MODERN CONTROL THEORY (SYLLABUS MTECH-EPS I SEM)

UNIT–I: MATHEMATICAL PRELIMINARIES
Fields, Vectors and Vector Spaces – Linear combinations and Bases – Linear Transformations
and Matrices – Scalar Product and Norms – Eigen-values, Eigen Vectors and a Canonical form
representation of Linear operators – The concept of state – State Equations for Dynamic systems
– Time invariance and Linearity – Non-uniqueness of state model – State diagrams for
Continuous-Time State models.
UNIT-II: STATE VARIABLE ANALYSIS
Linear Continuous time models for Physical systems– Existence and Uniqueness of Solutions to
Continuous-Time State Equations – Solutions of Linear Time Invariant Continuous-Time State
Equations – State transition matrix and its properties. General concept of controllability – General
concept of Observability – Controllability tests for Continuous-Time Invariant Systems –
Observability tests for Continuous-Time Invariant Systems – Controllability and Observability of
State Model in Jordan Canonical form – Controllability and Observability Canonical forms of State
model.

UNIT-III: NON LINEAR SYSTEMS
Introduction – Non Linear Systems - Types of Non-Linearities – Saturation – Dead-Zone -
Backlash – Jump Phenomenon etc;– Singular Points – Introduction to Linearization of nonlinear
systems, Properties of Non-Linear systems – Describing function–describing function analysis of
nonlinear systems – Stability analysis of Non-Linear systems through describing functions.
Introduction to phase-plane analysis, Method of Isoclines for Constructing Trajectories, singular
points, phase-plane analysis of nonlinear control systems.
UNIT-IV: STABILITY ANALYSIS
Stability in the sense of Lyapunov, Lyapunov’s stability and Lypanov’s instability theorems -
Stability Analysis of the Linear continuous time invariant systems by Lyapunov second method –
Generation of Lyapunov functions – Variable gradient method – Krasooviski’s method. State
feedback controller design through Pole Assignment – State observers: Full order and Reduced
order.
UNIT-V: OPTIMAL CONTROL
Introduction to optimal control - Formulation of optimal control problems – calculus of variations –
fundamental concepts, functional, variation of functional – fundamental theorem of theorem of
Calculus of variations – boundary conditions – constrained minimization – formulation using
Hamiltonian method – Linear Quadratic regulator.
TEXT BOOKS:
1. Modern Control System Theory by M.Gopal – New Age International -1984
2. Modern Control Engineering by Ogata.K – Prentice Hall - 1997
REFERENCES:
1. Optimal control by Kircks