From Qiang Xuesen [1], to Guan Zhaozhi [2], and finally to Han Jingqing [3], active disturbance rejection control (ADRC) arose from their unwavering conviction that theory must be connected to practice, and that control theory of any practical significance must not simply be a branch of mathematics, predicated on accurate mathematical model of physical processes. It is their vision and wisdom that have guided us through difficult times.

In particular, Han’s provoking question of “Is this a theory of control or a theory of model?” [3] awakened generations of scholars and compelled them to reexamine the very premise on which modern control theory has been built: what is the object of our study? Is it the control of a physical process, or is it the control of a mathematical model?

True to his conviction, Han went on to demonstrate, through ADRC, how to make control systems inherently immune to unmodeled dynamics and disturbances [4,5,6]. Such development would surely impact engineering practice, but not before it cleared one final hurdle: attaining backward compatibility with PID and with Bode and Nyquist’s language of frequency response. Ignorance of such hurdle arguably led to the stagnations of many well-established schools of so-called advanced control [7] and to the questioning of their relevance to engineering practice.

For ADRC, the turning point is the parameterization of all controller gains as functions of bandwidth [8], making it user friendly and a viable alternative to PID on the account of simplicity, robustness, performance, and ease of tuning. Furthermore, multiple researchers have shown independently that, with some simplification and for low order plants, ADRC is indeed backward compatible with PID. This helps to explain the staying power of PID and to pave the way for the bandwidth parameterization of the PID gains, with profound implications. Most notably, the seminal work of Ziegler and Nichols on PID tuning [9] is now made understandable by practitioners “in their own language of bandwidth and phase characteristics” [10].

And this was just a beginning.

Seeing the significant performance improvements, engineers would often ask: does ADRC achieve this at the expense of phase margin? Sheng Zhong and Yi Huang answered this question here resoundingly in their paper titled “Quantitative analysis on the phase margin of ADRC”. Against a typical second-order plant, phase margins of ADRC with four different ESOs are given analytically and verified in both simulation and experimentation. The results would put users at ease and give them design options. It also begs the question of “how to manage systematically various competing design objectives?” and it is addressed by the paper titled “On tuning of ADRC with competing design indices: a quantitative study”. Here, the relationship is finally established analytically between the ADRC tuning parameters and the following measures of any control system: stability margin, tracking, disturbance rejection, and noise sensitivity.

Engineers would also ask that, as ADRC is shown to be backward compatible to PID, does it really matter one or the other? In other words, why fix something that is not broken? In “On disturbance rejection proportional–integral–differential control with model-free adaptation”, readers will find an ingenious integration, in the standard PID form, of active disturbance rejection and parameter adaptation, leading to a new kind of model-free adaptive control, distinctly different from those well-known work in the literature. This helps to greatly expand the range of operation and disturbance rejection, while maintaining the simplicity and intuitiveness of PID.

If this still does not make this special issue a good read, there is more to come.

Popular and dominant as PID is, one bottleneck is the quality of differentiation in the real world, with noises abound. In the paper titled “On a novel tracking differentiator design based on iterative learning in a moving window”, the authors further improve the linear tracking differentiator by combining it with iterative learning, leading to better quality of differentiation with a smaller noise sensitivity, 500% smaller in one example.

Or how about this question: in the transition from PID to ADRC, how do users choose among various renditions of the latter? Such problem does not exist for PID, and the question could be bewildering for the novice. The paper “ADRC in output and error form: connection, equivalence, performance” helps users navigate their search for the right solution. Same can be said for the paper titled “Tuning and implementation variants of discrete-time ADRC”, which likewise provides various options for discrete implementations of error-based ADRC, even with the same set of parameters as in the continuous time without the usual parameter conversion.

Such work may not have gained high visibility in the past, as few academic researchers are well versed in the complexity and nuances of engineering practice, but they are nonetheless valuable and instrumental in their own right. These challenging questions from practitioners will continue to provide meaningful research topics and to inspire researchers to make their work count in the real world.

Equally appealing are the fresh new ideas and stimulations ADRC brought forth for theoretical research. In “On geometric interpretation of extended state observer—a preliminary study”, one finds strong and rigorous support of the extended state observer (ESO) in the well-established field of the geometric approach to linear system theory, pioneered by well-known researchers in the 1980s. It helps to establish the validity of ESO, premised on the assumption that the plant is “unknown-state unknown-input completely reconstructable”.

Finally, the paper “On the notions of normality, locality, and operational stability in ADRC” further conceptualizes what has been taken for granted in the literature on ADRC: the so called “canonical” form of linear and nonlinear dynamic system that dates back to 1979 [11] (normality); the notion of “local” characteristics referred by Han [3] (locality); and the stability in the engineering sense defined by Qian [1] (operational stability). The formalization of such basics concepts is perhaps the first step towards building a sound theoretical support for ADRC and, by extension, Engineering Cybernetics.

In conclusion, as guest editors we thank Control Theory and Technology for giving us the opportunity to organize this special issue; as witnesses to the transition of ADRC “from an enduring idea to an emerging technology” [11], we have enjoyed the ride and the company of the likeminded. It is evident, we believe, that ADRC is onto something, and the best is still to come.