Course Details
Subject {L-T-P / C} : EE6303 : Nonlinear Control { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Shubhobrata Rudra
Syllabus
Introduction to Nonlinear Systems [4L]: Modeling complex systems as nonlinear systems, motivating examples, detailed discussions on practical nonlinear systems and their salient features.
Analysis of second order Nonlinear systems[2L]: Phase Plane Analysis techniques, Poincare Bendixon theorem for limit cycle detection.
Analysis of Nonlinear Differential Equation[3 L]: Existence and Uniqueness of the solution, comparison lemma, parameter variation and sensitivity equation (introductory idea)
Stability Analysis of Autonomous Nonlinear Differential Equation [6 L]: Lyapunov stability analysis for nonlinear systems, Local and Global Stability, concept of stability basin, Cheatev's Instability Theorem, Condition of linearization and stability analysis of the linearized model near an equilibrium point, invariant set theorems and its importance.
Mid Sem
Advanced Stability Analysis of Nonlinear Differential Equation [5L]: Stability analysis of nonautonomous systems, use of comparison lemma to analyze stability, boundedness and ultimate boundedness, concept of input to state stability, center manifold theorems, region of attraction, invariance like theorems.
Input Output Stability Analysis [3L] : Introduction to L-P space, L Stability analysis of state modelys, small gain theorem.
Introduction to Passivity [2 L]: Basic Concept, L2 and Lyapunov Stability, Passivity Theorem.
Frequency Domain Analysis of Nonlinear Systems [2 L]: Circle Criteria, Popov Criteria, Harmonic Linearization and Describing Function.
Controller Design for Nonlinear Systems[ 4L]: Feedback Linearization: Motivation of designing a nonlinear control law, Input-State linearization, input-output linearization, Constraints of the feedback-based design, Sliding Mode Control, Lyapunov redesign, Backstepping based design, example of designing control law for the benchmark nonlinear systems (e.g. rotating pendulum system, TORA, VTOL, USV, WMR, etc.)
Course Objectives
- Elaborating salient features of the nonlinear differential equations
- Explaining the stability analysis tools of the nonlinear systems.
- Introducing different advanced analysis techniques for nonautonomous nonlinear systems.
- To introduce the design techniques of nonlinear controllers for different complicated dynamical systems.
Course Outcomes
After attending this course, students should be able to: <br />1) Recommend suitable order nonlinear models for capturing the critical information of complicated dynamical systems. <br />2) Analyse the stability of nonlinear systems using LaSalle's invariance theorem and determine the region of attraction for the same. <br />3)Determine a suitable analysis tool for assessing the stability of the autonomous and nonautonomous nonlinear systems <br />4)Utilize the concept of Lebsigue space to analyze the stability of the nonlinear systems subject to different excitation signals. <br />5)Discuss the passivity-based analysis and its relation with frequency response analysis of the same. <br /> <br />6)Design nonlinear control law to address the performance issues of complicated systems.
Essential Reading
- H. K. Khalil, Nonlinear Systems, Prentice Hall, 3rd ed., 2002
- J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991
Supplementary Reading
- Nijemjer and A. van der schaft, Nonlinear dynamical control systems, Springer, 1989
- M. Vidyasagar, Nonlinear Systems Analysis, Society for Industrial and Applied Mathematics, 2002.