PID Tuning via Desired Step Response Curve Fitting

TL;DR

This paper introduces a PID tuning method based on step response curve fitting that minimizes the error between desired and actual responses, offering a flexible and precise tuning approach.

Contribution

It proposes a novel PID tuning algorithm using curve fitting and optimization, outperforming traditional analytical methods.

Findings

The method accurately matches desired step responses.

It outperforms classical tuning methods like Ziegler Nichols and Lambda Tuning.

Open-source MATLAB implementation is provided.

Abstract

This paper presents a PID tuning method based on step response curve fitting (PID-SRCF) that utilizes L2-norm minimization for precise reference tracking and explicit transient response shaping. The algorithm optimizes controller parameters by minimizing the root-mean-square error between desired and actual step responses. The proposed approach determines optimal PID parameters by matching any closed-loop response to a desired system step response. Practically a first-order plus time delay model or a second-order system with defined settling time and overshoot requirements are preferred. The method has open-source implementation using constrained nonlinear optimization in MATLAB. Comparative evaluations demonstrate that PID-SRCF can replace known analytical methods like Ziegler Nichols, Lambda Tuning, Pole Placement, Dominant Pole and MATLAB proprietary PID tuning applications.