Title: Estimating perturbation in eigenvalues for robust vibration controller design: analytical derivation and simulation
Authors: Aalya Banu; Asan G.A. Muthalif
Addresses: Smart Structures Systems and Control Research Laboratory, Department of Mechatronics Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, Malaysia ' Smart Structures Systems and Control Research Laboratory, Department of Mechatronics Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, Malaysia
Abstract: Ordinary fixed controllers designed based on nominal parameters do not take into account the uncertainties present in and around the system and hence lose their effectiveness when subjected to uncertainties. To overcome this, a robust control system that accommodates uncertainties is crucial. Structural uncertainties could alter mass, damping and stiffness matrices of a system which in turn perturb its eigenvalues. Based on this, uncertainties in mass, damping and stiffness matrices are represented in terms of changes in eigenvalues. In this paper, an analytical solution for estimating the changes in eigenvalues of a plate-like structure when subjected to structural uncertainties is derived. The derived changes in eigenvalues are represented in terms of changes in mass and stiffness. The variation in eigenvalues obtained from analytical solution is then compared with numerical simulation. Based on the results obtained, the proposed estimation technique can aid in the design of robust controller for vibration control.
Keywords: robust control; eigenvalue perturbation; uncertainty estimation; simply-supported rectangular plates; eigenvalues; vibration control; controller design; numerical simulation; structural uncertainties; mass; damping; stiffness.
International Journal of Engineering Systems Modelling and Simulation, 2015 Vol.7 No.2, pp.95 - 102
Received: 05 Oct 2013
Accepted: 28 Jan 2014
Published online: 18 Mar 2015 *