Reduced-order performance of parallel and series-parallel identifiers with weakly observable parasitics

Abstract

The stability properties of discrete-time parallel and series-parallel identifiers with respect to a specific model-plant order mismatch are analyzed. While in a deterministic environment with no modeling error the two schemes give identical results, when used in a deterministic environment with modeling error their performance is different. We assume a singularly perturbed state representation for the plant where the modeling error consists of fast parasitics which are weakly observable in the plant output. Detailed bounds on parameter and output estimate errors are established and the robustness of the adaptive identifiers is established by showing that the error bound goes to zero as the modeling error goes to zero, i.e. as the parasitics become infinitely fast. The dependence of this residual identification error on the input signal, the neglected parasitics, and the initial error conditions is shown to be crucial. The bounds indicate possibilities for reducing the error by a proper choice of the input signal. © 1983.