MODULE 1

Introduction: Basic Components of a Control System, Open-Loop Control Systems and Closed-Loop Control Systems, Examples of control system

Feedback and its effects: Types of Feedback Control Systems, Linear versus Nonlinear Control Systems, Time-Invariant versus Time-Varying Systems.

Mathematical modelling of control systems: Electrical Systems and Mechanical systems.

Transfer Function from Block Diagrams and Signal Flow Graphs: impulse response and its relation with transfer function of linear systems. Block diagram representation and reduction methods, Signal flow graph and Mason’s gain formula 

Module 2:

Time Domain Analysis of Control Systems: Introduction- Standard Test signals, Time response specifications.

Time response of first and second order systems to unit step input and ramp inputs, time domain specifications.

Steady state error and static error coefficients.

Frequency domain analysis: Frequency domain specifications, correlation between time and frequency responses.

Module 3:

Stability of linear control systems: Concept of BIBO stability, absolute stability, Routh Hurwitz Criterion, Effect of P, PI & PID controllers.

Root Locus Techniques: Introduction, properties and its construction, Application to system stability studies. Illustration of the effect of addition of a zero and a pole.

Module 4

Nyquist stability criterion: Fundamentals and analysis

Relative stability: gain margin and phase margin. Stability analysis with Bode plot.

Design of Compensators: Need of compensators, design of lag and lead compensators using Bode plots.

Module 5:

State Variable Analysis of Linear Dynamic Systems: State variables, state equations, state variable representation of electrical and mechanical systems, dynamic equations, merits for higher order differential equations and solution.

Transfer function from State Variable Representation, Solutions of the state equations, state transition matrix

Concept of controllability and observability and techniques to test them - Kalman’s Test.