E1 248 - Sliding mode control and its applications (3:0)

Term & Timing: January - April 2025, Tue and Thurs: 2:00 PM-3:30 PM

First class on 2nd January 2024 (Thursday) 2:00-3:30 PM

Instructor: Kiran Kumari, Assistant Professor at the Department of Electrical Engineering

Email: kirank@iisc.ac.in 

Teaching Assistant:  

Rahul Jain; rahuljain@iisc.ac.in

Venue: B 303, Second Floor, EE Building 

Class Logistics: Registered students will be added to a Class group in Microsoft Teams. The link to join the Teams group is here. All the course correspondence will happen in this Teams group. 

Grading policy:

Assignments: 20%

Class Participation: 5%

Midterm: 10%

Project: 25% 

Endterm: 40%.

Prerequisites: Any basic course on control theory

Syllabus:

Module 1: Preliminaries–

• A brief introduction to state space representation

• Solution of linear systems

• Controllability and observability

• Fundamentals of nonlinear systems, linearization of nonlinear systems with examples

• Stability analysis tool: Lyapunov’s stability theorem, LaSalle's theorem

Module 2: Sliding mode control–

• Theory of conventional sliding mode: Filippov theory, reaching laws, finite-time stability, equivalent control method, advantages of sliding mode control

• Terminal sliding mode control: fast terminal sliding mode control, nonsingular terminal sliding mode, prescribed convergence law

• Sliding mode observers

• Integral sliding mode control

• Introduction to second-order sliding mode: relative degree, twisting algorithm, super twisting algorithm (as controller, differentiator, and observer)

• Higher order sliding mode (as continuous controller and differentiator)

• Discrete-time sliding mode control: Gao’s reaching law, Bartoszewicz’s reaching law

Module 3: Applications– Inverted pendulum, power converters, power systems, quadrotors, etc. These will be covered as a part of the course project.

Module 4: Optional topics (if time permits): multi-rate output feedback-based control.

References:

1. Sliding mode control and observation (Vol. 10. New York: Springer) by Yuri Shtessel, Christopher Edwards, Leonid Fridman, and Arie Levant, 2014.

2. Applications of sliding mode control (Vol. 79. Springer Singapore) by Derbel, Nabil, Jawhar Ghommam, and Quanmin Zhu, 2017.

3. Nonlinear systems (third edition) by Hassan K. Khalil, 2002.