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

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.