No More Differentiator in PID:Development of Nonlinear Lead for Precision Mechatronics

TL;DR

This paper introduces a novel nonlinear reset lead element for PID controllers, enhancing precision and stability in mechatronic systems by overcoming traditional linear control limitations, validated on a nanometer precision stage.

Contribution

A new nonlinear reset lead element is developed, providing improved precision and stability over traditional linear leads, with validation on a high-precision nanometer stage.

Findings

Enhanced precision and bandwidth demonstrated

Improved phase margin in practical setup

Validation in both time and frequency domains

Abstract

Industrial PID consists of three elements: Lag (integrator), Lead (Differentiator) and Low Pass Filters (LPF). PID being a linear control method is inherently bounded by the waterbed effect due to which there exists a trade-off between precision \& tracking, provided by Lag and LPF on one side and stability \& robustness, provided by Lead on the other side. Nonlinear reset strategies applied in Lag and LPF elements have been very effective in reducing this trade-off. However, there is lack of study in developing a reset Lead element. In this paper, we develop a novel lead element which provides higher precision and stability compared to the linear lead filter and can be used as a replacement for the same. The concept is presented and validated on a Lorentz-actuated nanometer precision stage. Improvements in precision, tracking and bandwidth are shown through two separate designs. Performance is validated in both time and frequency domain to ensure that phase margin achieved on the practical setup matches design theories.