# System Modeling and Control

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# Code(Credit) : CUTM1053 (3-1-0) 4

## Course Objectives

• To teach how to convert a physical systems consist of mechanical and electrical system into a mathematical model.
• Analysis of a live system in time domain and frequency domain and  application of controllers to get the desired response.

## Learning Outcomes

• Students will understand the basics of a system.
• Student  gain knowledge on stability of a system.
• Student will analyse the system and controller.
• Students will develop skill of designing automatic control system and controller for a particular application.

## Course Syllabus

Module I: Introduction (6 Hours)
Theory
Introduction to Control Systems: Basic Concepts of Control Systems, Open loop and closed loop systems; Servomechanisms, Laplace transform and Transfer functions using Laplace transform, Concept of Pole and Zero.

Practice: Hardware/MATLAB
1. Study of Temperature control system using open loop and closed loop control circuit.
2. Using MATLAB, find the poles, zeros, gain and draw the pole-zero plot of the transfer function.

Module II: System Dynamics (10 Hours)
Theory
Mathematical Models of Physical Systems: Differential Equations of Physical Systems, Mechanical Translational Systems, Rotational systems, Electrical Systems, Analogy between Mechanical and electrical quantities, Derivation of Transfer functions, Block Diagram Algebra, Signal Flow Graphs and Mason’s Gain Formula.

Practice: MATLAB
3. Using MATLAB, find the transfer function from given block diagram.

Module III: Time Response Analysis (8 Hours)
Theory
Time Response Analysis: Type Test Signals, Time response of first order systems to unit step and unit ramp inputs, Time Response of Second order systems to unit step input, Time Response specifications, Steady State Errors and Static Error Constants of different types of systems.

Practice: MATLAB/DYMOLA
4. Standard Test Signals
5. Time response of first order systems to unit step and unit ramp inputs
6. Time Response of Second order systems to unit step input
7. Using MATLAB, determine the steady state error of the given system.

Module IV: Stability in Time Domain (4 Hours)
Theory
Stability in Time Domain: Stability and Algebraic Criteria, concept of stability, Necessary conditions of stability, Hurwitz stability criterion, Routh stability criterion and Application of the Routh stability criterion to linear feedback system.

Module V: Root Locus Technique (5 Hours)
Theory
Root Locus Technique: Root locus concepts, Rules of Construction of Root locus and Determination of Roots from Root locus for a specified open loop gain.

Practice: MATLAB
8. Construct the root locus for 2nd & 3rd order system and analyze its stability (Gain)

Module VI: Frequency Response Analysis (6 Hours)
Theory
Frequency Response Analysis: Frequency domain specifications, correlation between Time and Frequency Response with respect to second order system, Bode plot, Determination of Gain Margin and Phase Margin from Bode plot.

Practice: MATLAB
9. Construct the bode plot for 2nd and 3rd order system and analyze its stability (PM & GM)

Module VII: Controllers (4 Hours)
Theory
Controllers: Concept of Proportional, Derivative and Integral Control actions, P, PD, PI and PID controllers.

Practice: MATLAB/DYMOLA
10. Design of P,PD, PI and PID Controller for 2ndor 3rdorder system

Text Books:
1. Saeed S. Hasan, “Automatic Control Systems,”Kataria Publication, 9th Edition-2017.

Reference Books:
1. Nagrath J. and Gopal M., “Control Systems Engineering,” New Age International Publishers, 6th Edition-2017.

## Session 1

Introduction to Control System: Basic Concepts of Control Systems

## Session 2

Open loop and closed loop systems, Servomechanisms

## Session 3

Laplace transform

## Session 4

Transfer functions, Concept of Pole and Zero

## Session 5

Practice: Study of Temperature control system (using Hardware)

## Session 6

Practice: Find the poles, zeros, gain and draw the pole-zero plot of the transfer function (using MATLAB)

## Session 7

Mathematical Models of Physical Systems & Differential equations

## Session 8

Mechanical Systems: Translational Systems, Rotational systems

## Session 9

Electrical Systems: Resistance,Inductance,Capacitance,R-L-C Series & Parallel circuit

## Session 10

Analogy between Mechanical & Electrical Quantities: Force-Voltage analogy,Force-Current analogy

## Session 12

Block Diagram Algebra: Definition,Block diagram reduction techniques

PPT: Block Diagram

## Session 13

Signal Flow Graph(SFG): Definition,Properties,Terminology,Methods to obtain SFG

## Session 14

Application of Mason's Gain Formula

## Session 15

Practice: Find the transfer function from given block diagram (using MATLAB)

## Session 16

Time Response Analysis: Basic Concepts,Standard Test Signals(Step,Ramp,Parabolic,Impulse)

## Session 17

Time Response of First order systems to unit step & unit ramp inputs: Derivation of Error and Output

## Session 18

Time Response of Second order system to unit step input : Derivation of output for Under damped,Over damped ,Critically damped cases

## Session 19

Time Response specifications: Delay time,Rise time,Peak time,Maximum overshoot,Settling time

## Session 20

Steady State Errors and Static Error Constants: Derivation,Static Error Constants of different types of systems

## Session 21

Practice: Time response of first order systems to unit step and unit ramp inputs (using MATLAB/DYMOLA)

## Session 22

Practice: Time Response of Second order systems to unit step input  (using MATLAB/DYMOLA)

## Session 23

Practice: Determine the steady state error of the given system (using MATLAB)

## Session 24

Stability and Algebraic Criteria: Definitions,Concept,condition,Hurwitz Stability Criterion

## Session 25

Stability and Algebraic Criteria : Routh Array,two-Special Cases

## Session 26

Application of the Routh's stability criterion to linear feedback system

## Session 27

Root Locus Techniques: Definition,Conditions

## Session 28

Steps to draw Root Locus

## Session 29

Construction of Root Locus

## Session 30

Determination of roots From Root Locus For a specified open loop gain

## Session 31

Practice: Construct the root locus for 2nd & 3rd order system and analyze its stability (Gain) (using MATLAB)

## Session 32

Frequency Response Analysis: Definition,Frequency domain specifications

## Session 33

Derivation of Resonant peak and Bandwidth

## Session 34

correlation between Time and Frequency Response with respect to second order system

## Session 35 & 36

Bode Plot: Definition,Steps to sketch the bode plot

PPT:  Bode Plot

## Session 37

Determination of G.M & P.M

## Session 38

Practice: Construct the bode plot for 2nd and 3rd order system and analyze its stability (PM & GM) (using MATLAB)

## Session 39

Controllers: Concept of Proportional, Derivative and Integral Control actions

## Session 40

Implementation of P,I,D,PI,PD,PID Controllers

## Session 41 & 42

Practice: Design of P,PD, PI and PID Controller for 2nd or 3rd order system (using MATLAB/DYMOLA)