JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives:

• 1. To provide various methods of analysis and design of nonlinear control systems.
• 2. To introduce nonlinear deterministic dynamical systems, and their applications to nonlinear circuits and control systems.

Course Outcomes

Upon the completion of this course, the student will be able to

• 1. Know control systems of practical importance are inherently nonlinear,
• 2. Analyze nonlinear systems and controllers.
• 3. Apply various stability criteria to control systems

UNIT - I

Phase plane analysis: Phase portraits, Singular points characterization. Analysis of non-linear systems using phase plane technique. Existence of limit cycles. Linearization: Exact linearization, input - state linearization, input - output linearization.

UNIT - II

Linear versus nonlinear systems - Describing function analysis: Fundamentals, common nonlinearities (saturation, dead-zone, on-off non-linearity, backlash, hysteresis) and their describing functions. Describing function analysis of nonlinear systems. Reliability of describing method analysis. Compensation and design of nonlinear system using describing function method.

UNIT - III

Concept of stability, stability in the sense of Lyapunov and absolute stability. Zero-input and BIBO stability. Second (or direct) method of Lyapunov stability theory for continuous and discrete time systems. Aizerman's and Kalman's conjecture. Construction of Lyapunov function - Methods of Aizerman, Zubov, Variable gradient method. Lure problem.

UNIT - IV

Popov's stability criterion, generalized circle criterion, Kalman - Yakubovich - Popov Lemma. Popov's hyperstability theorem.

UNIT - V

Concept of variable - structure controller and sliding control, reaching condition and reaching mode, implementation of switching control laws. Reduction of chattering in sliding and steady state mode. Some design examples of nonlinear systems such as the ball and beam, flight control, magnetic levitation and robotic manipulator etc.

TEXT BOOKS:

• 1. J. E. Slotine and Weiping LI, Applied Nonlinear Control, Prentice Hall,
• 2. Hassan K. Khalil, Nonlinear Systems, Prentice Hall, 1996

REFERENCES:

• 1. Sankar Sastry, Nonlinear Systems Analysis, Stability and Control.
• 2. M. Vidyasagar, Nonlinear Systems Analysis, Prentice - Hall International editions,1993. R19 M.TECH CONTROL ENGINEERING. / CONTROL SYSTEM M. Tech – I Year – II Sem. (Control Engg. / Control Sys.)