This presentation gives complete idea about definitions of stability, BIBO, Absolute and relative stability, Routh-Hurwitz Criterion, Special Cases and numerical examples.
This presnetation gives complete idea about block diagram representation and reduction techniques to find transfer function. Also gives complete idea about Signal flow graph method to find transfer function.
Root locus is a graphical representation of the closed-loop poles as a system parameter is varied.
It can be used to describe qualitatively the performance of a system as various parameters are changed.
It gives graphic representation of a system’s transient response and also stability.
We can see the range of stability, instability, and the conditions that cause a system to break into oscillation.
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.
State space analysis, eign values and eign vectorsShilpa Shukla
State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, Concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area.
This presnetation gives complete idea about block diagram representation and reduction techniques to find transfer function. Also gives complete idea about Signal flow graph method to find transfer function.
Root locus is a graphical representation of the closed-loop poles as a system parameter is varied.
It can be used to describe qualitatively the performance of a system as various parameters are changed.
It gives graphic representation of a system’s transient response and also stability.
We can see the range of stability, instability, and the conditions that cause a system to break into oscillation.
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.
State space analysis, eign values and eign vectorsShilpa Shukla
State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, Concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area.
Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively
This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.
automatic control, Basic Definitions, Classification of Control systems, Requ...Waqas Afzal
Why automatic controls is required
2. Process Variables
controlled variable, manipulated variable
3. Functions of Automatic Control
Measurement
Comparison
Computation
Correction
4.Basic Definitions
System, Plant, Process, Controller, input, output, disturbance
5. Classification of Control systems
Natural, Manmade & Automatic control system
Open-Loop, Close-Loop control System
Linear Vs Nonlinear System
Time invariant vs Time variant
Continuous Data Vs Discrete Data System
Deterministic vs Stochastic System
6. Requirements of an ideal Control system
Accuracy, Sensitivity, noise, Bandwidth, Speed, Oscillations
Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively
This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.
automatic control, Basic Definitions, Classification of Control systems, Requ...Waqas Afzal
Why automatic controls is required
2. Process Variables
controlled variable, manipulated variable
3. Functions of Automatic Control
Measurement
Comparison
Computation
Correction
4.Basic Definitions
System, Plant, Process, Controller, input, output, disturbance
5. Classification of Control systems
Natural, Manmade & Automatic control system
Open-Loop, Close-Loop control System
Linear Vs Nonlinear System
Time invariant vs Time variant
Continuous Data Vs Discrete Data System
Deterministic vs Stochastic System
6. Requirements of an ideal Control system
Accuracy, Sensitivity, noise, Bandwidth, Speed, Oscillations
This formula book gives simple and useful formulas related to control system. It helps students in solving numerical problems, in their competitive examinations
Transfer Function, Concepts of stability(critical, Absolute & Relative) Poles...Waqas Afzal
Transfer Function
The Order of Control Systems
Concepts of stability(critical, Absolute & Relative)
Poles, Zeros
Stability calculation
BIBO stability
Transient Response Characteristics
Analysis and Design of Control System using Root LocusSiyum Tsega Balcha
Root locus analysis is a powerful tool in control systems engineering used to analyze the behavior of a system's closed-loop poles as a function of a parameter, typically a controller gain. It provides engineers with valuable insights into how changing system parameters affect stability and performance, helping them design robust and stable control systems. Let's explore the key concepts, techniques, and practical implications of root locus analysis. At its core, root locus analysis focuses on the movement of the closed-loop poles in the complex plane as a control parameter varies. These poles represent the characteristic equation's roots, which determine the system's stability and transient response. By examining the pole locations as the parameter changes, engineers can gain a deeper understanding of the system's behavior and make informed design decisions.
ME-314 Introduction to Control Engineering is a course taught to Mechanical Engineering senior undergrads. The course is taught by Dr. Bilal Siddiqui at DHA Suffa University. This lecture is about basic rules of sketching root locus.
Mr. C.S.Satheesh, M.E.,
Routh Array Hurwitz Criterion
determining whether all the roots of a polynomial have negative real part or not.
characteristic equation.
the coefficients of the polynomial be positive.
coefficients are zero or negative
purely imaginary roots so the system is limitedly or marginally stable.
remaining roots lies on left half of S plane.
This chapter provides complete description of two port network parameters. It also provides relationship between different parameters. Also it provides condition for symmetry and reciprocity.
This chapter provides complete solution of different circuits using Laplace transform method and also provides information about applications of Laplace transforms.
This chapter provides complete solution of of first, Second order differential equations of series & parallel R-L, R-C, R-L-C circuits, bu using different methods.
This presentation explains about Network topology, Graph, Tree, Branches, Chords, Equilibrium equation on loop basis &
node basis Number of network equation required, Choice between nodal & loop analysis, Source
transformation, Network mutual inductance, Dot conventions, Concept of super mesh, Super node Concept of
duality & dual networks with numerical examples.
This presentation clearly explains about all theorems with numerical examples including Superposition, Thevenin’s, Norton’s, Reciprocity, Maximum power transfer, Substitution, Tellegen's theorem and example problems.
This presentation provides an explanation of Active & Passive Circuit Element: Independent & dependent voltage & current sources, R, L, C, and Their mathematical modes, Voltage current power relations, Series and Parallel circuits, Kirchhoff's Laws. It also provides an information about
Classification of elements with numerical examples.
This presentation explains clearly about the definition of controller and classification of controllers and explanation of individual controllers of P, I, D and combination of PI, PD and PID controllers with transfer function and block diagram. It explains effects of P,I PI, PD and PID controllers on system performance.
This presentation explains about the introduction of Bode Plot, advantages of bode plot and also steps to draw Bode plot (Magnitude plot and phase plot). It explains basic or key factors used for drawing Bode plot. It also explains how to determine Magnitude, phase and slope for basic factors. It also explains how to determine stability by using Bode Plot and also how to determine Gain Crossover Frequency and Phase Crossover Frequency, Gain Margin and Phase Margin. It also explains drawing Bode plot with an example and also determines stability by using Bode Plot and also determines Gain Crossover Frequency and Phase Crossover Frequency, Gain Margin and Phase Margin.
This presentation explains about the introduction of Nyquist Stability criterion. It clearly shows advantages and disadvantages of Nyquist Stability criterion and also explains importance of Nyquist Stability criterion and steps required to sketch the Nyquist plot. It explains about the steps required to sketch Nyquist plot clearly. It also explains about sketching Nyquist plot and determines the stability by using Nyquist Stability criterion with an example.
This presentation gives complete idea about time domain analysis of first and second order system, type number, time domain specifications, steady state error and error constants and numerical examples.
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
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2. Stability Definitions
Types of stability based on Natural response definition:
1. A system is STABLE if the natural response approaches zero as time
approaches infinity.
2. A system is UNSTABLE if the natural response approaches infinity
as time approaches infinity.
3. A system is MARGINALLY STABLE if the natural response neither
decays nor grows but remains constant or oscillates.
BIBO Definition:
1. A system is stable if every bounded input yields a bounded output.
2. A system is unstable if any bounded input yields an unbounded
output.
3. Bounded-Input Bounded-Output (BIBO) Stability
Let r(t), c(t) and g(t) be the input, output and impulse
response of a linear time-invariant system.
Therefore C(s) = R(s) ∙ G(s)
r(t )g( )dc(t) = 0
Taking the absolute value on both sides, we get
c(t) 0
r(t )g( )d
4. Since the absolute value of the integral is not greater than the
integral of the absolute value of the integrand
•The BIBO stability condition is satisfied if for every bounded input
( r ( t ) M 1 ) ( c(t) M 2 )
•Thus the notion of BIBO stability is satisfied if the impulse response
g(t) is absolutely integrable, i.e
g()d0
is finite
. The area under the absolute value curve of the impulse
response g(t) evaluated from t=0 to t= is finite
5.
6.
7. ABSOLUTE STABILITY AND RELATIVE STABILITY
ABSOLUTE STABILITY
Absolute stability is a qualitative measure of stability. It
refers to the condition of whether the system is stable
or unstable
RELATIVE STABILITY
Once the system is found to be stable, it is of interest to
determine how stable it is, and this degree of stability is
a measure of relative stability. Relative stability is a
quantitative measure of how fast transients die out in
the system.
8. RELATIVE STABILITY
Relative stability measurement- relative settling time of
each unit or pair of units
Relative settling time of complex conjugate pole is
inversely proportional to the real part of the roots
Root or pair of roots move farther away from imaginary
axis, the relative stability of the system improves
9. Necessary conditions for stability
The characteristic equation of an n th order system is given by
q(s) =a0sn+a1sn-1+…+an-1s+an =0; a0>0
1.All the coefficients of its characteristic equation be real and
have same sign.
2.None of the coefficients should be zero
However, these conditions are necessary not sufficient, because it is quite
possible that an equation with all its coefficients non-zero and of the same
sign may not have all the roots in the left-half of the s-plane.
10. The equation may be written in factored form
If sk and σi are positive all coefficients of the resulting polynomial
will be positive (roots have negative real part)
If one or more roots have positive real part coefficients of the
characteristic polynomial may or may not be positive.
Consider an nth order characteristic equation
q(s) =a0sn+a1sn-1+…+an-1s+an =0; a0>0
11. ROUTH STABILITY CRITERION
The Routh stability criterion is based on formulating an array
(or table) called Routh array (or Routh table) using the
coefficients of the characteristic equation.
The first row of the array consists of first third fifth, etc
coefficients
Second row consists of second, fourth, sixth, etc, coefficients
all counting from the highest terms
13. Example 1: Investigate whether the following systems represented by the
characteristic equations are stable or not.
s5
s4
6s3
12s2
18s 6 0
s5
S4
s3
s2
1 6 18
1 12 6
-6 12 0
14 6
s1
14.5
7
0
s0 6
There are two sign changes in
the first column of the Routh
array.
Hence there are two roots of
the characteristic equation in
the right-half of the s-plane.
Hence the system is unstable
14. s4
2s3
10s2
8s 3 0
s4 1 10 3
s3 2 8
s2
s1
s0
2
210 18
6
2
2 3 1 0
3
6 8 2 3
6
7 6
6 0 2 0
0
73 60
3
7
All the elements in the first column of the Routh array are positive.
So the system is stable
Example 2: Investigate whether the following systems represented by the
characteristic equations are stable or not.
15. s6
2s5
8 s4
1 5 s 3
s6 1 8
s5 2 15 16
s4 0.5 12 16
s3 -33 -48
s2 11.27 16
s1 -1.16 0
s0 16
There are four sign changes in the elements of first column of the Routh
array.
Hence there are four roots of the characteristic equation in the right-half of the
s-plane.
Hence the system is unstable
20s2
1 6 s 1 6 0
20 16
Example 3: Investigate whether the following systems represented by the
characteristic equations are stable or not.
16. Routh-Hurwitz Criterion: Special Cases Special Cases of Routh Array
The first element of any row of the Routh’s array is zero
All the elements of any row of the Routh’s array are zero.
Special Case 1: First Element of any row of the Routh’s array is zero
If any row of the Routh’s array contains only the first element as zero
and at least one of the remainingelements have non-zero
value, then replace the first element with a
small positive integer ε.
And then continue the process of completing the Routh’s table.
Now, find the number of sign changes in
the first column of the
Routh’s table by substituting ε tends to zero.
17. Example 4: Determine the stability of the closed-loop transfer
function
s5 1 3 5
s4 2 6 3
s3 0 3.5
s2
s1
s0
18. s5 1 3 5
s4 2 6 3
s3
𝜀 3.5 0
s2 3 0
s1 0 0
s0 3 0 0
For 𝜀 tending to 0, there will be two sign changes in first column.
Hence there are two roots of the characteristic equation in the right-half
of the s-plane. Hence the system is unstable.
19. 1 2 3
1 2 5
0
Example 5: Determine the stability of the system with the
characteristicequation
s5 1 2 3
s4 1 2 5
s3
0 -2
s2
s1
s0
20. s5 1 2 3
s4 1 2 5
s3
𝜀 -2 0
s2
5
s1
5
s0
5
As ϵ tends to 0, there will be two sign changes in first column.
Hence there are two roots of the characteristic equation in
the right-half of the s-plane. Hence the system is unstable.
21. ALTERNATE METHOD:
Transform the characteristic equation by replacing s by
and apply Routh’s test. Let the equation be
Replacing s by 1/z we have
22. z5 5 2 1
z4 3 2 1
z3
-1.33 -0.66 0
z2
0.5 1
z1
2
z0
1
There are two sign changes in first column. Hence
there are two roots of the characteristic equation in the
right-half of the s-plane. Hence the system is unstable
23. Special Case 2: All the Elements of any row of the
Routh’s array arezero.
This condition indicates that there are symmetrically located roots in the
s-plane, which may be
Pair of real roots with opposite sign
Pair of conjugate roots on the imaginary axis
Complex conjugate roots forming quadrates
Polynomial whose coefficients are the elements above the row of zeros
are called auxiliary equation.
Order of the auxiliary equation is always even.
To proceed with Routh’s table, replace the row of zeros with coefficient of
polynomial obtained by taking first derivative of the auxiliary polynomial.
24. Example 6: Determine the number of right hand plane poles in the closed-loop transfer
function
S5 1 6 8
s4 7 42 56
s4 1 6 8
s3 0 0
s2
s1
s0
25. A(s) =
S5 1 6 8
S4 1 6 8
S3 2 6
S2 3 8
S1 1/3 0
S0 8 0
All the elements in the first column of the Routh array are positive.
So the system is stable.
27. s5 1 24 -25
s4 2 48 -50
s3 8 96
s2
24 -50
s1
112.7
s0
-50
There is a single change of sign in the first column of the resulting array,
indicating that Solving the auxiliary equation,
there is one root with positive real part.
Solving the auxiliary equation, yields the roots
s2=1 and s2 =
28. Example 7: Determine the stability of the system
represented by the following characteristic equation
S6 1 5 8 4
S5 3 9 6
S4 2 6 4
S3 0 0
30. Factorizing A(s) we h ve
Solving the auxiliary we have
a
There are two pairs of non repeated roots on the
imaginary axis, hence the system is marginally stable
31. Example 8: Using the Routh criterion check whether the system
representedby the following characteristic equation is stable or
not. Determinethe frequency of oscillations if any.
S4 1 6 8
S3 2 8
S2 2 8
S1 0 0
S0
32. S4 1 6 8
S3 2 8
S2 2 8
S1 4 0
S0 8
Solving the auxiliary we have
So the system oscillates with frequency ω= 2 rad/sec
33. Application of Routh criterion to Linear Feedback Systems
Example 9: Consider a system with a closed loop transfer
function
Determine the range of K for which the system is stable.
The characteristic equation of the system is
34. S4 1 5 K
S3 5 4
S2 21/5 K
S1 (84/5-5K)/(2 1/5) 0
S0 K
Routh array is
For a stable system, all elements in the first column should be
positive. Therefore
35. Example 10: Determine the range of value of K for the system to
be stable
S4 1 13 K
S3 4 36
S2 4 K
S1 36-K 0
S0 K
For the system to be stable and