1) The document describes different types of nonlinearities that can occur in systems. It classifies nonlinearities based on their magnitude (incidental or intentional) and frequency (limit cycles, jump resonance, etc.).
2) Some common types of nonlinearities described include saturation, dead zones, backlash, relays, harmonics, and chaotic behavior.
3) Nonlinearities can cause issues like degradation of system performance, limit cycles, and even destabilization of systems. Understanding different nonlinear effects is important for analyzing system behavior.
This presentation gives the information about introduction to control systems
Subject: Control Engineering as per VTU Syllabus of Aeronautical Engineering.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Disclaimer:
The contents used in this presentation are taken from the text books mentioned in the references. I do not hold any copyrights for the contents. It has been prepared to use in the class lectures, not for commercial purpose.
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 gives the information about introduction to control systems
Subject: Control Engineering as per VTU Syllabus of Aeronautical Engineering.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Disclaimer:
The contents used in this presentation are taken from the text books mentioned in the references. I do not hold any copyrights for the contents. It has been prepared to use in the class lectures, not for commercial purpose.
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.
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
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.
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
Ch5 transient and steady state response analyses(control)Elaf A.Saeed
Chapter 5 Transient and steady-state response analyses. From the book (Ogata Modern Control Engineering 5th).
5-1 introduction.
5-2 First-Order System.
5-3 second-order system.
5-6 Routh’s stability criterion.
5-8 Steady-state errors in unity-feedback control systems.
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.
CONTROL SYSTEMS PPT ON A LEAD COMPENSATOR CHARACTERISTICS USING BODE DIAGRAM ...sanjay kumar pediredla
A LEAD COMPENSATOR CHARACTERISTICS USING BODE DIAGRAM FOR MAXIMUM OF 50 DEG PHASE ANGLE
THIS PPT IS SO USEFUL FOR THE ENGINEERING STUDENTS FOR CONTROL SYSTEMS STUDENTS AND THIS PPT ALSO CONTAINS A MATLAB CODING FOR THE LEAD COMPENSATOR AND THE RESULTS ARE ALSO PLOTTED IN THAT PPT AND THE PROBLEM CAN ALSO BE SOLVED BY USING THE DATA IN PPT AND IT IS SO USEFUL PPT
this is presentation about time response analysis in control engineering. this is presentation on its types and many more like time responses with best example
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 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
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.
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
Ch5 transient and steady state response analyses(control)Elaf A.Saeed
Chapter 5 Transient and steady-state response analyses. From the book (Ogata Modern Control Engineering 5th).
5-1 introduction.
5-2 First-Order System.
5-3 second-order system.
5-6 Routh’s stability criterion.
5-8 Steady-state errors in unity-feedback control systems.
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.
CONTROL SYSTEMS PPT ON A LEAD COMPENSATOR CHARACTERISTICS USING BODE DIAGRAM ...sanjay kumar pediredla
A LEAD COMPENSATOR CHARACTERISTICS USING BODE DIAGRAM FOR MAXIMUM OF 50 DEG PHASE ANGLE
THIS PPT IS SO USEFUL FOR THE ENGINEERING STUDENTS FOR CONTROL SYSTEMS STUDENTS AND THIS PPT ALSO CONTAINS A MATLAB CODING FOR THE LEAD COMPENSATOR AND THE RESULTS ARE ALSO PLOTTED IN THAT PPT AND THE PROBLEM CAN ALSO BE SOLVED BY USING THE DATA IN PPT AND IT IS SO USEFUL PPT
this is presentation about time response analysis in control engineering. this is presentation on its types and many more like time responses with best example
Introduction
Inter-area oscillations involve wide areas of the power grid and numerous power system components. Therefore, identifying the components influencing negatively the oscillations damping is extremely important. Power system oscillations usually contain multiple frequency components (modes), which are determined by generator inertia, transmission line impedance, governor, and excitation control, etc.
The oscillation behavior is sensitive to the following parameters:
The load model
The operating conditions
The presence of fast exciters
The topology
Electromagnetic relays used for power system .pptxNANDHAKUMARA10
In this relay, the armature is attracted to the pole of a magnet. The electromagnetic force exerted on the moving element is proportional to the square of the current flow through the coil. This relay responds to both the alternating and direct current.
For AC quantity the electromagnetic force developed is given as
equation-1The above equation shows that the electromagnetic relay consists two components, one constant independent of time and another dependent upon time and pulsating at double supply frequency. This double supply frequency produces noise and hence damage the relay contacts.
The difficulty of a double frequency supply is overcome by splitting the flux developing in the electromagnetic relay. These fluxes were acting simultaneously but differ in time phase. Thus the resulting deflecting force is always positive and constant. The splitting of fluxes is achieved by using the electromagnet having a phase shifting networks or by putting shading rings on the poles of an electromagnet.
The electromagnetic attraction relay is the simplest type of relay which includes a plunger (or solenoid), hinged armature, rotating armature (or balanced) and moving iron polarised relay.
Load flow analysis, also known as power flow analysis, is a fundamental tool in power system
engineering used to analyze and calculate the steady-state operating conditions of an electrical network.
The primary goal of load flow analysis is to determine the voltage magnitude and phase angles at various
buses in the system, as well as the real and reactive power flows on the transmission lines. Here are the
basics of load flow analysis. It analyses the power system in normal steady state operation. Its Purpose is to
calculate the voltages and once voltages are known for all buses, line flows and losses can be calculated.
1.2 Bus Types
➢ PQ Bus (P: Real Power, Q: Reactive Power): Represents a bus where both real and reactive
powers are specified.
➢ PV Bus (P: Real Power, V: Voltage Magnitude): Specifies real power and voltage
magnitude.
➢ Slack Bus (or Swing Bus): The reference bus where voltage magnitude and phase angle
are specified. It serves as the reference point for the entire system
1.3 Significance of Power Flow studies
Power flow studies are essential for understanding and optimizing the performance of electrical
power systems. They provide valuable insights that support planning, operation, and decisionmaking processes, contributing to the overall reliability and efficiency of the power grid. They are
Important in Planning future expansion of system and helps in determining the best operation of
existing system
2 Methods of Power Flow Analysis
2.1 Power Flow Equations and their solution techniques
• Formulation of network equations in nodal admittance results non-linear algebraic equations of
node currents
• For power systems, these are transformed to Power flow equations which can be solve by iterative
techniques
Load flow analysis, also known as power flow analysis, is a fundamental tool in power system
engineering used to analyze and calculate the steady-state operating conditions of an electrical network.
The primary goal of load flow analysis is to determine the voltage magnitude and phase angles at various
buses in the system, as well as the real and reactive power flows on the transmission lines. Here are the
basics of load flow analysis. It analyses the power system in normal steady state operation. Its Purpose is to
calculate the voltages and once voltages are known for all buses, line flows and losses can be calculated.
1.2 Bus Types
➢ PQ Bus (P: Real Power, Q: Reactive Power): Represents a bus where both real and reactive
powers are specified.
➢ PV Bus (P: Real Power, V: Voltage Magnitude): Specifies real power and voltage
magnitude.
➢ Slack Bus (or Swing Bus): The reference bus where voltage magnitude and phase angle
are specified. It serves as the reference point for the entire system
1.3 Significance of Power Flow studies
Power flow studies are essential for understanding and optimizing the performance of electrical
power systems. They provide valuable insights that support planning, operation
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.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
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.
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.
3. Nonlinearity
• Nonlinearity is the behavior of a circuit , in which the
output signal strength does not vary in direct
proportion to the input signal strength. E.g.: diode.
• Nonlinear system do not follow superposition
property.
3
4. Classification of Nonlinearities
• Nonlinearity can be classified in to :
• On the basis of magnitude
○ Incidental nonlinearity : present
inherently in the system.
○ Intentional nonlinearity : inserted in the
system to modify system characteristics.
• On the basis of frequency
4
5. On the basis of
Magnitude Frequency
1) Dead zone
2) Saturation
3) Friction
4) Backlash
5) Relay
1) Limit cycle
2) Jump resonance
3) Frequency entrainment
4) Beat frequency production
5) Self excitation
6) Harmonics
7) Chaotic behavior
5
6. 1) Saturation
• Output of the system is proportional to input in a
limited range of input signal.
• On exceeding range , output tends to become nearly
constant.
Eg: amplifiers,
torque and
speed saturation
in motors
6
7. • Limits max. achievable magnetic field in system
containing electromagnetic components
• In electronic circuits ferromagnetic core inductor- on
applying AC signal , nonlinearity can cause harmonics
and intermodulation distortion so we have to limit the
level of signal accordingly.
• Used to limit the current in saturable core transformer,
arc welding and ferroresonant transformer which serve
as voltage regulator.
7
8. 2) Friction
• Viscous friction
• Coulomb friction
• Stinction friction
8
•It comes in to existence when mechanical
surface comes in sliding contact.
9. E.g.: HDDs servo systems-
•It uses a voice-coil-motor
(VCM) actuator to actuate the
R/W recording arm assembly,
which consists of a pivot
with a ball bearing, a metal
arm and a rigid suspension that
holds the R/W header
and slider.
•The presence of friction in rotatory actuator pivot bearing
result in large residual errors and high frequency oscillation;
which may produce positioning error and deteriorate the
performance of the servo system.
9
10. 3)Dead zone
• Kind of nonlinearity in which the system doesn’t
respond to the given input until the input reaches a
particular level
Or
• Output becomes zero when input crosses certain
limiting value .
10
11. • Effect of dead zone:
• system performance degradation
• reduced positioning accuracy
• may destabilize system
• E.g.:
• Dead zone in actuators, such as hydraulic servo
valves, give rise to limit cycle and instability.
• Electronic devices like diode.
11
12. 4) Backlash
• The difference between the tooth space and tooth
width in mechanical system , which is essential for
rapid working gear transmission is known as
backlash.
12
• It is present in most of the
mechanical and hydraulic
systems.
• Increase with wear.
13. • When the backlash is traversed, no torque is
transmitted through the shaft and when the contact is
achieved, the resulted impact can destroy the gear and
cause a high frequency noise.
13
•Effect of backlash :
• gear backlash may
cause sustained oscillation
or chattering phenomenon
• system may turn
unstable for large backlash
14. 5) Relay
• It is intentional nonlinearity.
• Ideal relay is the extreme case of saturation.
• occurs when the linearity range is
shrunken to zero and slope in linearity
range become vertical .
• It can lead to chattering due
to discontinuity.
• Ideal characteristic can be
nearly achieved by SCR
switching .
14
15. • Practical relay has a definite amount of dead zone .
•Relay coil require a finite
amount of current to actuate
(cause of dead zone).
• To close the relay larger coil current
is needed , so relay characteristic exhibit hysteresis
also .
15
16. • Relay can be switched abruptly in any of these 3
states :
•off
•full forward
•full reverse
Therefore are used widely in control field .
• Application: • temperature control system
• aircraft and missile control system
• space-vehicle attitude control system
• power system
16
17. 1) Limit cycle
• It corresponds to an oscillation of fixed amplitude
and period.
• Limit cycle is a closed trajectory; other trajectories
about the limit cycle are spirals from various points
of phase plane.
• Limit cycle divides the
phase plane in to 2 zones.
17
18. • Stable limit cycle :
• signify – system will
approach an oscillatory
state regardless of the
initial condition.
• Semi stable limit cycle :
• in this case maintenance
of oscillation depends
on initial condition.
18
19. • Unstable limit cycle :
• Limit cycles are usually less sensitive to system
parameter variations.
• Although L.C. can be sustained over a finite range of
system parameters.
• E.g.: squealing door hinges, electric wires whistling
in the wind ,whirling shafts.
19
20. 2) Jump resonance
• It is a discontinuous change in the steady state
response of the system when a parameter (forcing
frequency) is slowly varied.
• Its produced around the system’s resonant frequency.
• Consist of multiple values of the amplitude and phase
of input signal when the amplitude or frequency of
the harmonic input signal is varied slowly.
20
21. • E.g. : hard spring
• As input frequency is increased
gradually from 0 ,response
follow curve ABC .
• At ‘C’- increment in frequency
resulted in discontinuous jump down to ‘D’.
• Further increase – response curve follows through
DE.
• If frequency is now decreased – curve EDF is
followed with a jump up to B from the point F and
then to A .
21
22. 3) Frequency entrainment
• It is because of the physical absorption of the
particular frequencies.
• Frequency absorbed by that system is not seen or
observed in the spectrum .
• E.g.:
water in pneumatic
system
22
23. 4) Beat frequency
• The system is sensitive to some
frequency only.
• E.g.:
guitar
sonometer
23
24. 5)Self excitation
• It may occur without any external or internal periodic
forcing.
• It appears due to specific internal properties of a
system.
• It is of 2 types:
• soft self excitation
• hard self excitation
24
25. • Soft self excitation :
•represented in phase space by a stable limit cycle.
• Hard self excitation :
•represented by unstable limit cycle.
•depending on initial conditions trajectory tends to
equilibrium point or to infinite; therefore this
type
is called catastrophic .
• E.g.: fluttering of airplane wings, shimming of
vehicle wheel , unwanted vibration during machining
processes (chatter).
25
26. 6) Harmonics
• Nonlinear system may contain frequencies other than
forcing frequency in input
• These frequencies are multiple of forcing frequency.
• If f(t)= A sin ωt
then oscillatory phenomenon of frequency ᾤ may
appear at certain points
here ω not equal to ᾤ
when ᾤ > ω it is superharmonic
when ᾤ < ω it is subharmonic
26
27. 7) Chaotic behavior and bifurcation
• Chaos – complex , irregular motion
that are extremely sensitive
to initial conditions.
• Bifurcation – qualitative or topological
change in system dynamics
produced by varying
system parameters .
27
28. • Bifurcation – periodic doubling
• chaos – series of periodic doubling
• The illustration above shows a bifurcation diagram of
the logistic map obtained by plotting as a function of a
series of values for obtained by starting with a random
value ,
28
29. iterating many times, and discarding the first points
corresponding to values before the iterates converge
to the attractor. In other words, the set of fixed points
of corresponding to a given value of are plotted for
values of increasing to the right.
Xn = r(n-1) (1-x(n-1))
• E.g.: Spur gear system with backlash ; vibration in it
have bifurcation and chaotic behavior depending
upon initial conditions .
29