Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior

Author

Lehman, Brad ; Bentsman, Joseph ; Lunel, Sjoerd Verduyn ; Verriest, Erik I.

Author_Institution

Sch. of Electr. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

39

Issue

5

fYear

1994

fDate

5/1/1994 12:00:00 AM

Firstpage

898

Lastpage

912

Abstract

This paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay. Averaging theory for fast oscillating, differential delay equations is presented and then applied to vibrational control. Conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also discussed. Illustrative examples are given which show 1) the feasibility of the theory to important applications and 2) the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations

Keywords

delays; differential equations; nonlinear control systems; stability; vibration control; averaging theory; bounded delay; fast oscillating differential delay equations; nonlinear time lag systems; ordinary differential equations; parametric vibrations; stabilizability; transient behavior; vibrational control; Continuous-stirred tank reactor; Control systems; Delay effects; Delay systems; Differential equations; Nonlinear control systems; Open loop systems; State feedback; Vibration control; Vibration measurement;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.284867

Filename

284867