Nonlinear Systems (EE612) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Nonlinear Systems EE612 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
N/A
Course Language English
Course Type Elective Courses
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery
Learning and Teaching Strategies .
Course Coordinator
Course Lecturer(s)
  • Prof. Dr. Reşat Özgür DORUK
Course Assistants
Course Objectives Teaching of advanced concepts in nonlinear system theory to aid the graduate students mastering in dynamical systems theory, control, power systems, neural networks and theoretical neuroscience.
Course Learning Outcomes The students who succeeded in this course;
  • Explain nonlinear phenomena
  • Distinguish linear and nonlinear systems
  • Describe equilibrium concept
  • Analyze local system behaviour around equilibrium
  • Assess stability of a nonlinear system both locally and globally.
  • Assess the stability of a general system by Lyapunov methods.
  • Define and determine the existence of a limit cycle
  • Analyze advanced nonlinear phenomena such as bifurcations.
Course Content Nonlinear models and nonlinear phenomena, qualitative behaviour of second order systems, Lyapunov stability, passivity, Poincaré and Bendixon theorems, frequency response of nonlinear systems and describing functions, applications of Lyapunov theory, advanced nonlinear phenomena such as bifurcations.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Nonlinear Phenomena: Linear and Nonlinear Systems
2 Equilibrium Points, Jacobian Linearization
3 Analysişs of second order systems in phase plane
4 Behaviour of system trajectories in the vicinity of equilibrium points. Local stability.
5 Stability in general, types of stability and Lyapunov methods
6 Applications of Lyapunov Stability I
7 Applications of Lyapunov Stability II
8 MIDTERM EXAM-I
9 Limit cycles, Poincare and Bendixon theorems
10 Frequency response and describing functions.
11 Advanced Nonlinear Phenomena: Bifurcations
12 Bifurcation in one dimensional systems
13 Bifurcation in two dimensional systems (generalizations to large order cases)
14 Bifurcation analysis approaches (MATCONT Package)
15 Bifurcation Control Approaches
16 MIDTERM EXAM-II

Sources

Course Book 1. Khalil, Hassan K. "Noninear systems." Prentice-Hall, New Jersey 2.5 (1996)
2. Vidyasagar, Mathukumalli. Nonlinear systems analysis. Vol. 42. Siam, 2002.
Other Sources 3. Instructor Notes

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 30
Final Exam/Final Jury 1 40
Toplam 3 70
Percentage of Semester Work
Percentage of Final Work 100
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Gains accumulated knowledge on mathematics, science and mechatronics engineering; develops an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems.
2 Develops ability to differentiate, identify, formulate, and solve complex engineering problems; develops ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems.
3 Develops ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; develops ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions includes economics, environment, sustainability, producibility, ethics, human health, social and political problems.)
4 Gains ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; develops ability to use information and communications technologies effectively.
5 Develops ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies.
6 Develops ability to work effectively on single disciplinary and multi-disciplinary teams; gains ability for individual work; develops ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines.
7 Develops ability to express creative and original concepts and ideas orally or written effectively, in Turkish and English language.
8 Develops ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; gains consciousness on the necessity of improvement and sustainability as a result of life-long learning; gains ability for monitoring the developments on science and technology; develops awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Gains ability to be conscious on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 Gains knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Gains knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; develops consciousness on these issues and develops awareness of legal results of engineering solutions.
12 Gains the competence on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Gains conciousness on the environmental and social responsibility and develops conciousness to be an individual in society. Gains ability to develop and implement projects and asses them with a critical view for their social implications and gains ability to change the related norms if necessary.
14 Gains the competence on developing strategy, policy and application plans on the mechatronics engineering and evaluating the results in the context of quality standarts.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 5 80
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 3 6
Prepration of Final Exams/Final Jury 1 5 5
Total Workload 139