# Complex order control for improved loop-shaping in precision positioning

## TL;DR

This paper introduces a complex order filter integrated into a PID controller to enhance precision positioning by achieving better loop-shaping, demonstrated through experiments on a planar stage.

## Contribution

The paper develops a nonlinear reset-based complex order filter that improves loop-shaping in PID controllers for precision positioning.

## Key findings

- Enhanced tracking precision without bandwidth compromise
- Superior performance compared to traditional PID and reset controllers
- Effective implementation of complex order filter in practical systems

## Abstract

This paper presents a complex order filter developed and subsequently integrated into a PID-based controller design. The nonlinear filter is designed with reset elements to have describing function based frequency response similar to that of a linear (practically non-implementable) complex order filter. This allows for a design which has a negative gain slope and a corresponding positive phase slope as desired from a loop-shaping controller-design perspective. This approach enables improvement in precision tracking without compromising the bandwidth or stability requirements. The proposed designs are tested on a planar precision positioning stage and performance compared with PID and other state-of-the-art reset based controllers to showcase the advantages of this filter.