1) The document discusses different variants of first order systems including: a) systems with non-unity steady state gain, and b) systems with time delay.
2) It then introduces second order systems, defined by a governing differential equation involving natural frequency, damping ratio, and input.
3) Based on the damping ratio value, second order systems can have complex conjugate poles (underdamped, ratio between 0-1), repeated real poles (critically damped, ratio equals 1), or distinct real poles (overdamped, ratio above 1). The implications of these cases will be explored next.
3 examples of PDE, for Laplace, Diffusion of Heat and Wave function. A brief definition of Fouriers Series. Slides created and compiled using LaTeX, beamer package.
In tis slide, an introduction to string theory has been given. Apart from that, a simple proof of 26 dimensions of bosonic string theory is given (following Zwiebach's approach).
I explained this presentation in two parts (on my YouTube channel). Here are the links
_______________________________________________
Part 1
https://www.youtube.com/watch?v=QQA4JQ6Y-eo&list=PLDpqC3uXLZGl0cDod6g30PcjeJ4DAZWhp
_______________________________________________
Part 2
https://www.youtube.com/watch?v=vhLCtLn79jE&list=PLDpqC3uXLZGl0cDod6g30PcjeJ4DAZWhp&index=2
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2 Dimensional Wave Equation Analytical and Numerical SolutionAmr Mousa
2 Dimensional Wave Equation Analytical and Numerical Solution
This project aims to solve the wave equation on a 2d square plate and simulate the output in an user-friendly MATLAB-GUI
you can find the gui in mathworks file-exchange here
https://www.mathworks.com/matlabcentral/fileexchange/55117-2d-wave-equation-simulation-numerical-solution-gui
3 examples of PDE, for Laplace, Diffusion of Heat and Wave function. A brief definition of Fouriers Series. Slides created and compiled using LaTeX, beamer package.
In tis slide, an introduction to string theory has been given. Apart from that, a simple proof of 26 dimensions of bosonic string theory is given (following Zwiebach's approach).
I explained this presentation in two parts (on my YouTube channel). Here are the links
_______________________________________________
Part 1
https://www.youtube.com/watch?v=QQA4JQ6Y-eo&list=PLDpqC3uXLZGl0cDod6g30PcjeJ4DAZWhp
_______________________________________________
Part 2
https://www.youtube.com/watch?v=vhLCtLn79jE&list=PLDpqC3uXLZGl0cDod6g30PcjeJ4DAZWhp&index=2
_______________________________________________
2 Dimensional Wave Equation Analytical and Numerical SolutionAmr Mousa
2 Dimensional Wave Equation Analytical and Numerical Solution
This project aims to solve the wave equation on a 2d square plate and simulate the output in an user-friendly MATLAB-GUI
you can find the gui in mathworks file-exchange here
https://www.mathworks.com/matlabcentral/fileexchange/55117-2d-wave-equation-simulation-numerical-solution-gui
I am Katherine Walters. I love exploring new topics. Academic writing seemed an exciting option for me. After working for many years with matlabassignmentexperts.com, I have assisted many students with their assignments. I can proudly say, each student I have served is happy with the quality of the solution that I have provided. I acquired my master's from the University of Sydney.
REPORT SUMMARYVibration refers to a mechanical.docxdebishakespeare
REPORT SUMMARY
Vibration refers to a mechanical phenomenon involving oscillations about a point. These oscillations can be of any imaginable range of amplitudes and frequencies, with each combination having its own effect. These effects can be positive and purposefully induced, but they can also be unintentional and catastrophic. It's therefore imperative to understand how to classify and model vibration.
Within the classroom portion of ME 345, we discussed damped and undamped vibrations, appropriate models, and several of their properties. The purpose of Lab 3 is to give us the corresponding "hands-on" experience to cement our understanding of the theory.
As it turns out, vibration can be modeled with a simple spring-mass system (spring-mass-damper system for damped vibration). In order to create a mathematical model for our simple spring-mass system, we apply Newton's second law and sum the forces about the mass. After applying some of our knowledge of differential equations, the result is a second order linear differential equation (in vector form). This can easily be converted to the scalar version, from which it's easy to glean various properties of the vibration (i.e. natural frequency, period, etc.).
In the lab, we were provided with a PASCO motion sensor, USB link, ramp, and accompanying software. All of the aforementioned equipment was already assembled and connected. The ramp was set up at an angle with a stop on the elevated end and the motion sensor on the lower end. The sensor was connected to the USB link, which was in turn connected to the computer. We chose to use the Xplorer GLX software to interface with the sensor and record our data. After receiving our equipment, we gathered data on our spring's extension with a known load to derive a spring constant. We were provided with a small cart to which we attached weights to increase its mass. In order to model free vibration, we placed the cart on the track and attached it to the stop at the top of the ramp with a spring. After displacing the cart a certain distance from its equilibrium point, the cart was released and was allowed to oscillate on the track while we recorded its distance from the sensor. This was done with displacements of -20cm, -10cm, +10cm, and +20cm from the system's equilibrium point. After gathering this data for the "free" case, a magnet was attached to the front of the car, spaced as far from the track as possible. As the track is magnetic, this caused a slight damping effect, basically converting our spring-mass system to an underdamped spring-mass-damper system. After repeating the procedure for the "free" case, we moved the magnets as close to the track as possible (causing the system to become overdamped) and again repeated the procedure for the "free" case.
We were finally able to determine the period, phase angle, damping coefficients, and circular and cyclical frequencies for the three systems. There were similarities and differ ...
Oscillatory motion control of hinged body using controllereSAT Journals
Abstract Due to technological revolution , there is change in daily life usuage of instrument & equipment.These usuage may be either for leisure or necessary and compulsory for life to live. In past there is necessity of a person to help other person but today`s fast life has restricted this helpful nature of human. This my project will helpful eliminate such necessity in certain cases. Oscillatory motion is very common everywhere. But its control is not upto now deviced tactfully. So it is tried to automate it keeping mind constraints such as cost, power consumption, safety,portability and ease of operating. Proper amalgamation of hardware and software make project flexible and stuff. The repetitive , monotonous and continuous operation is made simple by use of PIC microcontroller. There does not existing prototype or research paper on this subject. It probable first in it type.
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I am Martina J. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Maryland. I have been helping students with their assignments for the past 9 years. I solve assignments related to Signals and Systems.
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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.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
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About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
1. Control Systems
Prof. C. S. Shankar Ram
Department of Engineering Design
Indian Institute of Technology, Madras
Lecture – 18
First Order Systems
Part – 2
(Refer Slide Time: 00:18)
Other variants of 1st
Order system:
1) T
dy(t)
dt
+ y(t )=bu(t ),b∈ R,b≠1
→P(s)=
Y (s)
U (s)
=
b
Ts+1
Unit step response: U (s)=
1
s
,→Y (s)=P(s)U (s)=
b
s(Ts+1)
→ y (t)=b(1−e
−t
T
)
2. (Refer Slide Time: 00:30)
The steady state value of unit step response =
y (t )=lim
s→ 0
sY (s)=¿lim
s→0
s
b
s(Ts+1)
=b
lim
t→∞
¿
The dynamic characteristics remains the same; the settling time is still 4T, but now what will
happen you will see that if you substitute t = T, y(t) will be b times 0.632, that is why the
definition was 63.2 percent of the final value not just 0.632, if you look at the definition.
Similarly, if you calculate what is y at t = 4 t you will get 0.982 b. So, the output at our reach
98.2 percent of the final value which is b. So, that is what is called by steady state gain.
So, immediately you will see that this is a 2 parameter model; 2 parameter model or 2
parameter process, ok. So, this people call first order model with non unity steady state gain
right. So, that is the variant and a third variant which people can have which essentially
occurs in many practical processes you will see you will look at this variant even when you
come to the lab in many practical systems you may have a system like this.
2) T
dy(t)
dt
+ y(t )=bu(t−Td ),b∈ R,b≠1,Td>0,Td ∈R
So, Td is the time delay all right. So, we have encountered what was time delay before,
right. So, that is you give an input; output starts from 0 only after the interval of Td , right.
So, that is time delay.
3. Plant Transfer Function: P(s)=
Y (s)
U (s)
=
be
−Td s
Ts+1
=
b(2−Td s)
(Ts+1)(2+Td s)
(using Pade’s
approximation)
Now, how many parameters do we have? We have 3 parameters. So, this becomes a 3
parameter model ok. So, that is that is another variant, ok. So, this people will call as a first
order system with the non unity gain and time delay, ok. Some in chemical engineering
references and all you will see first order process plus time delay, ok. So, that is a term which
they will use ok. So, this is the model which is used and this is the transfer function which
comes over as a result ok. So, you see that you have 3 parameters.
So, once again the dynamic characteristics remain, the same the time constant definition is
the same. The steady state gain is once again b, only difference is and now we have added a
time delay factor, ok. So, that is that is the change that happens ok, is it clear?
(Refer Slide Time: 09:51)
So, now, we go to second order systems. So, once again to recap the big picture as to why we
are studying first order and second order systems the reason is that by and large when you
want to talk about performance right we talk about the fact that we have the dominant
dynamics or dominant poles to be either one or two other is like what is close to the
imaginary axis, right. That is why when you want to specify performance we look at either
first order or second order systems you know like that is the motivation behind looking at
4. first order and second order systems for deriving performance parameters, ok. So, that is the
big picture once again.
Second Order Systems:
So, a typically second order systems are motivated from vibration problems. Due to that
reason their governing equation is written in a certain structure ok, we will see how it is
written, ok. So, the governing equation of second order systems is typically taken as the
following,
d
2
y(t)
d t
2
+2ζ ωn
dy(t)
dt
+ωn
2
y(t )=ωn
2
u(t )
So, immediately you can see that n = 2, right. So, m for this particular case happens to be 0,
you can also have = 1, you can also have a derivative of u on the right hand side. can happen
as I told you we we would take it of to be of this particular structure and we will see what
happens when we have m to be 1, that is we have a term on the right hand side what really
happens to the systems response, that is something which we look at as we go along, ok.
So, we can see that immediately of course, before we calculate the poles you know like the
value ζ is what is called as the damping ratio ok, ωn is what is called as the natural
frequency of the system, ok. We would revisit these parameters and then I would ask you to
define these parameters like we are going to look at the physics behind these choices, right.
So, behind this choice of model, right, we will we will look at them. But, then like for
tomorrows or let us say for the next class you know I should say you know like please figure
out what is the definition of natural frequency and come, ok. So, a clear crisp definition of
what you mean by natural frequency, we discuss this as we go along.
And it so happens that we will we will figure out later that for stability of the system please
remember we can only talk about performance only if you have a stable system to begin with
right. It so happens that for stability of this class of systems the sufficient condition is ζ >
0, ωn>0 , ok. So, that is the sufficient condition of course, in general we will see that you
know like the system will be stable if ζ and ωn are real numbers of the same sign, ok.
Now, taking Laplace transform on both sides,
s
2
Y (s)−sy (0)−´y(0)+2ζ ωn(sY (s)− y(0))+ωn
2
Y (s)=ωn
2
U (s)
5. Apply zero initial conditions,
s
[¿¿2+2ζ ωn s+ωn
2
]Y (s)=ωn
2
U (s)
¿
→P(s)=
Y (s)
U (s)
=
ωn
2
s
2
+2ζ ωn s+ωn
2
So, what are the poles of this transfer function? How do you get the poles? We solve the
denominator polynomial equals 0
Poles: s=−ζ ωn±ωn√ζ
2
−1 .
Now, of course, it is a second order system value of n is 2; obviously, you get two poles,
right. Now, what can you say about these nature of these poles?
Immediately we can observe that the nature of the poles is depend on the value of zeta, right.
If zeta is between 0 and 1, what can I say about the poles?
If 0<ζ <1 the poles are complex conjugates
If ζ =1 Repeated poles at −ωn
If ζ >1 Distinct real poles.
So, those are three cases that we would look at depending on the value of zeta the location of
the poles changes and consequently the system behavior changes a lot, ok.
So, that is something which we are going to do in the next class. So, we look at what are
called under damped critically damped and over damped systems, depending on whether the
value of ζ is less than 1, exactly equal to 1 or greater than 1, respectively, ok. So, we look
at what is the physical what to say implication of those three cases and then how do we do the
analysis, ok. So, that is something which we will do in the next class, but before that you
know like please figure out the definitions of a natural frequency and damping ratio, and
come.