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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Introduction to Differential Equations01:20

Introduction to Differential Equations

A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...

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Related Experiment Videos

Dynamic uncertainty for compensated second-order systems.

Sascha Eichstädt1, Alfred Link, Clemens Elster

  • 1Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany. sascha.eichstaedt@ptb.de

Sensors (Basel, Switzerland)
|December 14, 2011
PubMed
Summary
This summary is machine-generated.

For metrology applications, finite impulse response (FIR) filtering offers lower uncertainty than infinite impulse response (IIR) filtering for compensating linear time-invariant (LTI) systems. This FIR approach is advantageous for real-time uncertainty evaluation.

Keywords:
deconvolutiondigital filterdynamic uncertaintysensor

Related Experiment Videos

Area of Science:

  • Metrology
  • Signal Processing
  • Control Systems

Background:

  • Uncertainty evaluation in metrology is crucial for accurate measurements.
  • Specific guidelines exist for uncertainty evaluation.
  • Recent schemes for uncertainty evaluation in finite impulse response (FIR) and infinite impulse response (IIR) filtering have been proposed.

Purpose of the Study:

  • To compare FIR and IIR filtering approaches for compensating a second-order linear time-invariant (LTI) system.
  • To evaluate the uncertainty associated with each filtering approach using proposed metrology schemes.
  • To determine which approach is superior for real-time uncertainty evaluation in metrology.

Main Methods:

  • Applied established uncertainty evaluation schemes to both FIR and IIR filtering methods.
  • Utilized the schemes to compensate a second-order LTI system relevant to metrology.
  • Quantitatively compared the uncertainties generated by the FIR and IIR compensation methods.

Main Results:

  • The FIR filtering approach resulted in significantly smaller uncertainties compared to the IIR approach.
  • The FIR approach demonstrated superior performance for real-time uncertainty evaluation.
  • Both methods were applied to a relevant second-order LTI system in metrology.

Conclusions:

  • The FIR approach is preferable for compensating LTI systems when real-time uncertainty evaluation is a requirement in metrology.
  • FIR filtering provides a more accurate and reliable method for uncertainty assessment in this context.
  • The study validates the utility of the proposed uncertainty evaluation schemes for comparing different filtering techniques.