Fractional observer to estimate periodical forces.

Area of Science:

• Mechanical Engineering
• Control Systems Theory
• Applied Mathematics

Background:

• Estimating forces in mechanical systems is crucial for control and analysis.
• Traditional observers may struggle with complex periodic forces.
• Fractional calculus offers advanced modeling capabilities.

Purpose of the Study:

• To propose a novel fractional state observer for estimating periodic forces.
• To design an observer using Fourier series approximation and damped harmonic oscillator dynamics.
• To validate the observer's performance using real-world experimental data.

Main Methods:

• Designing a fractional state observer with constant gain.
• Utilizing Fourier series to approximate the periodic external force.
• Employing the Adams-Bashforth-Moulton method for computing fractional derivatives (Liouville-Caputo sense).
• Integrating estimated Fourier series coefficients into the observer's dynamical system.

Main Results:

• The fractional state observer successfully estimates periodic forces.
• Force reconstruction is achieved by estimating Fourier series coefficients.
• Experimental validation confirms the observer's effectiveness and advantages over conventional methods.
• The observer leverages system displacement measurements for force estimation.

Conclusions:

• Fractional state observers provide an effective method for periodic force estimation in mechanical systems.
• The proposed observer demonstrates superior performance in force reconstruction tasks.
• This approach offers a valuable tool for analyzing and controlling systems subjected to periodic external forces.