• Alexey N. Zhirabok, Far Eastern Federal University (Vladivostok, Russia)
• Alexander V. Zuev, Institute of Marine Technology Problems FEB RAS (Vladivostok, Russia)

The problems of fault estimation in dynamics and sensors of technical systems described by linear dynamic models with time invariant parameters described by differential equations subject to the unknown external disturbances and measurement noise in sensors are studied. The purpose is to design a device using information about inputs and readings to estimate values of faults both in dynamics and sensors. Such information is necessary to compensate the influence of these faults by fault tolerant control systems based on control correction. A solution is based on so-called interval observers of minimal dimension insensitive to the external disturbances. Such observers are constructed based on the reduced-order model of the original system insensitive to the disturbances as well. To construct the reduced-order model, the appropriate relations are used based on the Jordan canonical form describing dynamics of the model and observer. The Jordan canonical form is necessary to use the appropriate properties of the observer. Based on such observer and differentiator which produces exact estimate in finite time, the interval estimate relations are derived producing the relations to estimate faults both in dynamics and sensors. Novelty of the paper is that unlike typical way of using the interval observer, a device for estimation is constructed based on the reduced-order model insensitive to the external disturbances. This allows reducing the computational complexity of the estimation procedure and increasing the accuracy of estimation due to insensitivity to the disturbances. Theoretical results are illustrated by an example of fault estimation in the electrical actuator of manipulation robot. Simulation based on the package Matlab confirms a correctness of theoretical results. It is shown that using the reduced-order model allows reducing the computational complexity of the estimation procedure. The obtained relations can be used to design fault tolerant systems.

linear systems, models, faults, interval observers

2026-09-03