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Feedback Control Via Eigenvalue Assignment for Time Delayed Systems Using the Lambert W Function

[+] Author Affiliations
Sun Yi, Patrick W. Nelson, A. Galip Ulsoy

University of Michigan, Ann Arbor, MI

Paper No. DETC2007-35711, pp. 783-792; 10 pages
doi:10.1115/DETC2007-35711
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

In this paper, we consider the problem of feedback controller design via eigenvalue assignment for systems of linear delay differential equations (DDEs). Unlike ordinary differential equations (ODEs), DDEs have an infinite eigenspectrum and it is not feasible to assign all closed-loop eigenvalues. However, we can assign a critical subset of them using a solution to linear DDEs in terms of the matrix Lambert W function. The solution has an analytical form expressed in terms of the parameters of the DDE, and is similar to the state transition matrix in linear ODEs. Hence, one can extend controller design methods developed based upon the solution form of ODEs to systems of DDEs, including the design of feedback controllers via eigenvalue assignment. We present such an approach here, illustrate using some examples, and compare with other existing methods.

Copyright © 2007 by ASME
Topics: Eigenvalues , Feedback

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