A Parameter Formula Connecting PID and ADRC

TL;DR

This paper establishes a mathematical connection between PID and ADRC control methods, providing a new tuning rule for PID and insights into ESO design, supported by theoretical analysis and simulations.

Contribution

It introduces a parameter formula linking PID and ADRC, offering a new PID tuning rule and a better understanding of ESO as a combination of PID terms.

Findings

A quantitative lower bound for ESO bandwidth is derived.

A new PID tuning rule ensuring robustness and tracking performance is proposed.

ESO can be expressed as a linear combination of PID terms, improving uncertainty estimation.

Abstract

This paper presents a parameter formula connecting the well-known proportional-integralderivative (PID) control and the active disturbance rejection control (ADRC). On the one hand, this formula gives a quantitative lower bound to the bandwidth of the extended state observer (ESO) used in ADRC, implying that the ESO is not necessarily of high gain. On the other hand, enlightened by the design of ADRC, a new PID tuning rule is provided, which can guarantee both strong robustness and nice tracking performance of the closed-loop systems under the PID control. Moreover, it is proved that the ESO can be rewritten as a suitable linear combination of the three terms in PID, which can give a better estimate for the system uncertainty than the single integral term in the PID controller. Theoretical results are verified also by simulations in the paper.