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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Related Experiment Video

Updated: Mar 26, 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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An innovative fixed-pole numerical approximation for fractional order systems.

Yiheng Wei1, Peter W Tse2, Bin Du3

  • 1Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China; Department of Automation, University of Science and Technology of China, Hefei 230027, China.

ISA Transactions
|February 7, 2016
PubMed
Summary

A new numerical method accurately approximates fractional order systems using an identification concept. This approach effectively solves initial value problems and outperforms existing fixed-pole finite model methods.

Keywords:
Caputo derivativeFixed-poleFractional order systemsIdentificationNon-zero initial conditionsNumerical approximation

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Area of Science:

  • Control Systems Engineering
  • Numerical Analysis
  • Applied Mathematics

Background:

  • Fractional order systems are increasingly utilized in various scientific and engineering fields.
  • Accurate numerical approximation schemes are essential for analyzing and controlling these systems.
  • Existing methods for fractional order systems, such as the fixed-pole finite model method, have limitations.

Purpose of the Study:

  • To propose a novel numerical approximation scheme for fractional order systems based on the concept of identification.
  • To derive an exact state-space model for fractional order systems.
  • To address the crucial issue of initial value problems in fractional order systems.

Main Methods:

  • Derivation of an identical equation to obtain the exact state-space model.
  • Development of a numerical approximation scheme based on system identification.
  • Analysis of initial value problems, demonstrating reduction to the Caputo case under specific conditions.
  • Simulation studies to validate the proposed scheme's effectiveness.

Main Results:

  • An effective scheme for obtaining the desired state-space model of fractional order systems was developed.
  • The proposed method successfully handles initial value problems.
  • Simulation results demonstrate the effectiveness and superiority of the novel scheme.
  • Comparison with the fixed-pole finite model method shows improved performance.

Conclusions:

  • The proposed numerical approximation scheme offers an effective and accurate approach for fractional order systems.
  • The method provides a robust solution for initial value problems in fractional dynamics.
  • This research contributes a valuable tool for the analysis and control of fractional order systems.