High-frequency nonlinear vibrational control

Author

Shapiro, B. ; Zinn, B.T.

Author_Institution

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

Volume

42

Issue

1

fYear

1997

fDate

1/1/1997 12:00:00 AM

Firstpage

83

Lastpage

90

Abstract

This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. (1986) investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace

Keywords

Jacobian matrices; control nonlinearities; feedback; feedforward; nonlinear control systems; robust control; stability criteria; vibration control; Jacobian matrix; averaging method; feedback; inverted pendulum; nonlinear systems; nonlinear vibrational control; nonlinearities; open loop control; stability criteria; Control systems; Feedback; Frequency; Jacobian matrices; Nonlinear control systems; Nonlinear systems; Open loop systems; Shape control; Vibration control; Vibration measurement;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.553689

Filename

553689