Sensitivity analysis of the discrete-to-continuous dynamic system transformation

A sensitivity analysis of the discrete-to-continuous transformation used in the 'indirect' modeling of continuous-time systems from sampled experimental data is presented. It is shown that small errors in the discrete-poles may yield large errors in corresponding continuous-time parameters, such as time-constants, natural frequencies, and damping factors, if very fast sampling is used. An important consequence of this phenomenon is the introduction of large errors in the modal parameter estimates of the lower frequency modes of a multiple degree-of=freedom system. In order to alleviate this problem appropriate sensitivity specifications are introduced and shown to lead to a lower bound on the allowable values of the sampling period.