors for a given nonlinear system and iii) to have a nonlinear systems point of view. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | Introduction to nonlinear phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical behavior. Planar dynamical systems, analysis using phase plane techniques. Describing functions. Input-output analysis and stability. Lyapunov stability theory. The Lure problem, Circle and Popov criterion. Feedback linearization and sliding mode control. |
|
|
Core Courses |
X
|
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation | Learning Outcome |
| 1 | Examples for nonlinear systems. Derivation of state equations of nonlinear circuits and control systems. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 2 | Equilibrium point, fixed point, multiple equilibria, existence and uniqueness of equilibrium points and fixed points. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 3 | Existence and uniqueness of solutions to nonlinear state equations. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 4 | Existence and uniqueness of nonlinear difference equations, nonexpansion mapping, contraction mapping, implicit and inverse function theorems. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 5 | Phase portraits for second order dynamical systems, existence of periodical solutions, Poincare-Bendixson Theorem | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 6 | Liapunov stability and asymptotical stability of an equilibrium point of a nonlinear system, Liapunov’s first method for stability. Hartman-Grobman Theorem | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 7 | Liapunov’s second method. Liapunov functions for linear and nonlinear, time-invariant and time-varying systems. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 8 | Lasalle’s Invariance Theorem. Necessary conditions for Liapunov stability. Complete stability. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 9 | 1. Midterm | ||
| 10 | Control problems as Liapunov stability problems. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 11 | Bounded-Input Bounded-Output stability for nonlinear systems. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 12 | Lure’s system. Aizerman’s conjecture. Sector conditions. Circle criteria. Popov criteria, | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 13 | 2. Midterm | ||
| 14 | State feedback linearization, output feedback linearization. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 15 | Sliding mode control, strict feedback control. | M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001 | |
| 16 | Review of the Semester |
| Course Notes/Textbooks | The textbook referenced above and lecture notes |
| Suggested Readings/Materials | Related Books |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
5
|
20
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
40
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
7
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
15
|
4
|
60
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
5
|
12
|
60
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
15
|
30
|
| Final Exam |
1
|
27
|
27
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
PC Sub | Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
|||
| 1 | Accesses information in breadth and depth by conducting scientific research in Electrical and Electronics Engineering; evaluates, interprets and applies information |
-
|
-
|
-
|
-
|
X
|
|
| 2 | Is well-informed about contemporary techniques and methods used in Electrical and Electronics Engineering and their limitations |
-
|
-
|
X
|
-
|
-
|
|
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines |
-
|
X
|
-
|
-
|
-
|
|
| 4 |
Is informed about new and upcoming applications in the field and learns them whenever necessary. |
-
|
-
|
X
|
-
|
-
|
|
| 5 | Defines and formulates problems related to Electrical and Electronics Engineering, develops methods to solve them and uses progressive methods in solutions. |
-
|
-
|
-
|
-
|
X
|
|
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. |
-
|
-
|
-
|
X
|
-
|
|
| 7 | Designs and implements studies based on theory, experiments and modeling; analyses and resolves the complex problems that arise in this process. |
-
|
-
|
-
|
-
|
X
|
|
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility. |
-
|
X
|
-
|
-
|
-
|
|
| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. |
-
|
-
|
X
|
-
|
-
|
|
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
X
|
-
|
-
|
-
|
-
|
|
| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Electrical and Electronics Engineering applications, knows their project management and business applications, and is aware of their limitations in Electrical and Electronics Engineering applications. |
X
|
-
|
-
|
-
|
-
|
|
| 12 |
Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. Adheres to the principles of research and publication ethics. |
X
|
-
|
-
|
-
|
-
|
|
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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