Linear Control Engineering

Academic Year 2025-26 (Odd)

The objectives of Control Engineering are as follows:

• To introduce the concept of open loop and closed loop (feedback) systems
• To provide knowledge of time domain and frequency domain analysis of control systems.
• To present the compensation technique that can be used to stabilize control systems

Course Outcomes:

At the end of the course the students will be able to: 

• Describe mathematical models of feedback control systems in terms of differential equations, transfer functions and state-space representation. (Understand)
• Apply Laplace transform to illustrate different specifications of the control system using transfer function model. (Apply) 
• Analyze the stability and system performance in time , frequency and state space domain. (Analyze) 
• Analyze the needs of different types of controllers and compensators to ascertain the required dynamic response from the system. (Analyze)
• Assess the techniques for improving the system performance in time and frequency domain. (Evaluate)
• Design mechanical and electrical control systems using Matlab /Simulink with control system. (Apply)

Text Books:

1. M.Gopal,"Control Systems - Principles and Design," TataMcGrawHill, 4th  Edition, 2012.
2. J. Nagrath and M. Gopal, "Control System Engineering,"  New Age International Publishers, 5th Edition, 2009.

Reference Books: 

1. Norman S. Nise, "Control Systems Engineering," 6th edition, Wiley, 2011.
2. Richard C. Dorfand, Robert H. Bishop, "Modern Control Systems," 12th Edition, Prentice Hall, 2011.
3. Benjamin C Kuo, "Automatic Control Systems," Prentice Hall of India, 6th Edition, 2013. 

Detailed Syllabus and Handouts:

Unit-I: Control Systems Modelling

1. Introduction to Control Systems: Terminology and Bacis Structure: 
2. Open Loop and Closed Loop Systems:
3. Feed Forward and Feedback Control Theory: 
4. Mechanical and Electrical Transfer Function Models: Handouts, video
5. Block Diagram Models: Handouts
6. Signal Flow Graph Models: 

Additional Problems: pdf

Unit-II: Time Response Analysis  Handouts: Part1, Part2

1. Transient response:
2. Steady State Response:
3. Measures of performance of the standard first order and second order systems:
4. Steady error constant and systems:
5. Type Number:
6. PID control and Analytical design for PD, PI and PID control systems.

Unit-III: Frequency Response and System Analysis

1. Close loop frequency response
2. Performance specification in frequency domain 
3. Frequency response of standard second order system
4. Bode plot
5. Polar plot
6. Nyquist plots
7. Design of compensators using Bode plots

Unit-IV: Stability Analaysis

1. Concept of Stability
2. Bounded Input Bounded Output Stability
3. Routh Stability: 
4. Root Locus: Handouts,  video1, video2
5. Nyquist Stability Criterion

Unit-V: Control System Analysis using State Variable Methods

1. State Variable Representation: Handouts
2. Conversion of state variable methods to transfer function
3. Conversion of transfer function to state variable models
4. Solution of state equations
5. Concepts of Controllability and Observability: Handouts
6. Stability of Linear Systems