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Transfer Function in Control Systems01:21

Transfer Function in Control Systems

2.0K
The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
2.0K
Transfer Function to State Space01:23

Transfer Function to State Space

985
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
985
State Space Representation01:27

State Space Representation

785
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
785
State Space to Transfer Function01:21

State Space to Transfer Function

691
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
691
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

1.3K
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
1.3K
Convolution Properties I01:20

Convolution Properties I

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Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
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Related Experiment Video

Updated: May 3, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Semiclassical initial-value representation of the transfer operator.

Haim Barak1, Kenneth G Kay1

  • 1Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a new semiclassical initial-value representation (IVR) method to accurately calculate energy levels for complex quantum systems, improving upon existing techniques for chaotic systems.

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Area of Science:

  • Quantum Mechanics
  • Computational Chemistry
  • Theoretical Physics

Background:

  • Traditional semiclassical initial-value representation (IVR) methods struggle with long classical trajectories, especially for large or chaotic systems.
  • Existing methods face limitations in accurately determining approximate energy levels for bound systems.

Purpose of the Study:

  • To develop a novel IVR expression that overcomes limitations of existing methods for calculating semiclassical energy levels.
  • To adapt the method for energy levels with specific symmetries and test its efficacy on integrable and chaotic systems.

Main Methods:

  • Developed a new IVR expression classically equivalent to Bogomolny's transfer matrix formula.
  • Applied the method to two-dimensional quartic oscillator systems (one integrable, one chaotic).
  • Utilized Monte Carlo phase space integrations and analyzed eigenvalues of transfer matrices.

Main Results:

  • The new IVR method successfully resolved all investigated energy levels for both integrable and chaotic systems.
  • The technique demonstrated more rapid convergence in Monte Carlo integrations compared to previous IVR methods.
  • Semiclassical energies were extracted from transfer matrix eigenvalues close to the theoretical minimum.

Conclusions:

  • The developed IVR theory offers a distinct semiclassical approximation to the transfer matrix compared to Bogomolny's theory.
  • The IVR method provides a more accurate prediction of energy levels for chaotic systems than Bogomolny's theory.
  • This approach avoids the need to search for special trajectories, simplifying energy level determination.