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

Krebs, Stefan; Schnurr, Christoph; Pfeifer, Martin; Weigold, Jorg; Hohmann, Sören

doi:10.1016/j.conengprac.2016.09.004

Cited by 18 publications

(22 citation statements)

References 34 publications

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“…Therefore, reduced-order interval observers do have certain advantages in the area of interval estimation. To be specific, [27] adopts a reduced-order interval observer method to estimate the states of an induction machine system which is time-variant and gets excellent interval estimation results.…”

Section: Introductionmentioning

confidence: 99%

Reduced-Order and Full-Order Interval Observers Design for Discrete-Time System

Ren

You

et al. 2020

IEEE Access

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In this paper, the design of reduced-order and full-order interval observers for discrete-time system is investigated. First, the original system is transformed into a descriptor system with the ability to estimate the unknown noise of sensors. Next, a reduced-order interval observer design method for descriptor system is presented. The state matrix of the system is obtained by linear transformation, and a Sylvester equation is constructed to find the appropriate observer gain matrix. Then, an existing design method of full-order interval observer is introduced in this paper. Finally, a simulation example is given to demonstrate that the reduced-order interval observer has more accurate interval estimation results than the full-order interval observer.

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Section: Introductionmentioning

confidence: 99%

Reduced-Order and Full-Order Interval Observers Design for Discrete-Time System

Ren

You

et al. 2020

IEEE Access

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“…then, the interval functional error (24) is Input-to-State Stable for any switching signal with the average dwell time (12),…”

Section: Resultsmentioning

confidence: 99%

“…Thus, the design of functional interval observers [17] that reconstruct directly an upper and a lower bounds of a linear function of the state is of a great importance. In [12] and [2] reduced interval observers have been proposed for linear time-variant 1 All authors are with IBISC Laboratory, Univ Evry, Paris-Saclay university, Evry, 91020, France. E-mail: {sara.ifqir, dalil.ichalal, naima.aitoufroukh, said.mammar} @univ-evry.fr and linear time-delay systems.…”

Section: Introductionmentioning

confidence: 99%

“…As compared to these works, functional interval observers are flexible and more general. Obviously, functional interval observer is a general form of interval observer because when the linear functions are chosen as the individual unknown states then the problem of functional estimation amounts to the problem of reduced state estimation as in [12], [2]. This feature is particularly advantageous in some applications, such as state feedback control and fault diagnosis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Unknown Input Switched Functional Interval Observer for Vehicle Lateral Velocity Estimation

Ifqir

Ichalal

Ait-Oufroukh

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Functional interval observer of dynamical switched systems provides significant advantages in practical applications. In view of the enlarged order of interval observers, applying interval functional observers can result in lower computational costs and more practicability in some applications such as output feedback control and fault diagnosis of these systems. In this paper, an unknown input functional state interval observer design for a class of switched uncertain systems is investigated. Necessary and sufficient conditions for observer existence are derived. Based on Input to State Stability (ISS) principle and Lyapunov theory, the stability and positivity conditions for the estimation errors are expressed in terms of Linear Matrix Inequalities. A design procedure algorithm of the state observer is given. Finally, the proposed estimation methodology is applied to vehicle lateral velocity estimation problem. Simulation results obtained, confirm the good accuracy and robustness of the proposed state estimation concept.

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“…However, approaches like the extended Luenberger Observer, the extended Kalman Filter, the High-Gain Observer, the Sliding Mode Observer, the

Observer, or the

-Gain Observer are not directly applicable with a priori assumptions on probability distributions or models of the uncertainties, because these are often unknown for practical applications. Furthermore, such methods, e.g., Sun et al [ 9 ], cannot be used because they do not provide necessary guaranteed error bounds [ 10 ]. Therefore, it is reasonable to utilize methods that assume that the uncertainties are unknown but their boundaries are specified, which is usually given for practical applications.…”

Section: Motivation and Overviewmentioning

confidence: 99%

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

Schwartz

Krebs

Hohmann

2021

Sensors

Self Cite

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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.

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

Cited by 18 publications

References 34 publications

Reduced-Order and Full-Order Interval Observers Design for Discrete-Time System

Reduced-Order and Full-Order Interval Observers Design for Discrete-Time System

An Unknown Input Switched Functional Interval Observer for Vehicle Lateral Velocity Estimation

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

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