Parameter and delay estimation of fractional order models from step response

Abstract

Listen

Translate article

An integral equation approach to estimate the parameters and the delay term of fractional order (FO) continuous-time models is proposed. Data from a single step response is used for the estimation assuming that the fractional orders are known. In the proposed methodology the FO differential equation is transformed into a FO integral equation. A least-squares equation is then formulated by expanding an integral term that allows the implicit time delay term to have an explicit appearance in the parameter vector. This facilitates direct estimation of the time delay simultaneously with other model parameters. The performance of the proposed method is demonstrated using simulation results. Identification results of a simulated distillation column are presented to demonstrate the applicability of the method.