Title: Identification and autotuning of IMC based PI/PID controller via an effective fractional order-relay feedback approach

Authors: Rahul B. Gaikwad; K. Raghu Raja Pandiyan; Uday Bhaskar Babu Gara

Addresses: Department of Chemical Engineering, National Institute of Technology Warangal, Telangana, 506004, India ' Department of Chemical Engineering, National Institute of Technology Warangal, Telangana, 506004, India ' Department of Chemical Engineering, National Institute of Technology Warangal, Telangana, 506004, India

Abstract: Low-order linear models with time delay are widely used in model-based control design and tuning. This study introduces a systematic approach for identifying higher-order processes as lower-order models, specifically First Order and Second Order Plus Time Delay processes, by utilising a relay with hysteresis and a fractional integrator. The inclusion of the fractional integrator enhances the frequency response at the position frequency point derived from the Describing Function method, improving identification accuracy. We propose a method to identify fractional-order integrators based on minimising Integral Absolute Error, which induces limit cycles in the outputs of higher-order processes. This allows us to approximate the processes using amplitude and critical period characteristics. Subsequently, we design fractional filter IMC-PI/PID controllers based on the identified models, leveraging the same relay feedback data. We evaluate the controllers' robustness and noise rejection capabilities, with comparative studies demonstrating the effectiveness of the proposed identification and control methods.

Keywords: relay feedback; higher order model; CSOPTD; critically damped second order plus time delay; FOPTD; first order plus time delay; model identification; fractional order integrator; fractional filter.

DOI: 10.1504/IJAAC.2025.149589

International Journal of Automation and Control, 2025 Vol.19 No.6, pp.727 - 760

Received: 25 Jul 2024
Accepted: 23 Sep 2024
Published online: 07 Nov 2025 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article