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Related Concept Videos

State Space Representation01:27

State Space Representation

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...
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Difference from Background: Limit of Detection01:05

Difference from Background: Limit of Detection

The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...
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...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Robust state estimation using desensitized Divided Difference Filter.

Christopher D Karlgaard1, Haijun Shen

  • 1Analytical Mechanics Associates, Inc., 303 Butler Farm Road, Suite 104A, Hampton, VA 23666, United States. karlgaard@ama-inc.com

ISA Transactions
|June 1, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a robust divided difference filtering method to improve state estimation accuracy. The novel approach reduces sensitivity to plant model parameter uncertainties in dynamic systems.

Keywords:
Divided difference filteringOptimal filteringParameter uncertaintyRobust filtering

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Last Updated: May 11, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Area of Science:

  • Control Systems Engineering
  • Signal Processing
  • Electrical Engineering

Background:

  • Kalman filtering is widely used for state estimation but sensitive to model parameter errors.
  • Parameter uncertainties in dynamic systems can degrade filter performance and lead to inaccurate state estimates.
  • Developing robust filtering techniques is crucial for reliable system operation.

Purpose of the Study:

  • To develop a robust divided difference filtering approach.
  • To enhance Desensitized Kalman Filtering by incorporating state sensitivity penalties.
  • To provide solutions for first and second-order Divided Difference Filters.

Main Methods:

  • Formulating filters using a minimum variance cost function.
  • Augmenting the cost function with a penalty for state sensitivities.
  • Developing first and second-order Divided Difference Filters.
  • Utilizing Monte Carlo simulations for algorithm validation.

Main Results:

  • The developed filters are non-minimum variance.
  • Filters demonstrate reduced sensitivity to deviations in plant model parameters.
  • Successful application to induction motor state estimation with parameter uncertainties.

Conclusions:

  • The proposed divided difference filtering approach effectively reduces sensitivity to parameter uncertainties.
  • The method offers improved robustness for state estimation in systems with model inaccuracies.
  • The technique is validated for practical applications like induction motor analysis.