THIS PPT IS SO USEFUL FOR THE CONTROL SYSTEM STUDENTS MOSTLY. THIS PPT MAINLY DISCUSSED ABOUT THE IMPULSE RESPONSE OF SECOND ORDER SYSTEM
AND THE CHARACTERISTICS OF THE SYSTEM AND STABILITY FACTOR OF THE SYSTEM AN THIS PPT CONTAINS A MATLAB CODING AND SIMULATION AND THE RESULTS ARE ALSO PLOTED IN THE PPT . SO IT IS SO USEFUL TO THE STUDENTS
It gives how states are representing in various canonical forms and how it it is different from transfer function approach. and finally test the system controllability and observability by kalman's test
This Presentation explains about the introduction of Frequency Response Analysis. This video clearly shows advantages and disadvantages of Frequency Response Analysis and also explains frequency domain specifications and derivations of Resonant Peak, Resonant Frequency and Bandwidth.
It gives how states are representing in various canonical forms and how it it is different from transfer function approach. and finally test the system controllability and observability by kalman's test
This Presentation explains about the introduction of Frequency Response Analysis. This video clearly shows advantages and disadvantages of Frequency Response Analysis and also explains frequency domain specifications and derivations of Resonant Peak, Resonant Frequency and Bandwidth.
Mathematical Modelling of Control SystemsDivyanshu Rai
Different types of mathematical modeling in control systems [which include Mathematical Modeling of Mechanical and Electrical System (which further includes, Force-Voltage and Force-Current Analogies)]
state space modeling of electrical systemMirza Baig
Introduction
As systems become more complex, representing them with differential equations or transfer functions becomes cumbersome. This is even more true if the system has multiple inputs and outputs. This document introduces the state space method which largely alleviates this problem. The state space representation of a system replaces an nth order differential equation with a single first order matrix differential equation. The state space representation of a system is given by two equations :
The first equation is called the state equation, the second equation is called the output equation. For an nth order system (i.e., it can be represented by an nth order differential equation) with r inputs and m outputs the size of each of the matrices is as follows:
Several features:The state equation has a single first order derivative of the state vector on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.The output equation has the output on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.
q is nx1 (n rows by 1 column)q is called the state vector, it is a function of timeA is nxn; A is the state matrix, a constantB is nxr; B is the input matrix, a constant u is rx1; u is the input, a function of time C is mxn; C is the output matrix, a constant D is mxr; D is the direct transition matrix, a constant y is mx1; y is the output, a function of time
Derivation of of State Space Model (Electrical)
To develop a state space system for an electrical system, they choosing the voltage across capacitors, and current through inductors as state variables. Recall that
so if we can write equations for the voltage across an inductor, it becomes a state equation when we divide by the inductance (i.e., if we have an equation for einductor and divide by L, it becomes an equation for diinductor/dt which is one of our state variable). Likewise if we can write an equation for the current through the capacitor and divide by the capacitance it becomes a state equation for ecapacitor
There are three energy storage elements, so we expect three state equations. Try choosing i1, i2 and e1 as state variables. Now we want equations for their derivatives. The voltage across the inductor L2 is e1 (which is one of our state variables)so our first state variable equation is
This equation has our input (ia) and two state variable (iL2 and iL1) and the current through the capacitor. So from this we can get our second state equation
Our third, and final, state equation we get by writing an equation for the voltage across L1 (which is e2) in terms of our other state variables
references:
http://lpsa.swarthmore.edu/Representations/SysRepSS.html
https://en.wikipedia.org/wiki/State-space_representation
Transfer Function and Mathematical Modeling
Transfer Function
Poles And Zeros of a Transfer Function
Properties of Transfer Function
Advantages and Disadvantages of T.F.
Translation motion
Rotational motion
Translation-Rotation counterparts
Analogy system
Force-Voltage analogy
Force-Current Analogy
Advantages
Example
state space representation,State Space Model Controllability and Observabilit...Waqas Afzal
State Variables of a Dynamical System
State Variable Equation
Why State space approach
Block Diagram Representation Of State Space Model
Controllability and Observability
Derive Transfer Function from State Space Equation
Time Response and State Transition Matrix
Eigen Value
Mathematical Modelling of Control SystemsDivyanshu Rai
Different types of mathematical modeling in control systems [which include Mathematical Modeling of Mechanical and Electrical System (which further includes, Force-Voltage and Force-Current Analogies)]
state space modeling of electrical systemMirza Baig
Introduction
As systems become more complex, representing them with differential equations or transfer functions becomes cumbersome. This is even more true if the system has multiple inputs and outputs. This document introduces the state space method which largely alleviates this problem. The state space representation of a system replaces an nth order differential equation with a single first order matrix differential equation. The state space representation of a system is given by two equations :
The first equation is called the state equation, the second equation is called the output equation. For an nth order system (i.e., it can be represented by an nth order differential equation) with r inputs and m outputs the size of each of the matrices is as follows:
Several features:The state equation has a single first order derivative of the state vector on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.The output equation has the output on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.
q is nx1 (n rows by 1 column)q is called the state vector, it is a function of timeA is nxn; A is the state matrix, a constantB is nxr; B is the input matrix, a constant u is rx1; u is the input, a function of time C is mxn; C is the output matrix, a constant D is mxr; D is the direct transition matrix, a constant y is mx1; y is the output, a function of time
Derivation of of State Space Model (Electrical)
To develop a state space system for an electrical system, they choosing the voltage across capacitors, and current through inductors as state variables. Recall that
so if we can write equations for the voltage across an inductor, it becomes a state equation when we divide by the inductance (i.e., if we have an equation for einductor and divide by L, it becomes an equation for diinductor/dt which is one of our state variable). Likewise if we can write an equation for the current through the capacitor and divide by the capacitance it becomes a state equation for ecapacitor
There are three energy storage elements, so we expect three state equations. Try choosing i1, i2 and e1 as state variables. Now we want equations for their derivatives. The voltage across the inductor L2 is e1 (which is one of our state variables)so our first state variable equation is
This equation has our input (ia) and two state variable (iL2 and iL1) and the current through the capacitor. So from this we can get our second state equation
Our third, and final, state equation we get by writing an equation for the voltage across L1 (which is e2) in terms of our other state variables
references:
http://lpsa.swarthmore.edu/Representations/SysRepSS.html
https://en.wikipedia.org/wiki/State-space_representation
Transfer Function and Mathematical Modeling
Transfer Function
Poles And Zeros of a Transfer Function
Properties of Transfer Function
Advantages and Disadvantages of T.F.
Translation motion
Rotational motion
Translation-Rotation counterparts
Analogy system
Force-Voltage analogy
Force-Current Analogy
Advantages
Example
state space representation,State Space Model Controllability and Observabilit...Waqas Afzal
State Variables of a Dynamical System
State Variable Equation
Why State space approach
Block Diagram Representation Of State Space Model
Controllability and Observability
Derive Transfer Function from State Space Equation
Time Response and State Transition Matrix
Eigen Value
The myphotonics project deals with the construction of opto-mechanical components and optical experiment implementation using modular systems such as LEGO®.
The components are low cost and the instructions that originated them are free to use. OpenAdaptonik and myphotonics can work together sharing the same purpose.
Here's the continuation of the report:
3.2.1 Parallel Plate Capacitor (continued)
As the IV fluid droplets move between the plates of the capacitor, the capacitance increases due to the change in the dielectric constant, resulting in the observation of a peak in capacitance.
3.2.2 Semi-cylindrical Capacitor
The semi-cylindrical capacitor consists of two semi-cylindrical conductors (plates) facing each other with a gap between them. The gap between the plates is filled with a dielectric material, typically the IV fluid.
When a potential difference is applied across the plates, electric field lines form between them. The dielectric material between the plates enhances the capacitance by reducing the electric field strength and increasing the charge storage capacity.
3.2.3 Cylindrical Cross Capacitor
The cylindrical cross capacitor is composed of two cylindrical conductors (rods) intersecting at right angles to form a cross shape. The space between the rods is filled with a dielectric material, such as the IV fluid.
When a potential difference is applied between the rods, electric field lines form between them. The dielectric material between the rods enhances the capacitance by reducing the electric field strength and increasing the charge storage capacity, similar to the semi-cylindrical design.
3.3 Advantages of Capacitive Sensing Approach
Capacitive sensing for IV fluid monitoring offers several advantages over other automated monitoring methods:
1. Non-invasive operation: The sensors do not require direct contact with the IV fluid, reducing the risk of contamination or disruption to the therapy.
2. High sensitivity: Capacitive sensors can detect minute changes in capacitance, enabling precise tracking of IV fluid droplets.
3. Low cost: The sensors can be constructed using relatively inexpensive materials, making them a cost-effective solution.
4. Low power consumption: Capacitive sensors typically have low power requirements, making them suitable for continuous monitoring applications.
5. Ease of implementation: The sensors can be easily integrated into existing IV setups without significant modifications.
6. Stable measurements: Capacitive sensors can provide stable and repeatable measurements across different IV fluid types.
Chapter 4: Experimental Setup and Results
4.1 Description of Experimental Setup
To evaluate the performance of capacitive sensors for IV fluid monitoring, an experimental setup was constructed. The setup included various capacitive sensor designs, such as parallel plate, semi-cylindrical, and cylindrical cross capacitors, positioned around an IV drip chamber.
The sensors were connected to a capacitance measurement circuit, which recorded the changes in capacitance as IV fluid droplets passed through the sensor's electric field. Multiple experiments were conducted using different IV fluid types and flow rates to assess the sensors' accuracy, repeatability, and sensitivity.
4.2 Measurements with
THIS DOCUMENT IS MAINLY PREPARED ON THE TIME RESPONSE OF A SECOND ORDER SYSTEM AND IN THIS DOCUMENT WE ALSO DONE THE SIMULATION BY USING MATLAB AND HERE WE ALSO DONE THE THEORETICAL MATHEMATICAL CALCULATIONS TO SHOW HOW THE SYSTEM IS BEHAVING IN DIFFERENT CONDITIONS AND HERE WE ALSO DONE THE MATLAB CODING AND THE RESULTS ARE ALSO PLOTTED IN THE DOCUMENT
THIS PPT IS DONE ON THE MICROGRID. IN THIS PPT WE DISCUSSED THE USES OF MICROGRIDS AND THEIR REAL-LIFE APPLICATIONS AND HOW THEY ARE INTERCONNECTED TO EACH OTHER AND THE MAJOR DIFFERENCE BETWEEN THE CONVENTIONAL GRIDS AND THE MICROGRIDS AND THEIR USES, ADVANTAGES ARE ALSO DISCUSSED IN THIS PRESENTATION AND USES IN FUTURE ALSO AND THIS PPT IS SO USEFUL TO MANY STUDENTS
THIS IS A PROJECT DONE BY USING SMALL ELECTRONICS COMPONENTS AND BY DOING THIS WE CAN SEE THE FADING OF LED BY UP AND DOWN AND FOR THIS WE MADE REPORT IN A SPECIFIED WAY AND IN THIS IS WE SHOWN EVERY STEP BRIEFLY HOW TO DO THE PROJECT AND THE RESULTS ARE ALSO COMING AND THIS PROJECT IS USEFUL FOR MANY TO DO PROJECTS
THIS DOCUMENT MAINLY CONTAINS THE HOW TO MODLE DC SERVO MOTOR BY USING THE MATLAB SIMULINK AND HOW IT WILL BEHAVE IS SHOWN IN THE MATHEMATICAL EQUATIONS AND THE PLOTTINGS ARE ALSO KEPT IN THIS DOCUMENT SO BY THIS IT IS USEFUL TO STUDY THE CHARACTRISTICS OF A DC SERVO MOTOR
THIS PPT IS MAINLY BASED ON HOW THE ELCTRONIC FUEL INJECTION SYSTEMS IN DIFFERENT VEHICLES AND IN THIS WE HAVE DISCUSSED DIFFERENT TECHNIQUES IN DIFFERENT VEHIOCLEWS AND THEIR MODELS ALSO AND THEIR SYSTEMS ALSO IN THE VEHICLES AND THEIR COMPONENTS AND THEIR USES ARE ALSO MENTIONED IN THIS PPT SO IT IS USEFUL FOR BOTH MECHANICAL AND ELECTRONICS STUDENTS
THIS PPT IS MAINLY CONTAINS THE GREEN ENERGY TECHNIQUES AND THE USES OF USING RENEWABLE ENERGY RESOURCES AND IN THIS WE ALSO DISCUSSED THE VARIOUS TYPES OF ENERGIES AVAILABLE AND THEIR REQUIREMENTS IN THE FUTURE AND IT IS USEFUL
THIS DOCUMENT CONTAINS THE DIGITAL ELECTRONICS DESIGN OF 3 BIT MAJORITY CIRCUIT. IN THIS DOCUMENT THERE IS A BRIEF EXPLANATION ABOUT THE CIRCUIT HOW TO DESIGN AND IMPLEMENTATION OF CIRCUIT AND THE THEORETICAL CALCULATIONS,TRUTH TABLES ARE ALSO DONE IN THIS DOCUMENT AND THIS IS USEFUL FOR THE ELECTRONICS STUDENTS
THIS PPT IS MAINLY BASED ON ELECTRICAL CIRCUIT ANALYSIS PROBLEM AND THIS PPT ALSO SOLVED THEORETICALLY AND SOLVED BY USING THE MATLAB SOFTWARE AND THIS ALSO CONTAINS THE CODE AND RESULTS ARE ALSO THERE.SO THIS IS USEFUL
power systems ppt on Arc welding and Electric welding equipment and compariso...sanjay kumar pediredla
this ppt is mainly based on the power systems related topic and in this ppt mainly consists of ac and dc weldings and which welding is used mainly and the importance of arc welding and electric welding and the techniques are also discussed in this and it is so helpful .and the safety requirements and the equipment used is also discussed in this topic
CONTROL SYSTEM PPT ON DETERMINATION OF SABILITY OF SYSTEM USING NYQUIST PLOT ...sanjay kumar pediredla
THIS PPT CONTAINS A PPT ABOUT THE STABILITY F A SYSTEM BY USING A NYQUIST CRITERIA AND THIS PPT ALSO CONTAINS A MATLAB CODING AND THE PLOTS OF THE SYSTEM AND IN THIS PPT I ALSO SOLVED A SUM PRACTICALLY IN A MATLAB AND I KEPT A RESULTS TOO .SO THIS PPT IS SO USEFUL FOR THE STUDENTS
CONTROL SYSTEMS PPT ON A UNIT STEP RESPONSE OF A SERIES RLC CIRCUIT sanjay kumar pediredla
THIS PPT IS SO USEFUL TO KNOW ABOUT THE SERIES RLC CIRCUIT AND IN THIS WE CAN ALSO HOW THE RESPONSE WILL BE THERE FOR A UNIT STEP RESPONSE AND I ALSO KEPT A MATLAB CODING AND GRAPHS FOR THE SERIES RLC CIRCUIT
DESIGN OF CIRCUIT DEBITS THE GIVEN VALUE TO THE DEFAULT VALUE WITH COST ANAL...sanjay kumar pediredla
THIS REPORT IS BASED ON THE DESIGN OF CIRCUIT DEBITS THE GIVEN VALUE TO THE DEFAULT VALUE WITH COST ANALYSIS AND DEBIT RANGE IS (0-7) AND DEFAULT VALUE “11". AND BY SEEING THIS REPORT WE CAN GET A IDEA ABOUT THE ELECTRONIC CIRCUITS HOW TO DESIGN THE CIRCUITS AND BY USING THE COSTING TECHNIQUES WE CAN KNOW ABOUT HOW TO DESIGN THE CIRCUITS BY LOW-COST ANALYSIS SO IN THIS REPORT WE CAN SEE THAT THE COST ANALYSIS OF THE IC'S ALSO SO THIS REPORT IS ALSO USEFUL FOR THE ENGINEERING STUDENTS THOSE WHO ARE DESIGNING THE CIRCUITS AND HOW TO DO THE COSTING ANALYSIS ON THE CIRCUITS
THIS REPORT IS BASED ON THE PROBLEM SOLVING ON THE MUTUAL INDUCTANCE OF COUPLED CIRCUIT AND THIS REPORT ALSO CONTAINS THE PROBLEM SOLVING BY USING THE CIRCUIT ANALYSIS . AND ALSO REPORT IS PREPARED ON THE NORMS AND THIS REPORT DESCRIPTION IS ALSO GOOD AND THE EQUATIONS ARE ALSO WRITTEN IN THIS REPORT AND THIS MATLAB CODIMG AND THE REULTS ARE PLOTTED IN THIS REPORT AND THE GRAPHICAL REPRESENTATION IS ALSO SHOWN IN THIS REPORT SO THIS IS USEFUL
THIS REPORT IS BASED ON THE SIMULATION OF DC SERIES MOTOR CHARACTERISTICS AND THIS REPORT IS PREPARED WELL ACCORDING TO THE NORMS AND THE REPORT ALSO CONTAINS A MATLAB SIMULINK OF THE DC MOTOR DESIGN AND THE RESULTS ARE ALSO PLOTTED IN THIS REPORT AND THE DESCRIPTION ALSO ABOUT THE REPORT IS ALSO PREPARED WELL IN THIS REPORT AND THIS IS USEFUL FOR THE ENGINEERING STUDENTS
THIS REPORT IS BASED ON THE GREEN ENERGY ELECTRIC POWER CONVERTER AND THIS REPORT IS PREPARED ON THE BASE OF FORMAT WHICH IS STANDARD AND THIS REPORT ALSO CONTAINS DIFFERENT ENERGY SOURCES WHICH IS RENEWABLE SOURCES SO THIS USEFUL FOR ENGINEERING STUDENTS
THIS REPORT IS BASED ON THE POWER FACTOR CORRECTION ON THE POWERPLANT AND IN THIS REPORT IS PREPARED BASED ON THE REPORT MAKING AND THIS REPORT IS USEFUL TO SUBMIT THE REPORTS IN THIS FORMAT AND THIS FORMAT IS ALSO GOOD
THIS PPT IS ABOUT THE ANALYZE THE STABILITY OF DC SERVO MOTOR USING NYQUIST PLOT AND IN THIS PPT WE CAN ALSO SEE THE DIFFERENT CHARACTERISTICS EQUATION FOR THE DC SERVO MOTOR AND THE EXAMPLE GRAPHS ARE ALSO SHOWN IN THIS PPT AND THIS PPT IS SO USEFUL FOR THE CONTROL SYSTEM STUDENTS AND ANALYSIS OF THE EQUATIONS ARE ALSO AVAILABLE IN THIS PPT
THIS IS THE REPORT OF THE CONTROL SYSTEMS QUESTION AND THIS REPORT IS USEFUL TO SOLVE THE QUESTIONS AND THIS REPORT ALSO CONTAINS THE MATLAB SIMULATION CODE AND THE PLOTTINGS OF THE RESULT AND THIS REPORT IS PREPARED BASED ON THE DIFFERENT SUB HEADINGS AND IT IS CATEGORIZED IN THIS WAY SO IT IS USEFUL TO THE CONTROL SYSTEM ENGINEERING STUDENTS
THIS PPT MAINLY DISCUSS ABOUT DOUBLE CAGE INDUCTION MOTOR AND IT'S CONSTRUCTION AND THIS PPT MAINLY CONTAINS THE DIFFERENT CHARACTERISTICS OF THE MACHINE IN VARIOUS FACTORS ANTHE PLOTTINGS ARE ALSO WE CAN SEE IN THIS PPT SO IT IS SO USEFUL TO ELECTRICAL MACHINES STUDENTS
THIS PPT IS BASED ON THE WIRELESS POWER TRANSMISSION AND THIS PPT IS MAINLY BASED ON THE UPCOMING WIRELESS TRANSMISSION IN THE CHARGING OF VEHICLES AND MOBILE PHONES THROUGH THE UPCOMING TECHNOLOGY IN THE POWER TRANSMISSION AND THIS IS SO HELP FULL TO THE ELECTRICAL AND ELECTRONICS ENGINEERING STUDENTS
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
1. Department of Electrical & Electronics Engineering
Raghu Engineering College (Autonomous)
CASE STUDY
ON
IMPULSE RESPONSE OF SECOND ORDER
SYSTEM
BACHELOR OF TECHNOLOGY
IN
ELECTRICAL AND ELECTRONICS ENGINEERING
Under the Supervision of
Mr.P.SIVA RAMA RAO
Assistant Professor
Mr P.Eswar sai 18981A0237
Mr P.Mohan 18981A0238
Ms P.Supriya 18981A0239
Mr.P.Nitish 18981A0240
Mr.P.Sanjay Kumar 18981A0241
By
Head of the department
Dr.P.SASI KIRAN
Professor
2. ANALYSIS OF SECOND ORDER SYSTEM
Damping Ratio : The damping is measured by a factor called as
damping ratio.
It is denoted by 𝜀 .
So when zeta is maximum ; it produces maximum opposition to the
oscillatory behaviour of system.
19. A general second-order system is characterized
by the following transfer function:
We can re-write the above transfer function in
the following form (closed loop transfer function):
20. According the value of ζ, a second-order system can be
set into one of the four categories:
1. OVER DAMPED : when the system has two real distinct poles (𝜖 >1).
2. UNDER DAMPED :
when the system has two complex conjugate
poles (0 <𝜖 <1)
3. UN-DAMPED : when the system has two imaginary poles (𝜖 = 0).
4. CRITICALLY DAMPED :
when the system has two real but equal poles
(𝜖 = 1).
21. IMPULSE RESPONSE OF THE SECOND ORDER SYSTEM:
„Laplace transform of the unit impulse is R(s)=1
„Impulse response :-
„Transient response for the impulse function, which is simply is the derivative
of the response to the unit step: derivative of the response to the unit step:
25. When 𝜀 > 1,
OVERDAMPING :-
0,1)(
1
))((
)(
1
)(
))((
2
)(
21
11
21
2
21
2
21
2
22
2
tekek
pp
ty
spsps
sY
s
sX
psps
ss
sC
tptpn
n
n
nn
n
26. • The transfer function can be rewritten as:
22
2
222222
2
22
2
2
2
)(
dn
n
nnnn
n
nn
n
s
ss
ss
sC
27. • The step response, after some simplification, can be written as:
• Hence, the response of this system eventually settles to a steady-
state value of 1. However, the response can overshoot the
steady-state value and will oscillate around it, eventually settling
in to its final value.
n
d
d
t
n
n
where
ttety n
1
tan
0,sin1)(
28. IMPULSE RESPONSE:
The first pulse has a width T and height 1/T, area of the pulse will be 1. If we halve
the duration and double the amplitude we get second pulse. The area under the
second pulse is also unity
The pulse for which the duration tends to zero and amplitude tends to infinity is
called impulse. Impulse function also known as delta function.