Wave analysis and control of multiple cascade-connected damped mass-spring systems

Abstract

This paper considers wave analysis and control of multiple cascade-connected damped mass spring systems. The systems are a general extension of the double cascade-connected case considered in our previous work. Formulas for the characteristic equation and eigen vectors of the coefficient matrix of the recurrent formula are first derived. Properties of the secondary constants (propagation constants and characteristic admittances) as analytic functions are examined in detail next. Analyticity and some required properties of the propagation constants are discussed to justify the harmonic analysis in the wave analysis. Positive real property of the characteristic admittances is also discussed for the closed loop stability. A numerical example of the triple cascade-connected case is conducted to illustrate the derived results and show effectiveness of the impedance matching controller for vibration control.

Keywords

• vibration control
• wave analysis and control
• damped mass-spring system
• impedance matching
• multiple cascade-connection