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Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a
Libor Pekař1, Radek Matušů2, Roman Prokop3
1Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic.
Plos One
|June 9, 2017
Summary
This study introduces a simple numerical algorithm to find stability margins in systems with multiple time delays. The method efficiently estimates system stability, crucial for biological and human-related dynamics.
Area of Science:
- Control Systems Engineering
- Applied Mathematics
- Biocybernetics
Background:
- Time delays significantly impact the stability of human-related and biological systems.
- Analyzing these delays often requires complex mathematical approaches.
- Understanding stability margins is critical for system design and performance.
Purpose of the Study:
- To present a computationally simple numerical gridding algorithm for determining stability margin delay values.
- To provide a method for analyzing multiple-delay linear systems.
- To offer a precise and accessible tool for stability analysis.
Main Methods:
- Iterative discretization of the characteristic quasi-polynomial using pre-warped bilinear transformation.
- Linear and quadratic interpolation to derive an associated characteristic polynomial.
- Regula Falsi interpolation to enhance the switching root locus for stability border analysis.
Main Results:
- The algorithm accurately estimates the roots of the characteristic quasi-polynomial, correlating with system eigenvalues.
- Demonstrated effectiveness on a bio-cybernetic example of human movement stabilization.
- Achieved rapid computation of polynomial zeros with high precision.
Conclusions:
- The novel algorithm offers a computationally efficient and mathematically accessible method for stability analysis in multiple-delay systems.
- Applicable to systems with non-commensurate delays.
- Facilitates rapid stability margin determination using standard technical computing tools.
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