System identification with measurement noise compensation based on polynomial modulating function for...

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Signal Processing

Background:

• Fractional-order systems are prevalent in various scientific and engineering fields.
• Accurate system identification is crucial for control and analysis.
• Existing methods often struggle with noise and time delays.

Purpose of the Study:

• To develop a robust system identification method for fractional-order systems with time delays.
• To address the challenges posed by input and output noise in time-domain identification.
• To provide an effective algorithm for identifying complex dynamic systems.

Main Methods:

• Utilizing polynomial modulating functions and fractional-order integration by parts.
• Transforming fractional-order differential equations into algebraic equations.
• Employing numerical integration formulas and least squares for system identification.
• Incorporating a noise compensation method with an auxiliary high-order fractional-order system.

Main Results:

• The proposed method successfully transforms differential equations into algebraic forms.
• A least squares approach is derived for system identification.
• The noise compensation technique effectively mitigates the impact of measurement noise.
• Simulation and experimental results validate the algorithm's effectiveness.

Conclusions:

• The developed polynomial modulating function-based method provides accurate identification of fractional-order systems with time delays.
• The noise compensation strategy enhances the robustness of the identification algorithm.
• The approach is validated through simulations and real-world thermal system experiments.