# JNTU Syllabus

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

IV Year B.Tech EEE. II-Sem T P C
4+1* 0 4
(ELECTIVE – III)
Objective :
This subject deals with state space, describing function, phase plane and stability analysis including
controllability and observability. It also deals with modern control and optimal control systems.
UNIT – I STATE SPACE ANALYSIS
State Space Representation, Solution of State Equation, State Transition Matrix, Canonical Forms –
Controllable Canonical Form, Observable Canonical Form, Jordan Canonical Form.
UNIT – II CONTROLLABILITY AND OBSERVABILITY
Tests for controllability and observability for continuous time systems – Time varying case, minimum
energy control, time invariant case, Principle of Duality, Controllability and observability form Jordan
canonical form and other canonical forms.
UNIT – III DESCRIBING FUNCTION ANALYSIS
Introduction to nonlinear systems, Types of nonlinearities, describing functions, describing function
analysis of nonlinear control systems.
UNIT-IV PHASE-PLANE ANALYSIS
Introduction to phase-plane analysis, Method of Isoclines for Constructing Trajectories, singular points,
phase-plane analysis of nonlinear control systems.
UNIT-V STABILITY ANALYSIS
Stability in the sense of Lyapunov., Lyapunov’s stability and Lypanov’s instability theorems. Direct method
of Lypanov for the Linear and Nonlinear continuous time autonomous systems.
UNIT – VI MODAL CONTROL
Effect of state feedback on controllability and observability, Design of State Feedback Control through
Pole placement. Full order observer and reduced order observer.
UNIT-VII CALCULUS OF VARIATIONS
Minimization of functionals of single function, Constrained minimization. Minimum principle. Control
variable inequality constraints. Control and state variable inequality constraints. Euler Lagrangine
Equation.
UNIT –VIII OPTIMAL CONTROL
Formulation of optimal control problem. Minimum time, Minimum energy, minimum fuel problems. State
regulator problem. Output regulator problem. Tracking problem, Continuous-Time Linear Regulators.

TEXT BOOKS:
1. Modern Control System Theory – by M. Gopal, New Age International Publishers, 2nd edition,
1996

REFERENCE BOOKS:
1. Modern Control Engineering – by K. Ogata, Prentice Hall of India, 3rd edition, 1998
2. Control Systems Engineering by I.J. Nagarath and M.Gopal, New Age International (P) Ltd.
3. Digital Control and State Variable Methods – by M. Gopal, Tata Mc Graw-Hill Companies, 1997.
4. Systems and Control by Stainslaw H. Zak , Oxford Press, 2003.