Process Identification using Nonideal Step Inputs

Abstract

Methods to estimate the parameters and the time delay of continuous time transfer function models using different nonideal step inputs are presented. By nonideal step inputs we refer to excitation signals that initially change gradually or in smaller steps to a final value unlike the ideal step that requires a sudden jump equalling the size of the step. Many different forms of such input signals can be designed. We consider four types namely the saturated ramp, the staircase input, the saturated sinusoid and the filtered step input. Two approaches are taken for the parameter estimation. First, estimation equations are directly obtained for the particular inputs and second, equivalent ideal step responses are generated from the nonideal step responses and step response method is used to estimate the parameters. The estimation equations are based on the integral equation approach. The necessary mathematical derivations are provided taking a first order plus time delay model as an example. Simulation results for both first and second order models are presented to demonstrate the efficacy of the proposed methodologies.