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Data-driven control of singularly perturbed hybrid systems with multi-rate sampling.

Yan He1, Defu Zhu1, Chao Chen2

  • 1College of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450000, China.

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|March 29, 2024
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This study ensures exponential stability for singularly perturbed hybrid systems using multi-rate sampling. Novel methods analyze error subsystems and sampling intervals for robust control design.

Keywords:
Data-drivenHybrid systemsMulti-rate samplingStability analysis

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Systems Analysis
  • Hybrid Dynamical Systems

Background:

  • Singularly perturbed systems are crucial in control engineering, often exhibiting complex dynamics.
  • Multi-rate sampling introduces challenges in analyzing system stability due to varying time scales.
  • Hybrid systems combine continuous and discrete dynamics, requiring specialized stability analysis techniques.

Purpose of the Study:

  • To investigate the exponential stability of nonlinear singularly perturbed hybrid systems with multi-rate sampling.
  • To develop a data-driven mechanism and a multi-rate sampling controller for these systems.
  • To analyze the influence of system parameters and sampling ratios on stability.

Main Methods:

  • Development of a hybrid model for nonlinear singularly perturbed systems.
  • Design of a data-driven mechanism and a multi-rate sampling controller.
  • Proposal of a novel error function and inequalities for error subsystem analysis.
  • Estimation of sampling interval bounds and analysis of parameter effects.

Main Results:

  • Establishment of a framework for analyzing exponential stability in the targeted systems.
  • Identification of bounds for fast and slow sampling intervals.
  • Demonstration of how perturbation parameters and sampling ratios impact stability.
  • Validation of the proposed methods using a DC motor model.

Conclusions:

  • The proposed methodology effectively addresses the exponential stability problem for singularly perturbed hybrid systems with multi-rate sampling.
  • The findings provide valuable insights into the design and analysis of robust control systems operating under multi-rate sampling conditions.
  • The study offers a practical approach, validated by a DC motor example, for enhancing control system performance.