Linear ADRC is equivalent to PID with set-point weighting and measurement filter

TL;DR

This paper demonstrates that linear ADRC tuned with the bandwidth method is mathematically equivalent to a specific form of PID control with set-point weighting and measurement filtering, providing simple implementation formulas.

Contribution

It establishes the equivalence between linear ADRC and PID with set-point weighting, offering practical formulas for implementation in standard PID frameworks.

Findings

Linear ADRC and PID with set-point weighting are mathematically equivalent.

Provided simple formulas for implementing linear ADRC using standard PID components.

Validated the equivalence through response analysis of first and second-order systems.

Abstract

We show that linear Active Disturbance-Rejection Control (ADRC) tuned using the "bandwidth method" is equivalent to PI(D) control with set-point weighting and a lowpass filter on the measurement signal. We also provide simple expressions that make it possible to implement linear ADRC for first and second-order systems using commonplace two degree-of-freedom PID implementations. The expressions are equivalent to ADRC in the response from measurements, and a slight approximation in the response from references.