Control of the vibrating structures is desirable in various engineering applications for preventing fatigue and failure. It can be achieved by passive means using dynamic absorbers or by active means using sensors and actuators. In some cases, it is also not practical to apply a desirable control force in those locations at which the dynamics of the structure are to be controlled. In recent years, dynamic absorption schemes are investigated in which control strategies that absorb a steady state motion of a desired location in the structure have been developed. Such a vibration control strategy is termed as zero assignment. Unlike conventional full-state feedback control, which requires all the states of the system to be measured, zero assignment requires least numbers of sensors and actuators (depending on the number of dynamic absorption points) for estimating the control gains and, hence, it may provide economical engineering solution. However, while applying control strategy by active zero assignment, small time delay from the sensors and actuators in the feedback loop is unavoidable and they influence the control gains as well as the stability of the system. In this paper, we have developed vibration control strategy by active zero assignment and obtained closed form control gains for systems with and without time delays by using truncated and full Taylor series expansion. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the active dynamic absorption and the effects of time delay on control gains. The effect of delay in the stability of the controlled system is also summarized.
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April 2011
Research Papers
Closed Form Control Gains for Zero Assignment in the Time Delayed System
Kumar Vikram Singh,
Kumar Vikram Singh
Department of Mechanical and Manufacturing Engineering,
e-mail: singhkv@muohio.edu
Miami University
, Oxford, OH 45056
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Biswa Nath Datta,
Biswa Nath Datta
Department of Mathematical Sciences,
Northern Illinois University
, De Kalb, IL 60115
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Mayank Tyagi
Mayank Tyagi
Department of Petroleum Engineering,
Louisiana State University
, Baton Rouge, LA 70803
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Kumar Vikram Singh
Department of Mechanical and Manufacturing Engineering,
Miami University
, Oxford, OH 45056e-mail: singhkv@muohio.edu
Biswa Nath Datta
Department of Mathematical Sciences,
Northern Illinois University
, De Kalb, IL 60115
Mayank Tyagi
Department of Petroleum Engineering,
Louisiana State University
, Baton Rouge, LA 70803J. Comput. Nonlinear Dynam. Apr 2011, 6(2): 021002 (9 pages)
Published Online: October 20, 2010
Article history
Received:
September 30, 2009
Revised:
January 4, 2010
Online:
October 20, 2010
Published:
October 20, 2010
Citation
Singh, K. V., Datta, B. N., and Tyagi, M. (October 20, 2010). "Closed Form Control Gains for Zero Assignment in the Time Delayed System." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021002. https://doi.org/10.1115/1.4002340
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