The control of systems with uncertain dynamics and unpredictable disturbances has raised some challenging problems. This is particularly important when high system performance is to be guaranteed at all times. Recently, Time Delay Control has been suggested as an alternative control scheme. The proposed control system does not require an explicit plant model nor does it depend on the estimation of specific plant parameters. Rather, it combines adaptation with past observations to directly estimate the effect of the plant dynamics. This paper outlines the Time Delay Control law for a class of linear dynamic systems and then presents a sufficient condition for stability of linear uncertain systems with time delay. The ideas of Nyquist and Kharitonov are used in the development of a sufficient condition, which does not resort to using approximations for time delay. Like Nyquist, the condition depends on maps of the Nyquist path and, like Kharitonov, stability depends on four functions each yielding a stable system. In this paper we combine these ideas to determine the stability of systems where the Time Delay Controller is applied to single input single output, linear time-invariant plants whose coefficients are known to vary within certain defined intervals. The development is carried out in the context of Time Delay Control but it can be applied in more general cases. Two examples will illustrate the approach and the usefulness of the technique.
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December 1991
Research Papers
Stability of Uncertain Linear Systems With Time Delay
K. Youcef-Toumi,
K. Youcef-Toumi
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
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J. Bobbett
J. Bobbett
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Search for other works by this author on:
K. Youcef-Toumi
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
J. Bobbett
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
J. Dyn. Sys., Meas., Control. Dec 1991, 113(4): 558-567 (10 pages)
Published Online: December 1, 1991
Article history
Received:
September 19, 1990
Revised:
January 31, 1991
Online:
March 17, 2008
Citation
Youcef-Toumi, K., and Bobbett, J. (December 1, 1991). "Stability of Uncertain Linear Systems With Time Delay." ASME. J. Dyn. Sys., Meas., Control. December 1991; 113(4): 558–567. https://doi.org/10.1115/1.2896458
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