Achievable dynamic responses of general damped mass-chain systems

Abstract

The problem of achievable dynamic responses of general damped mass-chain systems with controllers installed between the first two masses are investigated in this paper. Achievable dynamic response of a system is the sets of functions that system transfer functions can achieve with all linear time-invariant (LTI) stabilizing controllers. The problem arises in the disturbance control of damped multi-degree-of-freedom (MDOF) vibration systems, such as vehicle suspension systems subject to road and load disturbances and multi-storey building systems subject to seismic and wind disturbances. The sets of functions that system transfer functions can achieve with stabilizing controllers and different system measurements are obtained by the Youla parametrization. By analysing achievable functions of system transfer functions, necessary and sufficient conditions (or complete sets of constraints) of system transfer functions are derived. It can be shown that compared with our previous work on achievable dynamic responses of an undamped mass-chain system, the necessary and sufficient conditions of transfer functions of a damped mass-chain system distribute only in the low-frequency range and the high-frequency range. This work generalizes the results of achievable dynamic responses of two-degree-of-freedom (2-DOF) vibration systems into MDOF vibration systems. The results obtained in this work present the boundaries of the transfer functions of damped MDOF vibration systems, and determine frequency-domain constraints of system transfer functions regardless what stabilizing controllers are used.