Course Details
Subject {L-T-P / C} : EE6306 : Nonlinear Control { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Shubhobrata Rudra
Syllabus
| Module 1 : |
Introduction and Mathematical Preliminaries [3 L]: Modeling complex systems as nonlinear systems, motivating examples, detailed discussions on practical nonlinear systems and their salient features, necessary mathematical tools. |
| Module 2 : |
Analysis of second order Nonlinear systems [2L]: Phase Plane Analysis techniques, Poincare Bendixon theorem for limit cycle detection. |
| Module 3 : |
Stability of equilibrium points and Region of Attractions [10 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. Stability analysis of nonautonomous systems, use of comparison lemma to analyze stability, |
| Module 4 : |
Mid Semester |
| Module 5 : |
Input-state and Input-output stability [5L]: Boundedness and ultimate boundedness, concept of input to state stability, Input Output Stability Analysis, Introduction to L-P space, L Stability analysis of state models, small gain theorem. |
| Module 6 : |
Passivity [4 L]: Memoryless functions and Sector Nonlinearities, PRTF & Lyapunov Feedback systems, Lure’s Problem, Circle & Popov Criteria |
| Module 7 : |
Controller Design for Nonlinear Systems [6L]: Normal form, Controller form, Concepts & linearization, Feedback linearization, Sliding Mode Control |
Course Objective
| 1 . |
Elaborating salient features of the nonlinear differential equations |
| 2 . |
Explaining the stability analysis tools of the nonlinear systems. |
| 3 . |
Introducing different advanced analysis techniques for nonautonomous nonlinear systems. |
| 4 . |
To introduce the design techniques of nonlinear controllers for different complicated dynamical systems. |
Course Outcome
| 1 . |
Find out the fixed point of a given nonlinear dynamical system and explore the possibilities of carrying out linear analysis. |
| 2 . |
Analyse the stability of nonlinear systems using LaSalle's invariance theorem and determine the region of attraction for the same. |
| 3 . |
Determine a suitable analysis method for assessing the stability of the autonomous and nonautonomous nonlinear systems |
| 4 . |
Utilize the Lebsigue space concept to analyse the nonlinear systems' stability subject to different excitation signals. |
| 5 . |
Carry out the passivity analysis for a given system. |
| 6 . |
Design nonlinear control law to address the performance issues of complicated nonlinear systems. |
Essential Reading
| 1 . |
H. K. Khalil, , Nonlinear Systems, , Prentice Hall, 3rd ed., 2002 |
| 2 . |
J. J. E. Slotine and W. Li, , Applied Nonlinear Control,, Prentice Hall, 1991 |
Supplementary Reading
| 1 . |
H. Nijemjer and A. van der schaft,, Nonlinear dynamical control systems, Springer, 1989 |
Journal and Conferences
| 1 . |