This document discusses unconditionally stable finite-difference time-domain (FDTD) methods for solving Maxwell's equations numerically. It outlines FDTD algorithms such as Yee's method from 1966 which discretize the equations on a staggered grid. It also discusses the von Neumann stability analysis and compares implicit Crank-Nicolson and alternating-direction implicit methods to conventional explicit FDTD methods. The document examines the advantages and disadvantages of unconditionally stable FDTD approaches.
modeling of MECHANICAL system (translational), Basic Elements Modeling-Spring...Waqas Afzal
This document summarizes modeling of mechanical translational systems. It discusses modeling basic elements like springs, masses, and dampers and provides their equations of motion. Examples are given of modeling multiple springs, masses and dampers connected together in different configurations. The state equations and state diagram are obtained for a sample mechanical translational system with multiple springs and dampers connecting different masses.
ELKOMP 2019: Beredskapsforskriften, ny oppdatering med veiledning - Helge Uls...Trainor Elsikkerhet AS
KJENNER DU TIL DEN NYE OPPDATERINGEN AV BEREDSKAPSFORSKRIFTEN?
Helge Ulsberg er sjefsingeniør i NVE og jobber nettopp med utvikling av selve forskriften og veiledningen til den. Med observatørstatus i Beredskapsrådet og Sjøkabelberedskap i REN og flere års erfaring fra arbeid med Sikkerhetsloven, Energiloven, som medlem av NK 14 Krafttransformatorer og NordBER (nordisk elforsyningsberedskap), er han en nestor innen kraftforsyningsberedskap og elsikkerhet. på Elsikkerhetskompetanse 2019 ga han bransjen et viktig innblikk i en svært relevant forskrift.
This document discusses unconditionally stable finite-difference time-domain (FDTD) methods for solving Maxwell's equations numerically. It outlines FDTD algorithms such as Yee's method from 1966 which discretize the equations on a staggered grid. It also discusses the von Neumann stability analysis and compares implicit Crank-Nicolson and alternating-direction implicit methods to conventional explicit FDTD methods. The document examines the advantages and disadvantages of unconditionally stable FDTD approaches.
modeling of MECHANICAL system (translational), Basic Elements Modeling-Spring...Waqas Afzal
This document summarizes modeling of mechanical translational systems. It discusses modeling basic elements like springs, masses, and dampers and provides their equations of motion. Examples are given of modeling multiple springs, masses and dampers connected together in different configurations. The state equations and state diagram are obtained for a sample mechanical translational system with multiple springs and dampers connecting different masses.
ELKOMP 2019: Beredskapsforskriften, ny oppdatering med veiledning - Helge Uls...Trainor Elsikkerhet AS
KJENNER DU TIL DEN NYE OPPDATERINGEN AV BEREDSKAPSFORSKRIFTEN?
Helge Ulsberg er sjefsingeniør i NVE og jobber nettopp med utvikling av selve forskriften og veiledningen til den. Med observatørstatus i Beredskapsrådet og Sjøkabelberedskap i REN og flere års erfaring fra arbeid med Sikkerhetsloven, Energiloven, som medlem av NK 14 Krafttransformatorer og NordBER (nordisk elforsyningsberedskap), er han en nestor innen kraftforsyningsberedskap og elsikkerhet. på Elsikkerhetskompetanse 2019 ga han bransjen et viktig innblikk i en svært relevant forskrift.
This document discusses time response specifications for second order systems, including delay time, rise time, peak time, and peak overshoot. It provides equations to calculate each specification based on the natural frequency (ωn) and damping ratio (δ) of the system. Rise time is defined as the time to rise from 10-90% of the final value and is calculated as (π - cos^-1δ)/ωn√(1-δ^2). Peak time is the time to reach the first peak and is calculated as π/ωn√(1-δ^2). Peak overshoot is calculated as 100e^(-δπ)/√(1-δ^2)
Олесь Гончар:«Дякую Богові, що він дав мені народитися українцем». estet13
Олесь Гончар – видатний письменник, великий майстер слова, чиї твори заслужено вважаються класикою української літератури. Впродовж усього творчого шляху його ломили, трощили, але — не зламали! Мужній солдат, він переніс усі удари долі, бо чітко знав, для чого прийшов у цей світ. Він не згаяв на дріб’язкове, неістотне ані хвилини, постійно думав про велике – про Україну та її народ і всіх закликав до цього.
Шанувальникам творчості письменника добре знайома і його багатогранна злободенна публіцистика, яка ввібрала в себе думки про українське духовне відродження, про видатні постаті нашої культури, про все, що хвилювало, тривожило його.
Голос Олеся Гончара на захист України і її талантів, як найціннішого
скарбу, завжди звучав всесильно. Як громадський діяч, мужньо відстоював він
ідеали демократії і незалежності України, брав участь у І Всесвітньому з'їзді
«Зеленого світу», виступав на І з'їзді Товариства української мови
ім. Т. Г. Шевченка і благословляв його на подвижницьку діяльність по відродженню нашої духовності.
Письменник стояв біля витоків РУХу, підтримував голодуючих студентів у
жовтні 1990 року. Йому першому серед письменників Незалежної України було
надано почесне звання «Інтелектуал світу 1993 року». Його по праву назвали великим Українцем, совістю нації, подвижником її духовного відродження.
Чернігівська обласна бібліотека для дітей пропонує літературний ювілейний до 105-річчя від дня народження Олеся Гончара.
This document discusses frequency response analysis, which involves analyzing a system's response to sinusoidal inputs. It describes three main advantages of the frequency response method: it can be obtained directly from experiments, it is easy to analyze effects of sinusoidal inputs, and it is easy to analyze stability with delay elements. The key aspects covered include:
- Defining the frequency response as the ratio of the complex vectors of the steady-state output to sinusoidal input.
- Two approaches to obtain the frequency response: experimental measurement and deductive using the transfer function.
- Graphically representing the frequency response using rectangular coordinates, polar plots, and Bode diagrams. Bode diagrams use logarithmic scales to show both low and high frequency
This document contains a mid-term test for a signals and systems engineering diploma assessment. The test contains 4 questions that assess topics such as determining if signals are periodic or aperiodic, sketching signals, evaluating convolution sums and integrals, defining Laplace and z-transforms, and using properties like shifting to find impulse responses of linear time-invariant systems. The test aims to evaluate students' understanding of fundamental concepts in signals and systems.
The document discusses mathematical modeling of mechanical systems, including rotational motion with gears, gear trains, and electromechanical systems. It covers modeling assumptions, system components, torque-speed curves, and linearization techniques. Specifically, it describes linearizing nonlinear systems by finding the nonlinear component, equilibrium point, and using Taylor series expansion to analyze the linearized system for small signal inputs approaching zero.
This document summarizes key concepts in digital signal processing systems. It defines a system as a combination of elements that processes an input signal to produce an output signal. Systems are classified as continuous or discrete time, lumped or distributed parameter, static or dynamic, causal or non-causal, linear or non-linear, time variant or invariant, and stable or unstable. Convolution and the discrete Fourier transform (DFT) are also introduced as important tools in digital signal processing. The DFT transforms a signal from the time domain to the frequency domain.
Dcs lec03 - z-analysis of discrete time control systemsAmr E. Mohamed
The document discusses discrete time control systems and their mathematical representation using z-transforms. It covers topics such as impulse sampling, the convolution integral method for obtaining the z-transform, properties of the z-transform, inverse z-transforms using long division and partial fractions, and mapping between the s-plane and z-plane. Examples are provided to illustrate various concepts around discrete time systems and their analysis using z-transforms.
This document is the final project report for controlling an inverted pendulum system. It includes modeling the nonlinear dynamics of the pendulum cart system and deriving the state space equations. The goal is to balance the pendulum in the vertically upward unstable equilibrium position using feedback control. The report outlines modeling the system, linearizing about the unstable point, designing a feedback controller using linear quadratic regulation, and simulating the closed-loop response. Parameter perturbations are also analyzed through simulation to study the transient behavior and stability margins of the controlled system.
This document provides an overview of analog control systems and Laplace transforms. It introduces key concepts like Laplace transforms, common time domain inputs, transfer functions, and modeling electrical, mechanical and electromechanical systems using block diagrams and mathematical models. Examples are provided to illustrate Laplace transforms, transfer functions, and analyzing system response using poles, zeros and stability analysis.
Formulario integrali proprietà e alcuni integrali particolari (mia)Domenico Tafuni
Integrali indefiniti, proprietà, integrazione per semplice trasformazione dell'integrando, integrazione per decomposizione in somma, integrazione delle funzioni razionali
This document discusses time response specifications for second order systems, including delay time, rise time, peak time, and peak overshoot. It provides equations to calculate each specification based on the natural frequency (ωn) and damping ratio (δ) of the system. Rise time is defined as the time to rise from 10-90% of the final value and is calculated as (π - cos^-1δ)/ωn√(1-δ^2). Peak time is the time to reach the first peak and is calculated as π/ωn√(1-δ^2). Peak overshoot is calculated as 100e^(-δπ)/√(1-δ^2)
Олесь Гончар:«Дякую Богові, що він дав мені народитися українцем». estet13
Олесь Гончар – видатний письменник, великий майстер слова, чиї твори заслужено вважаються класикою української літератури. Впродовж усього творчого шляху його ломили, трощили, але — не зламали! Мужній солдат, він переніс усі удари долі, бо чітко знав, для чого прийшов у цей світ. Він не згаяв на дріб’язкове, неістотне ані хвилини, постійно думав про велике – про Україну та її народ і всіх закликав до цього.
Шанувальникам творчості письменника добре знайома і його багатогранна злободенна публіцистика, яка ввібрала в себе думки про українське духовне відродження, про видатні постаті нашої культури, про все, що хвилювало, тривожило його.
Голос Олеся Гончара на захист України і її талантів, як найціннішого
скарбу, завжди звучав всесильно. Як громадський діяч, мужньо відстоював він
ідеали демократії і незалежності України, брав участь у І Всесвітньому з'їзді
«Зеленого світу», виступав на І з'їзді Товариства української мови
ім. Т. Г. Шевченка і благословляв його на подвижницьку діяльність по відродженню нашої духовності.
Письменник стояв біля витоків РУХу, підтримував голодуючих студентів у
жовтні 1990 року. Йому першому серед письменників Незалежної України було
надано почесне звання «Інтелектуал світу 1993 року». Його по праву назвали великим Українцем, совістю нації, подвижником її духовного відродження.
Чернігівська обласна бібліотека для дітей пропонує літературний ювілейний до 105-річчя від дня народження Олеся Гончара.
This document discusses frequency response analysis, which involves analyzing a system's response to sinusoidal inputs. It describes three main advantages of the frequency response method: it can be obtained directly from experiments, it is easy to analyze effects of sinusoidal inputs, and it is easy to analyze stability with delay elements. The key aspects covered include:
- Defining the frequency response as the ratio of the complex vectors of the steady-state output to sinusoidal input.
- Two approaches to obtain the frequency response: experimental measurement and deductive using the transfer function.
- Graphically representing the frequency response using rectangular coordinates, polar plots, and Bode diagrams. Bode diagrams use logarithmic scales to show both low and high frequency
This document contains a mid-term test for a signals and systems engineering diploma assessment. The test contains 4 questions that assess topics such as determining if signals are periodic or aperiodic, sketching signals, evaluating convolution sums and integrals, defining Laplace and z-transforms, and using properties like shifting to find impulse responses of linear time-invariant systems. The test aims to evaluate students' understanding of fundamental concepts in signals and systems.
The document discusses mathematical modeling of mechanical systems, including rotational motion with gears, gear trains, and electromechanical systems. It covers modeling assumptions, system components, torque-speed curves, and linearization techniques. Specifically, it describes linearizing nonlinear systems by finding the nonlinear component, equilibrium point, and using Taylor series expansion to analyze the linearized system for small signal inputs approaching zero.
This document summarizes key concepts in digital signal processing systems. It defines a system as a combination of elements that processes an input signal to produce an output signal. Systems are classified as continuous or discrete time, lumped or distributed parameter, static or dynamic, causal or non-causal, linear or non-linear, time variant or invariant, and stable or unstable. Convolution and the discrete Fourier transform (DFT) are also introduced as important tools in digital signal processing. The DFT transforms a signal from the time domain to the frequency domain.
Dcs lec03 - z-analysis of discrete time control systemsAmr E. Mohamed
The document discusses discrete time control systems and their mathematical representation using z-transforms. It covers topics such as impulse sampling, the convolution integral method for obtaining the z-transform, properties of the z-transform, inverse z-transforms using long division and partial fractions, and mapping between the s-plane and z-plane. Examples are provided to illustrate various concepts around discrete time systems and their analysis using z-transforms.
This document is the final project report for controlling an inverted pendulum system. It includes modeling the nonlinear dynamics of the pendulum cart system and deriving the state space equations. The goal is to balance the pendulum in the vertically upward unstable equilibrium position using feedback control. The report outlines modeling the system, linearizing about the unstable point, designing a feedback controller using linear quadratic regulation, and simulating the closed-loop response. Parameter perturbations are also analyzed through simulation to study the transient behavior and stability margins of the controlled system.
This document provides an overview of analog control systems and Laplace transforms. It introduces key concepts like Laplace transforms, common time domain inputs, transfer functions, and modeling electrical, mechanical and electromechanical systems using block diagrams and mathematical models. Examples are provided to illustrate Laplace transforms, transfer functions, and analyzing system response using poles, zeros and stability analysis.
Formulario integrali proprietà e alcuni integrali particolari (mia)Domenico Tafuni
Integrali indefiniti, proprietà, integrazione per semplice trasformazione dell'integrando, integrazione per decomposizione in somma, integrazione delle funzioni razionali