Discrete-time modeling and identification of continuous-time systems: a general framework

Abstract

A general framework for modeling of a time-varying continuous-time SISO system from its sampled input and output while retaining the system parameters with their physical interpretation is presented. The theory can be specialized to the Poisson moment functional approach, the integrated sampling approach, the instantaneous sampling approach or the use of state variable filters. In all methods, the initial conditions can be removed by applying an appropriate discrete-time operator. Digital filtering is used to explicitly or implicitly reconstruct the time-derivatives of the sampled continuous-time signals involved. A thorough study of the approximations resulting from converting the continuous-time model to a discrete-time version is presented. It is shown how these errors can be controlled and that system parameter estimates can be obtained with an arbitrary accuracy. The digital filtering approach to integrated sampling and instantaneous sampling exhibit optimal properties among all methods that fit in the general framework. Moreover, using digital filter designs instead of numerical integration allows slower sampling. A maximum likelihood estimator is derived for time-invariant systems in an errors-in-variables stochastic framework. Finally, the theory is verified through simulations.

This work is supported by the Belgian National Fund for Scientific Research (NFWO) and the Flemish Community (concerned action IMMI).