A new time-discretization method for the development of a sampled-data representation of a nonlinear continuous-time input-driven system with time delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between numerical and system-theoretic properties. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. The resulting time-discretization provides a finite-dimensional representation for nonlinear control systems with time-delay enabling the application of existing controller design techniques. The performance of the proposed discretization procedure is evaluated using the case study of a two-degree-of-freedom mechanical system that exhibits nonlinear behavior. Various sampling rates and time-delay values are considered.
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e-mail: nikolas@wpi.edu
e-mail: kitchong@moak.chonbuk.ac.kr
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March 2005
Technical Briefs
Control-Relevant Discretization of Nonlinear Systems With Time-Delay Using Taylor-Lie Series
Nikolaos Kazantzis,
e-mail: nikolas@wpi.edu
Nikolaos Kazantzis
Department of Chemical Engineering
, Worcester Polytechnic Institute Worcester, MA 01609-2280
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K. T. Chong,
e-mail: kitchong@moak.chonbuk.ac.kr
K. T. Chong
Department of Mechanical Engineering
, Texas A&M University, College Station, Texas 77843-3123
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J. H. Park,
J. H. Park
Department of Mechanical Engineering
, Texas A&M University, College Station, Texas 77843-3123
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Alexander G. Parlos
e-mail: a-parlos@tamu.edu
Alexander G. Parlos
Department of Mechanical Engineering
, Texas A&M University, College Station, Texas 77843-3123
Search for other works by this author on:
Nikolaos Kazantzis
Department of Chemical Engineering
, Worcester Polytechnic Institute Worcester, MA 01609-2280e-mail: nikolas@wpi.edu
K. T. Chong
Department of Mechanical Engineering
, Texas A&M University, College Station, Texas 77843-3123e-mail: kitchong@moak.chonbuk.ac.kr
J. H. Park
Department of Mechanical Engineering
, Texas A&M University, College Station, Texas 77843-3123
Alexander G. Parlos
Department of Mechanical Engineering
, Texas A&M University, College Station, Texas 77843-3123e-mail: a-parlos@tamu.edu
J. Dyn. Sys., Meas., Control. Mar 2005, 127(1): 153-159 (7 pages)
Published Online: April 9, 2004
Article history
Received:
March 13, 2003
Revised:
April 9, 2004
Citation
Kazantzis, N., Chong, K. T., Park, J. H., and Parlos, A. G. (April 9, 2004). "Control-Relevant Discretization of Nonlinear Systems With Time-Delay Using Taylor-Lie Series." ASME. J. Dyn. Sys., Meas., Control. March 2005; 127(1): 153–159. https://doi.org/10.1115/1.1870046
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