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

• Wave analysis and wave control of double cascade-connected damped-mass spring systems are provided.
• Properties of propagation constants are precisely investigated.
• Impedance matching controller is derived to eliminate reflected waves.
• A numerical example of a tensegrity beam is conducted.

This paper presents wave analysis and control for double cascade-connected damped mass-spring systems, whose mass is connected beyond the adjacent masses. The system is motivated by a cantilevered tensegrity beam supporting tensile and compressive forces. The wave solution is derived from a recurrent formula, and the properties of the propagation constants are precisely investigated. Elimination of reflected waves provides the impedance matching controller. We show that the impedance matching controller can be constructed from a similarity transformation of the characteristic impedance matrix by a matrix composed of the propagation constants. A numerical example of vibration control of a tensegrity beam is shown.