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    Area of Science:

    • Control Systems Engineering
    • Signal Processing
    • Dynamic Systems Analysis

    Background:

    • Quasiperiodic disturbance estimation in dynamic control systems is challenging due to submerged signals and unknown frequencies.
    • Existing methods often assume known frequencies or measurable disturbances, limiting their applicability.
    • The coupling between disturbance separation and frequency identification complicates existing approaches.

    Purpose of the Study:

    • To develop a robust method for quasiperiodic disturbance estimation in dynamic control systems without prior frequency knowledge.
    • To address the challenge of submerged disturbance signals and their complex interaction with frequency identification.
    • To provide a framework capable of handling nonlinear system models and time-varying frequencies.

    Main Methods:

    • An iterative Expectation-Maximization (EM) framework is proposed for joint disturbance signal separation and frequency identification.
    • The E-step reconstructs the quasiperiodic signal using the current frequency estimate.
    • The M-step updates the frequency estimate by maximizing the log-likelihood function.
    • An online EM algorithm utilizing forward-only smoothing techniques is developed for recursive estimation.

    Main Results:

    • The proposed EM framework effectively separates submerged quasiperiodic disturbances and identifies their frequencies.
    • The iterative approach overcomes the limitations of methods requiring prior frequency knowledge.
    • The developed online EM algorithm enables recursive frequency estimation.
    • The method demonstrates extensibility to nonlinear systems and time-varying frequencies.

    Conclusions:

    • The novel EM-based approach provides a significant advancement in quasiperiodic disturbance estimation for dynamic control systems.
    • This method offers a practical solution for scenarios with unknown or time-varying frequencies and submerged signals.
    • The framework's adaptability to nonlinear models and time-varying frequencies enhances its broad applicability in control engineering.