There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Active disturbance rejection control (ADRC) can be summarized as follows: it inherits from proportional-integral-derivative (PID) the quality that makes it such a success: the error driven, rather than model-based, control law; it takes from modern control theory its best offering: the state observer; it embraces the power of nonlinear feedback and puts it to full use; it is a useful digital control technology developed out of an experimental platform rooted in computer simulations ADRC is made possible only when control is taken as an experimental science, instead of a mathematical one It is motivated by the ever increasing demands from industry that requires the control technology to move beyond PID, which has dominated the practice for over 80 years Specifically, there are four areas of weakness in PID that we strive to address: 1) the error computation; 2) noise degradation in the derivative control; 3) oversimplification and the loss of performance in the control law in the form of a linear weighted sum; and 4) complications brought by the integral control Correspondingly, we propose four distinct measures: 1) a simple differential equation as a transient trajectory generator; 2) a noise-tolerant tracking differentiator; 3) the nonlinear control laws; and 4) the concept and method of total disturbance estimation and rejection Together, they form a new set of tools and a new way of control design Times and again in experiments and on factory floors, ADRC proves to be a capable replacement of PID with unmistakable advantage in performance and practicality, providing solutions to pressing engineering problems of today With the new outlook and possibilities that ADRC represents, we further believe that control engineering may very well break the hold of classical PID and enter a new era, an era that brings back the spirit of innovations

From PID to Active Disturbance Rejection Control

https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

A new set of tools, including controller scaling, controller parameterization and practical optimization, is presented to standardize controller tuning. Controller scaling is used to frequency-scale an existing controller for a large class of plants, eliminating the repetitive controller tuning process for plants that differ mainly in gain and bandwidth. Controller parameterization makes the controller parameters a function of a single variable, the loop-gain bandwidth, and greatly simplifies the tuning process. Practical optimization is defined by maximizing the bandwidth subject to the physical constraints, which determine the limiting factors in performance. Collectively, these new tools move controller tuning in the direction of science.

https://academic.csuohio.edu/cact/ACC03_ISA0030Final.pdf

Scaling and bandwidth-parameterization based controller tuning

The question addressed in this paper is: just what do we need to know about a process in order to control it? With active disturbance rejection, perhaps we don't need to know as much as we were told. In fact, it is shown that the unknown dynamics and disturbance can be actively estimated and compensated in real time and this makes the feedback control more robust and less dependent on the detailed mathematical model of the physical process. In this paper we first examine the basic premises in the existing paradigms, from which it is argued that a paradigm shift is necessary. Using a motion control metaphor, the basis of such a shift, the active disturbance rejection control, is introduced. Stability analysis and applications are presented. Finally, the characteristics and significance of the new paradigm are discussed.

https://academic.csuohio.edu/cact/publications/Gao_ACC2006.pdf

Active disturbance rejection control: a paradigm shift in feedback control system design

An alternative framework for control design is presented in this paper. It compliments the existing theory in that: 1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; 2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. An overview of this design philosophy and associated algorithms are first introduced, followed by the summaries of preliminary analysis results and practical applications. It is evident that the proposed framework lends itself well in providing innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology, namely PID.

https://academic.csuohio.edu/aerl/papers/CDC01-Paradigm.pdf

An alternative paradigm for control system design

This paper concerns with stability characteristics of active disturbance rejection control for nonlinear time-varying plants that are largely unknown. In particular, asymptotic stability is established where the plant dynamics is completely known. In the face of large dynamic uncertainties, estimation and tracking errors are shown to be bounded, with their bounds monotonously decreasing with their respective bandwidths.

https://academic.csuohio.edu/cact/publications/ADRCproof.pdf

On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics

In this paper, it is shown that the problem of automatic control is, in essence, that of disturbance rejection, with the notion of disturbance generalized to symbolize the uncertainties, both internal and external to the plant. A novel, unifying concept of disturbance rejector is proposed to compliment the traditional notion of controller. The new controller–rejector pair is shown to be a powerful organizing principle in the realm of automatic control, leading to a Copernican moment where the model-centric design philosophy is replaced by the one that is control–centric in the following sense: the controller is designed for a canonical model and is fixed; the difference between the plant and the canonical model is deemed as disturbance and rejected.

https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1288&context=enece_facpub

Zhiqiang Gao

Papers

Scaling and bandwidth-parameterization based controller tuning

Active disturbance rejection control: a paradigm shift in feedback control system design

An alternative paradigm for control system design

On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics

On the centrality of disturbance rejection in automatic control