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. For the transformation of poles it is shown that small errors in the discrete-time domain 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 multiple degree-of-freedom systems. In order to alleviate this problem appropriate sensitivity specifications, leading to a lower bound for the allowable values of the sampling period, are introduced. The transformation of residues by the step approximation method is also examined, and, the results of the analysis are finally used for the development of guidelines for the appropriate selection of the sampling period so that the transformation sensitivity be confined within prespecified design limits.