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- 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.

- 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.

**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.

Introduction to Control System: Basic Concepts of Control Systems

Open loop and closed loop systems, Servomechanisms

**Practice:** Study of Temperature control system (using Hardware)

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

Mathematical Models of Physical Systems & Differential equations

Mechanical Systems: Translational Systems, Rotational systems

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

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

Derivation of Transfer Functions(TF): Definition,Advantages,Disadvantages,Procedure,Terminology

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

**PPT:** Signal Flow Graph

Application of Mason's Gain Formula

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

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

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

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

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

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

**PPT:** Steady State Error

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

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

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

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

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

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

Steps to draw Root Locus

Construction of Root Locus

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

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

Frequency Response Analysis: Definition,Frequency domain specifications

Derivation of Resonant peak and Bandwidth

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

Determination of G.M & P.M

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

Controllers: Concept of Proportional, Derivative and Integral Control actions

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

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

Amit Kumar Sahoo has completed his PhD in 2021 from Birla Institute of Technology, Mesra, India. In 2010, he has completed his Master’s degree in Electrical & Electronics Engineering from National Institute of Technology, Rourkela, India with Power System and Control specialization. He is presently working as an Assistant Professor […]

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