EE404 NONLINEAR CONTROL SYSTEMS
| Course Code: | 5670404 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 5.0 |
| Department: | Electrical and Electronics Engineering |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. UMUT ORGUNER |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of the course
- students will be able to comprehend basic concepts related to nonlinear systems.
- students will be able to understand the concepts related to the periodic trajectories observed in nonlinear systems.
- students will be able to make describing function analysis.
- students will be able to comprehend the concept of stability for nonlinear systems.
Course Content
State-space analysis methods. Isocline Lienard`s methods, classification of singularities. Analytic techniques of periodic phenomena: Perturbation method. Stability definitions. Lyapunov`s second method; Popov stability criterion. The method of harmonic realization: Describing functions. Dual-input describing functions. Equivalent linearization and oscillations in nonlinear feedback systems.
Course Learning Outcomes
Course Objective 1: Students will be able to comprehend the concept of stability for nonlinear systems.
Learning Outcomes: Students will be able to
- Find the equilibrium points of a nonlinear system.
- Classify the equilibrium points of a second-order nonlinear system (node, saddle, centroid etc.)
- Draw the approximate trajectories of a second-order nonlinear system on the phase plane
Course Objective 2: Students will be able to understand the concepts related to the periodic trajectories observed in nonlinear systems.
Learning Outcomes: Students will
- Know the definition of a limit cycle.
- Apply the basic results on the existence and non-existence of limit cycles to predict or rule out limit cycles.
Course Objective 3: Students will be able to make describing function analysis.
Learning Outcomes: Students will be able to
- Derive the describing functions for common non-linear elements with and without memory (relay, saturation, dead zone, hysteresis, backlash etc.).
- Determine the existence and stability of a limit cycle along with its parameters based on the describing function analysis.
Course Objective 4: Students will be able to comprehend the concept of stability for nonlinear systems.
Learning Outcomes: Students will
- Understand the definition of the stability of equilibrium points in nonlinear systems.
- Make stability analysis for nonlinear systems based on Lyapunov’s indirect method (linearization).
- Make stability analysis for nonlinear systems based on Lyapunov’s direct method.
- Know the distinction between different stability types like local-global stability, asymptotical stability etc.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics | ✔ | |||
| 2 | An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors | ✔ | |||
| 3 | An ability to communicate effectively with a range of audiences | ✔ | |||
| 4 | An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts. | ✔ | |||
| 5 | An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives | ✔ | |||
| 6 | An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions | ✔ | |||
| 7 | An ability to acquire and apply new knowledge as needed, using appropriate learning strategies | ✔ | |||