Course Title and Code
Control of Nonlinear Dynamical Systems (EE5515)
Programme
PG
Course Credit
3-0-0-3 (Lecture-Tutorial-Practical-Credit)
Course Category
ERC
Prerequisite Course
Elementary knowledge of linear systems and differential equations
Consent of Teacher
Yes (for BTech)
Course Contents
| Sl. No. | Topic | Lecture (hours) |
|---|---|---|
| 1 | Introduction to Dynamical Systems: Nonlinear Models and Nonlinear Phenomena; Examples from mechanics, electric circuits, biological systems; common nonlinearities; Introduction to vector fields, flows, and integral curves of differential equations. | 2 |
| 2 | Dynamical Systems: Qualitative behavior of linear systems; Multiple equilibria; Examples; Qualitative behavior near the equilibrium points; Jacobian linearization; limit cycles; Construction of phase portraits; Existence of periodic orbits; State space model; Stability notions; Examples. | 6 |
| 3 | Stability: Nonlinear Systems; Autonomous system; Lyapunov stability; Lyapunov’s stability theorem; revisiting pendulum model; global stability notion; LaSalle’s Invariance principle; Comparison functions; Nonautonomous systems; Linear time-varying systems and linearization; input-to-state stability; the small gain theorem; passivity; Examples. | 12 |
| 4 | Nonlinear Feedback Control: Local coordinates transformations; Exact linearization via feedback; Zero dynamics; Local asymptotic stabilization; noninteracting control; Achieving relative degree via dynamic extension; Exact Linearization of input-output response; Examples. | 10 |
| 5 | Nonlinear Design Tools: Full-state Linearization; stabilization and tracking; input-output linearization; Asymptotic output tracking and regulation; Lyapunov based-feedback control design; passivity-based control; Examples. | 12 |
Total: 42 hours
Assignments
Students will be given assignments after each unit where they will learn to apply appropriate mathematical techniques. As a part of the course project, students will be required to read/present a research paper based on applications (electrical/mechanical/chemical) to understand the stability and control design techniques.
Learning Objectives
The course focuses on understanding the behavior of nonlinear systems of interest to engineers. It aims at providing the necessary background for stability analysis and control of nonlinear systems. The course will emphasize recent as well as classical techniques and methodologies for designing control systems for nonlinear dynamical systems. Application of nonlinear control design ranging from aerospace to robotics will be considered throughout the course.
Learning Outcomes
- Have an understanding of how nonlinear dynamics and control is a key aspect of everyday systems.
- Have an introduction to the tools and techniques of nonlinear control analysis and the various aspects of controller design philosophy.
- Identify what tools will be useful for a specific nonlinear dynamics/control problem.
Teaching Methodology
Classroom lectures
Assessment Methods
Written examinations/quiz/presentation, continuous assessment
Textbooks
- H. Khalil, Nonlinear Systems (3rd edition), Prentice Hall, 2002. (ISBN-13: 978-0023635410)
- J.J.E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991. (ISBN-13: 978-0130408907)
Reference Textbooks
- A. Isidori, Nonlinear Control Systems I, 3rd edition, Springer Verlag, 1996. (ISBN 978-1-84628-615-5)
- A. Nijemjer and A. van der Schaft, Nonlinear Dynamical Control Systems, Springer, 1989. (ISBN 978-1-4757-2101-0)