Wave analysis and control of two-dimensionally connected damped mass-spring systems (Analysis based on analytic properties of secondary constants)

Abstract

This paper considers wave analysis and control of two-dimensionally connected damped mass-spring systems, focusing on the properties of the secondary constants as an analytic function of the Laplace transform variable s. Mass motion in the longitudinal direction is considered. The system can be viewed as a cascade connection of layers comprising the lateral direction elements. The dynamics can be described by a first order recurrence formula in the Laplace transform domain. We show that the characteristic polynomial of the coefficient matrix can be decomposed into second order polynomials, which reveals analyticity of the secondary constants in the open right-half plane, as well as the separation property of the propagation constants and the positive real property of the characteristic admittances. These properties justify the harmonic analysis in the wave analysis and guarantee the closed loop stability of the impedance matching controller. Numerical examples illustrate the derived results and show effectiveness for vibration control.