ELE754 - NONLINEAR SYSTEMS
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| NONLINEAR SYSTEMS | ELE754 | Any Semester/Year | 3 | 0 | 3 | 10 |
| 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. Ä°sidori 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 | 9 | 126 |
| 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 | 70 | 263 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1. Has highest level of knowledge in certain areas of Electrical and Electronics Engineering. | X | ||||
| 2. Has knowledge, skills and and competence to develop novel approaches in science and technology. | X | ||||
| 3. Follows the scientific literature, and the developments in his/her field, critically analyze, synthesize, interpret and apply them effectively in his/her research. | X | ||||
| 4. Can independently carry out all stages of a novel research project. | X | ||||
| 5. Designs, plans and manages novel research projects; can lead multidisiplinary projects. | X | ||||
| 6. Contributes to the science and technology literature. | X | ||||
| 7. Can present his/her ideas and works in written and oral forms effectively; in Turkish or English. | X | ||||
| 8. Is aware of his/her social responsibilities, evaluates scientific and technological developments with impartiality and ethical responsibility and disseminates them. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest