Achievable dynamic responses of general undamped mass-chain systems

Abstract

The attention of this work is focused on the achievable dynamic responses, i.e., the sets of all possible frequency responses of system transfer functions with all possible proper rational stabilizing controllers, of general undamped mass-chain systems. The Youla parametrization is adopted to obtain all possible proper rational stabilizing controllers and all possible frequency spectrums of a transfer function of the general undamped mass-chain system according to different system measurements. Some conclusions are presented to show the relation of the achievable responses of a transfer function using different system measurements. The achievable dynamic responses of the transfer function from the vibration source to the top mass block using some two-feedback-signal measurements and the full-signal measurement are first obtained, from which the achievable dynamic disturbance responses of other transfer functions are then deduced. The conclusions, which are obtained in this work, explain some classical results of 2-degree-of-freedom undamped vibration systems, and generalizes these results into arbitrary n-degree-of-freedom undamped systems.