# Department of Electrical and Electronics Engineering

Course Details

#### ELE654 - Nonlinear Systems

2022-2023 Fall term information
The course is not open this term
ELE654 - Nonlinear Systems
 Program Theoretýcal hours Practical hours Local credit ECTS credit MS 3 0 3 8
 Obligation : Elective Prerequisite courses : - Concurrent courses : - Delivery modes : Face-to-Face Learning and teaching strategies : Lecture, Question and Answer, Problem Solving 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 : A student completing the course successfully is expected to understand the nature of nonlinear systems. be aware of difficulties involving nonlinear systems. be able to use some techniques to analyse nonlinear systems. be able to use some techniques to design controllers for nonlinear systems. have a suitable background to follow further studies in nonlinear systems and control. 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. Ýsidori 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
1 Nonlinear models and nonlinear phenomena and some example systems. Lienard?s equation, Van der Pol equation.
2 Second order systems, phase plane, multiple Equilibria.
3 Qualitative behavior near equilibrium points, limit cycles, existence of periodic orbits, Poincare-Bendixson criterion, Bendixson criterion, bifurcation.
4 Solution of nonlinear state equations, existence and uniqueness, Lipschitz condition, continuous dependence on initial conditions and parameters, differentiability of solutions and sensitivity equations.
5 Lyapunov stability: autonomous systems.
6 Lyapunov stability: the invariance principle, linearization and local stability, comparision functions.
7 Lyapunov stability: nonautonomous systems, boundedness and ultimate boundedness, input-to- state stability.
8 Input-output stability.
9 Passivity.
10 Midterm Exam.
11 Frequency domain analysis of feedback systems: absolute stability, circle criterion, Popov criterion.
12 Frequency domain analysis of feedback systems: describing functionmethod .
13 Feedback linearization.
14 Sliding mode control.
15 Preparation for the final exam.
16 Final exam.
Assessment 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
Quiz 0 0
Midterms 1 30
Final exam 1 40
Total 100
Percentage of semester activities contributing grade success 60
Percentage of final exam contributing grade success 40
Total 100
Course activities Number Duration (hours) Total workload
Course Duration 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, etc.) 14 5 70
Presentation / Seminar Preparation 0 0 0
Project 0 0 0
Homework assignment 6 8 48
Quiz 0 0 0
Midterms (Study duration) 1 25 25
Final Exam (Study duration) 1 25 25
Matrix Of The Course Learning Outcomes Versus Program Outcomes
Key learning outcomes Contribution 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.
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.
3. Follows and interprets scientific literature and uses them efficiently for the solution of engineering problems.
4. Designs and runs research projects, analyzes and interprets the results.
5. Designs, plans, and manages high level research projects; leads multidiciplinary projects.
6. Produces novel solutions for problems.
7. Can analyze and interpret complex or missing data and use this skill in multidiciplinary projects.
8. Follows technological developments, improves him/herself , easily adapts to new conditions.
9. Is aware of ethical, social and environmental impacts of his/her work.
10. Can present his/her ideas and works in written and oral form effectively; uses English effectively.
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest