Robust Identification of Continuous-time Systems from Sampled Data

Abstract

Whilst most physical systems occur naturally in continuous time, it is necessary to deal with sampled data for identification purposes. In principle, one can derive an exact sampled data model for any given linear system by integration. However, conversion to sampled data form implicitly involves folding of high-frequency system characteristics back into the lower-frequency range. This means that there is an inherent loss of information. The sampling process is reversible provided one has detailed knowledge of the relationship between the low-frequency and folded components so that they can be untangled from the sampled model. However, it is clear from the above argument that one has an inherent sensitivity to the assumptions that one makes about the folded components. The factors that contribute to the folded components include

• the sampling rate

• the nature of the input between samples (i.e., is it generated by a firstorder hold or not, or is it continuous-time white noise or not)

• the nature of the sampling process (i.e., has an anti-aliasing filter been used and, if so, what are its frequency domain characteristics)

• the system relative degree (i.e., the high-frequency roll-off characteristics of the system beyond the base band)

• high-frequency poles and or zeros that lie outside the base band interval.