Fractional-order controller tuning via minimization of integral of time-weighted absolute error without multiple closed-loop tests

TL;DR

This paper introduces a non-iterative, cost-effective method for tuning linear fractional-order controllers by minimizing the ITAE criterion without multiple experiments, using a fictitious reference signal derived from collected data.

Contribution

The proposed approach eliminates the need for repeated closed-loop tests in FO controller tuning by reformulating the ITAE minimization with a fictitious reference signal.

Findings

Reduces tuning cost and complexity for FO controllers.

Effectively suppresses overshoot and steady-state error.

Validated through numerical simulations.

Abstract

This study presents a non-iterative tuning technique for a linear fractional-order (FO) controller, based on the integral of the time-weighted absolute error (ITAE) criterion. Minimizing the ITAE is a traditional approach for tuning FO controllers. This technique reduces the over/undershoot and suppresses the steady-state error. In contrast to conventional approaches of ITAE-based controller tuning, the proposed approach does not require multiple closed-loop experiments or model-based simulations to evaluate the ITAE. The one-shot input/output data is collected from the controlled plant. A fictitious reference signal is defined on the basis of the collected input and output signal, which enables us to evaluate the closed-loop response provided by the arbitrary controller parameters. To avoid repeated experiments that are necessary in the conventional approach, we reformulate the ITAE minimization problem using the fictitious reference signal. The desired FO controller parameters minimizing the ITAE are obtained by solving the optimization problem that is based on the fictitious reference signal. The validity of the proposed approach is demonstrated by a numerical study. The avoidance of repeated experiments significantly reduces the development cost of linear FO controllers, thereby facilitating their practical application.