A Simulative Study on Active Disturbance Rejection Control (ADRC) as a Control Tool for Practitioners

TL;DR

This paper presents a comprehensive examination of linear Active Disturbance Rejection Control (ADRC) as a practical tool for engineers, focusing on ESO-based disturbance estimation to enable robust control with coarse plant models. It develops first- and second-order ADRC formulations, detailing explicit observer and controller structures, tuning guidelines, and the relationship to internal-model-based state-space control. Through extensive continuous-time and discrete-time simulations, it demonstrates ADRC’s robustness to parameter variations, dead time, saturation, and structural uncertainties, and compares its disturbance rejection capabilities to PI and PID controllers. The study also introduces optimized discrete-time implementations with latency reductions and precomputation strategies to make ADRC viable for real-time, high-dynamic-range applications. Overall, the work supports ADRC as a practical, adaptable alternative to traditional control strategies in engineering practice, with clear guidance for practitioners on tuning and implementation.

Abstract

As an alternative to both classical PID-type and modern model-based approaches to solving control problems, active disturbance rejection control (ADRC) has gained significant traction in recent years. With its simple tuning method and robustness against process parameter variations, it puts itself forward as a valuable addition to the toolbox of control engineering practitioners. This article aims at providing a single-source introduction and reference to linear ADRC with this audience in mind. A simulative study is carried out using generic first- and second-order plants to enable a quick visual assessment of the abilities of ADRC. Finally, a modified form of the discrete-time case is introduced to speed up real-time implementations as necessary in applications with high dynamic requirements.

Figures (21)

• Figure 1: Control loop structure with ADRC for a first-order process.
• Figure 2: Control loop structure with active disturbance rejection control (ADRC) for a second-order process.
• Figure 3: Experiment \ref{['sec:exp_adrc1_kt']}: fixed first-order ADRC controlling first-order process with varying parameters. Nominal process parameters: $K = 1$, $T = 1$. ADRC parameters: $b_0 = \frac{K}{T} = 1$, $T_\mathrm{settle} = 1$, $s^\mathrm{ESO} = 10 \cdot s^\mathrm{CL}$. (a) Variation of $K$, closed loop step response; (b) Controller output $u$ for (a); (c) Variation of $T$, closed loop step response; (d) Controller output $u$ for (c).
• Figure 4: Experiment \ref{['sec:exp_adrc1_eso']}: effect of pole locations for the extended state observer (ESO) on a fixed first-order ADRC controlling first-order process with varying parameter, $T$. Nominal process parameters: $K = 1$, $T = 1$. ADRC parameters: $b_0 = \frac{K}{T} = 1$, $T_\mathrm{settle} = 1$, $s^\mathrm{ESO}$ varying. (a) Closed loop step response, $s^\mathrm{ESO} = 100 \cdot s^\mathrm{CL}$; (b) Controller output $u$ for (a); (c) Closed loop step response, $s^\mathrm{ESO} = 10 \cdot s^\mathrm{CL}$; (d) Controller output $u$ for (c); (e) Closed loop step response, $s^\mathrm{ESO} = 5 \cdot s^\mathrm{CL}$; (f) Controller output $u$ for (e).
• Figure 5: Control loop structure of first-order ADRC considering actuator saturation.