On the Identification of Continuous Time Dynamical Systems

Abstract

The aim of this paper is to give insights into the problem of estimating continuous time systems based on discrete time measurements. To understand how a high sampling rate will influence our estimate, we will study continuous time prediction error methods. It is shown that the choice of noise model set is crucial. By choosing a noise filter with relative degree greater than zero, we must differentiate the data to find the continuous time prediction error estimate. Hence one should try to use noise filters with relative degree zero. This can indirectly be achieved by using prefilters. Since a discrete time prediction error method will converge to a continuous time prediction error method as the sampling interval decrease, we can use the insights from the theory of continuous time prediction error methods to avoid some difficulties, s.a. approximate differentiation. It is shown that it is less sensitive to use parameterizations that can be viewed as approximation of continuous time parameterizations, e.g. the coefficient of the numerator and denominator polynomial in the so-called Delta operator. An important aspect that will limit the choice of sampling rate is the effects of quantization errors in the A/D converters. For fast samplings intervals the effects of quantization errors can be drastic, and consequently destroy the estimates.