ELE654 - NONLINEAR SYSTEMS
Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
---|---|---|---|---|---|---|
NONLINEAR SYSTEMS | ELE654 | Any Semester/Year | 3 | 0 | 3 | 8 |
Prequisites | None | |||||
Course language | Turkish | |||||
Course type | Elective | |||||
Mode of Delivery | Face-to-Face | |||||
Learning and teaching strategies | Lecture Question and Answer Problem Solving | |||||
Instructor (s) | Department Faculty | |||||
Course objective | In practice many systems are nonlinear. The objective of the course is to provide necessary background to understand, analyze and control such systems. These include nonlinear models and nonlinear phenomena; second-order systems, phase portraits; some fundamental properties of nonlinear state equations such as existence, uniqueness; stability analysis (Lyapunov, input-output, passivity); frequency domain analysis; controller design methods for nonlinear systems such as feedback linearization and sliding-mode control. | |||||
Learning outcomes |
| |||||
Course Content | Introduction to nonlinear systems and some examples. Second order systems and phase plane. Lyapunov stability. Input-output stability. Passivity. Frequency domain analysis: absolute stability, circle criterion, Popov criterion, describing function method . Nonlinear control systems design: feedback linearization and sliding-mode control. | |||||
References | 1. Khalil H. K., Nonlinear Systems, 3rd Ed., Prentice Hall, 2002. 2. Slotine J. J. E. and Li W., Applied Nonlinear Control, Prentice Hall, 1991. 3. İsidori A., Nonlinear Control Systems, 3rd Ed., Fall/ Springer, 1995. 4. Vidyasagar M., Nonlinear Systems Analysis, 2nd Ed., Prentice Hall, 1993. 5. Sastry S., Nonlinear Systems: Analysis, Stability and Control, Fall/ Springer-Verlag, 1999. |
Course outline weekly
Weeks | Topics |
---|---|
Week 1 | Nonlinear models and nonlinear phenomena and some example systems. Lienard?s equation, Van der Pol equation. |
Week 2 | Second order systems, phase plane, multiple Equilibria. |
Week 3 | Qualitative behavior near equilibrium points, limit cycles, existence of periodic orbits, Poincare-Bendixson criterion, Bendixson criterion, bifurcation. |
Week 4 | Solution of nonlinear state equations, existence and uniqueness, Lipschitz condition, continuous dependence on initial conditions and parameters, differentiability of solutions and sensitivity equations. |
Week 5 | Lyapunov stability: autonomous systems. |
Week 6 | Lyapunov stability: the invariance principle, linearization and local stability, comparision functions. |
Week 7 | Lyapunov stability: nonautonomous systems, boundedness and ultimate boundedness, input-to- state stability. |
Week 8 | Input-output stability. |
Week 9 | Passivity. |
Week 10 | Midterm Exam. |
Week 11 | Frequency domain analysis of feedback systems: absolute stability, circle criterion, Popov criterion. |
Week 12 | Frequency domain analysis of feedback systems: describing functionmethod . |
Week 13 | Feedback linearization. |
Week 14 | Sliding mode control. |
Week 15 | Preparation for the final exam. |
Week 16 | Final exam. |
Assesment methods
Course activities | Number | Percentage |
---|---|---|
Attendance | 0 | 0 |
Laboratory | 0 | 0 |
Application | 0 | 0 |
Field activities | 0 | 0 |
Specific practical training | 0 | 0 |
Assignments | 6 | 30 |
Presentation | 0 | 0 |
Project | 0 | 0 |
Seminar | 0 | 0 |
Midterms | 1 | 30 |
Final exam | 1 | 40 |
Total | 100 | |
Percentage of semester activities contributing grade succes | 0 | 60 |
Percentage of final exam contributing grade succes | 0 | 40 |
Total | 100 |
WORKLOAD AND ECTS CALCULATION
Activities | Number | Duration (hour) | Total Work Load |
---|---|---|---|
Course Duration (x14) | 13 | 3 | 39 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Specific practical training | 0 | 0 | 0 |
Field activities | 0 | 0 | 0 |
Study Hours Out of Class (Preliminary work, reinforcement, ect) | 14 | 5 | 70 |
Presentation / Seminar Preparation | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework assignment | 6 | 8 | 48 |
Midterms (Study duration) | 1 | 25 | 25 |
Final Exam (Study duration) | 1 | 25 | 25 |
Total Workload | 35 | 66 | 207 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
D.9. Key Learning Outcomes | Contrubition level* | ||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
1. Has general and detailed knowledge in certain areas of Electrical and Electronics Engineering in addition to the required fundamental knowledge. | X | ||||
2. Solves complex engineering problems which require high level of analysis and synthesis skills using theoretical and experimental knowledge in mathematics, sciences and Electrical and Electronics Engineering. | X | ||||
3. Follows and interprets scientific literature and uses them efficiently for the solution of engineering problems. | X | ||||
4. Designs and runs research projects, analyzes and interprets the results. | X | ||||
5. Designs, plans, and manages high level research projects; leads multidiciplinary projects. | X | ||||
6. Produces novel solutions for problems. | X | ||||
7. Can analyze and interpret complex or missing data and use this skill in multidiciplinary projects. | X | ||||
8. Follows technological developments, improves him/herself , easily adapts to new conditions. | X | ||||
9. Is aware of ethical, social and environmental impacts of his/her work. | X | ||||
10. Can present his/her ideas and works in written and oral form effectively; uses English effectively | X |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest