Active assignment of eigenvalues and eigen-sensitivities for robust stabilization of friction-induced vibration

Liang, Yao, Yamaura, Hiroshi and Ouyang, Huajiang ORCID: 0000-0003-0312-0326 (2017) Active assignment of eigenvalues and eigen-sensitivities for robust stabilization of friction-induced vibration. MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 90. pp. 254-267.

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Abstract

As friction couples tangential and lateral degrees-of-freedom of a structure at contact interfaces, the resulting asymmetric dynamic system is prone to dynamic instability. Using state-feedback control, such a frictional asymmetric system can be stabilized through assigning the system desirable eigenvalues; but uncertainties in system parameters can cause assigned eigenvalues to deviate from desired locations and thus stability may be lost. This study presents a robust stabilization method that assigns both desirable eigenvalues and their sensitivities and thus render assigned eigenvalues stable and insensitive to perturbations in uncertain contact parameters (the friction coefficient, contact damping, and contact stiffness). This method utilizes receptances of the corresponding symmetric part of the asymmetric system. The optimal control input location is first determined by minimizing the Frobenius norm of the normalized eigen-sensitivity matrix. The normalized eigen-sensitivities indicate that the friction coefficient and contact stiffness intrinsically have similar crucial effects on the stability of the system. To demonstrate the application of the proposed control method, the eigen-sensitivities with respect to only the friction coefficient are assigned. A constrained over-determined least-squares problem is solved to assign both required eigenvalues and eigen-sensitivities. Numerical examples validate the effectiveness of the proposed robust control scheme by Monte Carlo simulations.

Item Type:	Article
Additional Information:	publisher: Elsevier articletitle: Active assignment of eigenvalues and eigen-sensitivities for robust stabilization of friction-induced vibration journaltitle: Mechanical Systems and Signal Processing articlelink: http://dx.doi.org/10.1016/j.ymssp.2016.12.011 content_type: article copyright: © 2016 Elsevier Ltd. All rights reserved.
Uncontrolled Keywords:	Asymmetric system, Friction-induced vibration (FIV), Receptance, Eigenvalue assignment, Eigen-sensitivity assignment, Monte Carlo simulation
Depositing User:	Symplectic Admin
Date Deposited:	13 Feb 2017 08:38
Last Modified:	19 Jan 2023 07:19
DOI:	10.1016/j.ymssp.2016.12.011
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005766