System Modeling and Control
Teacher
Dr. Amit Kumar Sahoo
Category
Core Courses
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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.
Course Outcomes
| COs | Course outcomes | Mapping COs with POs (High-3, Medium-2, Low-1) |
| CO1 | Able to gain Knowledge on action of controller and its application to control a system |
PO1 ( 3), |
| CO2 | Able to analyze the system and controller | PO2(3), PO5(2) |
| CO3 | Acquire skill of designing automatic control system and controller for a particular application. |
PO3(3) |
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 Plan
Session 1
Introduction to Control System: Basic Concepts of Control Systems
Introduction to Control System: Basic Concepts of Control Systems
Session 2
Open loop and closed loop systems, Servomechanisms
Session 4
Transfer functions, Concept of Pole and Zero
PPT: Transfer Function
https://www.youtube.com/watch?v=20UH_CJJbvE
Session 5
Practice: Study of Temperature control system (using Hardware)
https://www.youtube.com/watch?v=bZNKURutM3g
Session 6
Practice: Find the poles, zeros, gain and draw the pole-zero plot of the transfer function (using MATLAB)
https://www.youtube.com/watch?v=3pvntT0Sdr8
Session 7
Mathematical Models of Physical Systems & Differential equations
PPT: Mathematical Models of Physical Systems
https://www.youtube.com/watch?v=r8vfbfjJAmU&list=PLBlnK6fEyqRjJX8dN7-tHsDePtmTsRkYE
Session 8
Mechanical Systems: Translational Systems, Rotational systems
https://www.youtube.com/watch?v=glUrzUxbepE
Session 9
Electrical Systems: Resistance,Inductance,Capacitance,R-L-C Series & Parallel circuit
Electrical Systems Resistance,Inductance,Capacitance,R-L-C Series & Parallel circuit
https://www.youtube.com/watch?v=01hhrkDa6ZE
Session 10
Analogy between Mechanical & Electrical Quantities: Force-Voltage analogy,Force-Current analogy
https://www.youtube.com/watch?v=RUwQkXroaig
Session 11
Derivation of Transfer Functions(TF): Definition,Advantages,Disadvantages,Procedure,Terminology
https://www.youtube.com/watch?v=WrVk_lT60dk
Session 12
Block Diagram Algebra: Definition,Block diagram reduction techniques
PPT: Block Diagram
https://www.youtube.com/watch?v=t_k7oRICmWo
Session 13
Signal Flow Graph(SFG): Definition,Properties,Terminology,Methods to obtain SFG
PPT: Signal Flow Graph
https://www.youtube.com/watch?v=vr4Hc0SNghQ
Session 14
Session 15
Practice: Find the transfer function from given block diagram (using MATLAB)
https://www.youtube.com/watch?v=viVu50wYESY
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
https://www.youtube.com/watch?v=AnB6VR-g6PI
Session 18
Time Response of Second order system to unit step input : Derivation of output for Under damped,Over damped ,Critically damped cases
https://www.youtube.com/watch?v=6wzGCM_EJgU
Session 19
Time Response specifications: Delay time,Rise time,Peak time,Maximum overshoot,Settling time
PPT: Time Response Specification
https://www.youtube.com/watch?v=09KiUkzR2nA
Session 20
Steady State Errors and Static Error Constants: Derivation,Static Error Constants of different types of systems
PPT: Steady State Error
https://www.youtube.com/watch?v=_p6w7oztrwQ
Session 21
Practice: Time response of first order systems to unit step and unit ramp inputs (using MATLAB/DYMOLA)
https://www.youtube.com/watch?v=vhwwro2Pg8Y
Session 22
Practice: Time Response of Second order systems to unit step input (using MATLAB/DYMOLA)
https://www.youtube.com/watch?v=RfjQeS7sOWk
Session 23
Practice: Determine the steady state error of the given system (using MATLAB)
https://www.youtube.com/watch?v=smYnPJLwQjI
Session 24
Stability and Algebraic Criteria: Definitions,Concept,condition,Hurwitz Stability Criterion
https://www.youtube.com/watch?v=cyannwIgg1E
Session 25
Stability and Algebraic Criteria : Routh Array,two-Special Cases
https://www.youtube.com/watch?v=yg1ZJccfoQE
Session 26
Application of the Routh's stability criterion to linear feedback system
https://www.youtube.com/watch?v=nzZ19jKm-jk&list=PLBlnK6fEyqRgyaWjvSyL5A3ozNcg8_ziw
Session 27
Root Locus Techniques: Definition,Conditions
PPT: Root Locus Technique
https://www.youtube.com/watch?v=4cMHfTsPz3M&list=PLgwJf8NK-2e78NzXFirvPmyRzH_JE53tW
Session 29
Construction of Root Locus
https://www.youtube.com/watch?v=4cMHfTsPz3M&list=PLgwJf8NK-2e78NzXFirvPmyRzH_JE53tW
Session 30
Determination of roots From Root Locus For a specified open loop gain
https://www.youtube.com/watch?v=SxmS7C2ppbA
Session 31
Practice: Construct the root locus for 2nd & 3rd order system and analyze its stability (Gain) (using MATLAB)
https://www.youtube.com/watch?v=6-TDhsCUIZA
Session 32
Frequency Response Analysis: Definition,Frequency domain specifications
https://www.youtube.com/watch?v=Rvyus824Gfs
Session 33
Session 34
correlation between Time and Frequency Response with respect to second order system
https://www.youtube.com/watch?v=KKHsh-KohJE
Session 38
Practice: Construct the bode plot for 2nd and 3rd order system and analyze its stability (PM & GM) (using MATLAB)
https://www.youtube.com/watch?v=6Zl_B4AcmRM
Session 39
Controllers: Concept of Proportional, Derivative and Integral Control actions
PPT: Controllers
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)
https://www.youtube.com/watch?v=O0MORdtWG6M
Case Studies
Case Studies
Our Main Teachers
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 Associate Professor […]