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

This paper gives a unified and historical review of observer design for the benefit of practitioners. It is unified in the sense that all observers are examined in terms of: 1) the assumed dynamic structure of the plant; 2) the required information, including the input signals and modeling information of the plant; and 3) the implementation equation of the observer. This allows a practitioner, with a particular observer design problem in mind, to quickly find a suitable solution. The review is historical in the sense that it follows the evolution of ideas in observer design in the last half century. From the distinction in problem formulation, required modeling information and the observer design goal, we can see two schools of thought: one is developed in the framework of modern control theory; the other is based on disturbance estimation, which has been, to some extent, overlooked.

/pdf/a-survey-of-state-and-disturbance-observers-for-b5mvoxe6ux.pdf

A survey of state and disturbance observers for practitioners

Mechanical (direct-drive) systems designed for high-speed and high-accuracy applications require control systems that eliminate the influence of disturbances like cogging forces and friction. One way to achieve additional disturbance rejection is to extend the usual (P(I)D) controller with a disturbance observer. There are two distinct ways to design, represent, and implement a disturbance observer, but in this paper it is shown that the one is a generalization of the other. A general systematic design procedure for disturbance observers that incorporates stability requirements is given. Furthermore, it is shown that a disturbance observer can be transformed into a classical feedback structure, enabling numerous well-known tools to be used for the design and analysis of disturbance observers. Using this feedback interpretation of disturbance observers, it will be shown that a disturbance observer based robot tracking controller can be constructed that is equivalent to a passivity based controller. By this equivalence not only stability proofs of the disturbance observer based controller are obtained, but it also provides more transparent controller parameter selection rules for the passivity based controller.

Disturbance Observers for Rigid Mechanical Systems: Equivalence, Stability, and Design

A brief review of developments in disturbance observers, leading up to the extended state observer (ESO), is first presented. Various digital implementations of the ESO are investigated and compared. The realization in current discrete estimator form evidently helps to maintain stable operation at low sampling rates. Digitization using zero order hold is derived symbolically to further improve accuracy while preserving the simplicity of single parameter tuning. Finally, the ESO is reformulated using a generalized disturbance model which provides a wider range of solutions for disturbance estimation problems. Application of the proposed algorithm is shown on a realistic motion control simulation platform with favorable results.

Discrete implementation and generalization of the extended state observer

Observer theory for constant-coefficient, linear systems is extended to systems with unknown, inaccessible inputs. Two types of observers for such systems are defined, and simplified criteria for their existence are developed. A theorem regarding the structure of these observers is given which allows the application of results for systems with single unknown inputs to systems with multiple unknown inputs.

J. S. Meditch

Papers

On the generalization of observers to systems with unmeasurable, unknown inputs