Modern Control Theory

15A02704

UNIT – I

STATE VARIABLE DESCRIPTION AND SOLUTION OF STATE EQUATION

Concept of State – Derivation of State Space models for Linear Continuous time Systems from Schematic Models, Differential equations, Transfer functions and block diagrams – Non uniqueness of state model – State diagrams for continuous time state models – Solution of state equations – State transition matrix. Complete response of continuous time systems.

 
UNIT – II

CONTROLLABILITY, 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 of state models in Jordan canonical form and other canonical forms. Effect of state feedback on controllability and observability.

UNIT – III

STATE FEEDBACK CONTROLLERS AND OBSERVERS

Design of State Feedback Controllers through Pole placement. Full-order observer and reduced-order observer. State estimation through Kalman Filters.

UNIT – IV

ANALYSIS OF NONLINEAR SYSTEMS

Introduction to nonlinear systems, Types of nonlinearities, Concept of describing functions, Derivation of describing functions for Dead zone, Saturation, backlash, relay with dead zone and Hysteresis – Jump Resonance. 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 Linear and Nonlinear continuous time autonomous systems.

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