scholarly journals Guaranteed State Estimation Using a Bundle of Interval Observers with Adaptive Gains Applied to the Induction Machine

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2584
Author(s):  
Manuel Schwartz ◽  
Stefan Krebs ◽  
Sören Hohmann
Keyword(s):  
State Estimation ◽  
Linear Time ◽  
Induction Machine ◽  
Adaptive Observer ◽  
Critical Systems ◽  
Reduced Order ◽  
System States ◽  
Interval Observer ◽  
Guaranteed State Estimation ◽  
Interval Observers

The scope of this paper is the design of an interval observer bundle for the guaranteed state estimation of an uncertain induction machine with linear, time-varying dynamics. These guarantees are of particular interest in the case of safety-critical systems. In many cases, interval observers provide large intervals for which the usability becomes impractical. Hence, based on a reduced-order hybrid interval observer structure, the guaranteed enclosure within intervals of the magnetizing current’s estimates is improved using a bundle of interval observers. One advantage of such an interval observer bundle is the possibility to reinitialize the interval observers at specified timesteps during runtime with smaller initial intervals, based on previously observed system states, resulting in decreasing interval widths. Thus, unstable observer dynamics are considered so as to take advantage of their transient behavior, whereby the overall stability of the interval estimation is maintained. An algorithm is presented to determine the parametrization of reduced-order interval observers. To this, an adaptive observer gain is introduced with which the system states are observed optimally by considering a minimal interval width at variable operating points. Furthermore, real-time capability and validation of the proposed methods are shown. The results are discussed with simulations as well as experimental data obtained with a test bench.

Reduced-order hybrid interval observer for verified state estimation of an induction machine

2016 ◽  
Vol 57 ◽  
pp. 157-168 ◽  
Author(s):  
Stefan Krebs ◽  
Christoph Schnurr ◽  
Martin Pfeifer ◽  
Jörg Weigold ◽  
Sören Hohmann
Keyword(s):  
State Estimation ◽  
Induction Machine ◽  
Reduced Order ◽  
Interval Observer

scholarly journals Interval State Estimation of Linear Multicellular Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Zhaoxia Huang ◽  
Jun Liu ◽  
Fucai Qian
Keyword(s):  
State Estimation ◽  
Feedback Linearization ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Set Valued Mapping ◽  
Time Varying Systems ◽  
Linear Time Invariant Systems ◽  
Interval Observer ◽  
Lipschitz Systems ◽  
Multicellular System

Linear multicellular system is a type of differential inclusion system, which can be deemed as an extension of linear control system with set-valued mapping. As an important issue in existing control systems, interval state estimation has been widely applied in engineering practices. Over the years, the objects of the studies on interval state estimation have been extended from the initial linear time-invariant systems to linear time-varying systems, chaotic systems, feedback linearization systems, and nonlinear Lipschitz systems. However, there is no report on the design of interval observer for linear multicellular system. To make up for this gap, this chapter attempts to explore the design of an interval observer for linear multicellular systems.

scholarly journals Robust Functional Interval Observer for Multivariable Linear Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Luc Meyer
Keyword(s):  
Linear System ◽  
Linear Function ◽  
Continuous Time ◽  
State Vector ◽  
Internal State ◽  
Design Procedure ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Interval Observer ◽  
Interval Observers

The study of a continuous-time multivariable linear system may not need the knowledge of the entire internal state vector, but only of a linear function of it. In this case, instead of designing a complete observer, only a functional (also called reduced order) observer is used. In this field of research, this paper focuses on robust functional cooperative interval observers. Such an observer is proposed and its properties (in particular, its convergence) are established. Then, a design procedure is given for practical use. Finally, the theoretical contributions are illustrated in examples.

scholarly journals Reduced-order state estimation for linear time-varying systems

2009 ◽  
Vol 11 (6) ◽  
pp. 595-609
Author(s):  
In Sung Kim ◽  
Bruno O. S. Teixeira ◽  
Jaganath Chandrasekar ◽  
Dennis S. Bernstein
Keyword(s):  
State Estimation ◽  
Linear Time ◽  
Time Varying ◽  
Reduced Order ◽  
Time Varying Systems ◽  
Order State

scholarly journals Interval numerical observer: Application to a discrete time nonlinear fish model

2008 ◽  
Vol Volume 11, 2009 - Special... ◽  
Author(s):  
Aboudramane Guiro ◽  
Abderrahman Iggidr ◽  
Diène Ngom
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Fish Population ◽  
Nous Allons ◽  
Time Model ◽  
Fish Model ◽  
International Audience ◽  
System States ◽  
Interval Observer ◽  
Time Systems

International audience The aim of this work is to reconstitute the state of a discrete-time nonlinear system representing a dynamical model of a harvested fish population. For this end, we are going to use a numerical method of building an interval observer for the consider discrete-time model fish population. We adapt to this model an algorithm called "Interval Moving Horizon State Estimation" (IMHSE) which gives an estimated interval of the system states. This algorithm is carried out in [8] and work well for a general class of discrete-time systems. Le but de ce travail est de reconstruire les états d’un système discret non linéaire représentant la dynamique d’une population de poissons soumise à l’action de la pêche. Pour cela nous allons utiliser une méthode numérique de synthèse d’un observateur intervalle du modèle discret de la population de poissons considéré. Nous adaptons à ce modèle un algorithme appelé "Interval Moving Horizon State Estimation" (IMHSE) qui permet d’estimer les états du système par des intervalles. Cet algorithme est développé dans [8] et marche bien pour une classe générale de systèmes discrets.

scholarly journals Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries

2020 ◽  
Vol 53 (2) ◽  
pp. 3683-3688
Author(s):  
Erik Hildebrandt ◽  
Julia Kersten ◽  
Andreas Rauh ◽  
Harald Aschemann
Keyword(s):  
State Estimation ◽  
Fractional Order ◽  
Observer Design ◽  
Interval Observer
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