Research Article Open Access

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Sun Yi1, Wonchang Choi2 and Taher Abu-Lebdeh2
  • 1 Department of Mechanical Engineering, North Carolina A and T State University, United States
  • 2 Department of Civil, Architectural and Environmental Engineering, North Carolina A and T State University, Greensboro, United States

Abstract

Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use of the Lambert W function and analytical solutions of scalar first-order Delay Differential Equations (DDEs). The Lambert W function has been known to be useful in solving delay differential equations. From the solutions in terms of the Lambert W function, the dominant characteristic roots can be obtained and used to estimate time-delays. The function is already embedded in various software packages (e.g., MATLAB) and thus, the presented method can be readily used for time-delay systems. Results: The presented method and the provided examples show ease of formulation and accuracy of time-delay estimation. Conclusion: Estimation of time-delays can be conducted in an analytical way. The presented method will be extended to general systems of DDEs and application to physical systems.

American Journal of Applied Sciences
Volume 9 No. 6, 2012, 955-960

DOI: https://doi.org/10.3844/ajassp.2012.955.960

Submitted On: 25 January 2012 Published On: 7 April 2012

How to Cite: Yi, S., Choi, W. & Abu-Lebdeh, T. (2012). Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations. American Journal of Applied Sciences, 9(6), 955-960. https://doi.org/10.3844/ajassp.2012.955.960

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Keywords

  • Delay Differential Equations (DDEs)
  • Finite Spectrum Assignments (FSA)
  • Ordinary Differential Equations (ODEs)
  • various software packages