Linear Control Systems
- 1. Models for Control System
1.1 Introduction: Open loop and closed loop systems; feedback and feed-forward control structure; examples of control systems.
1.2 Mathematical Modelling: Types of models; Impulse response model; State Variable model and Transfer function model for Electrical, Mechanical and Thermal systems
1.3 Manipulations: Block Diagram Representation of complex systems, Block diagram reduction, Signal flow graph and the Mason’s gain rule for determining overall transfer
- 2. Time Response Analysis
2.1 Dynamic Response: Standard test signals; Transient and steady state behaviour of first and second order systems
2.2. Performance Specifications for a second order system and derivations for rise time, settling time, peak time, peak overshoot and steady state error
2.3. Steady State errors in feedbackcontrol systems and their types, Error constants and type of system
- 3. State Variable Models
3.1 State variable models: State variable models of electrical systems
3.2 State transition equation: Concept of state transition matrix; Properties of state transition matrix; Solution of homogeneous systems; solution of non-homogeneous systems
3.3 Controllability and Observability: Concept of controllability; Controllability analysis of LTI systems; Concept of observability; Observability analysis of LTI systems using Kalman approach
- 4. Stability Analysis in Time Domain
4.1 Concepts of Stability: Concept of absolute, relative and robust stability; Routh stability criterion
4.2 Root Locus Analysis: Root-locus concepts; General rules for constructing root-locus; Root-locus analysis of control systems
5. Stability Analysis in Frequency Domain
5.1 Introduction: Frequency domain specifications, Response peak and peak resonating frequency; Relationship between time and frequency domain specifications of system; Stabili