Infinity Norm Measurement of Sensitivity for Closed-Loop Systems Using Chirp as Excitation

A simple identification method based on a closed-loop experiment is proposed to measure the infinity norm of sensitivity function. A chirp signal, modified to have desired band-limited characteristic and finite duration, is used as the excitation in the experiment, and the sensitivity function is calculated using Fourier transform of input and error signals before the infinity norm is evaluated through maximization of the magnitude of sensitivity function. With an additional feature of providing values of gain margin and phase margin at a little extra effort, this method can be used in the identification step of a controller auto-tuning procedure, as having been supported by simulation results showing its capability of providing fast and accurate estimates for a large variety of processes.