503103: Non Linear Control Systems
Teaching Scheme Examination Scheme
Theory: 3 Hrs/Week Paper: 100 Marks
Unit I: Introduction to Non Linear System
Classification of non-linearity, types of non-linearity in physical system, jump phenomena and critical
jump resonance curve, methods of analysis of non-linear systems and comparison, linearization, slope,
isoclines, singular point, limit cycle. (6 Hrs.)
Unit II: Phase Plane Analysis
Concept of phase plane, phase trajectory, phase portraits, methods of plotting phase plane trajectories
Vander Pol’s equation, stability from phase portrait, time response from trajectories, isoclines method,
Pell's method of phase trajectory, Delta method of phase trajectory construction. (6 Hrs.)
Unit III: Frequency Domain Analysis
Absolute stability, circle criterion, Popov criterion Describing function, DF of typical nonlinearities
stability analysis using DF method, DIDF, pole zero shifting transformation. (6 Hrs.)
Unit IV: Liapunov Stability
Autonomous Systems: Stability of equilibrium point. Concepts of positive definite/semi definite,
negative definite/ semi definite, indefinite functions, Lyapunov function Liapunov Stability:
asymptotic stability, global asymptotic stability. (6 Hrs.)
Unit V: Stability Criterion
Linear systems, linearization of nonlinear systems about equilibrium point. Liapunov's indirect
method. Stability analysis of nonlinear system using Liapunov's theorem. (8 Hrs.)
Unit VI: Nonlinear Control Design
Feedback linearization, Input Output linearization, sliding mode control (4 Hrs.)
Text Book:
1. Automatic Control System: George J. Thaler Brown, Jaico Publications
2. Nonlinear Systems: Hasan A. Khalil, Printece Hall of India
Reference Book:
1. Control Systems Theory and Application: Samarjit Ghosh, Pearson Education
2. Control System Engineering: Nagrath and Gopal, Wiley Eastern
3. Introduction to Control Engineering: A. K. MandaI, New Age International Publications
Reference http://www.unipune.ernet.in/stud_info/Syllabi/Syllabus_2008.html
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