Interval observers for LPV systems and application to the guaranteed state estimation of an induction machine

Krebs, Stefan; Gellrich, Thomas; Hohmann, Sören

doi:10.1016/j.ifacol.2017.08.629

Cited by 2 publications

(3 citation statements)

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“…The idea behind the so-called hybrid interval observer is to design dynamical systems with monotone error dynamics that are activated on certain switching conditions guarding the states which change the monotonicity of the system [ 10 , 15 ]. These systems enclose all the state trajectories, generated by the original uncertain system, by estimating a lower and an upper boundary for each state in a guaranteed way [ 16 , 17 ].…”

Section: Motivation and Overviewmentioning

confidence: 99%

“…Within previously published guaranteed interval estimation techniques [ 1 , 10 , 15 , 26 , 27 ], realistic sensor errors have not been considered and interval widths need to be minimized further in order to be applied for a practical algorithm (e.g., fault detection). For such practical usage of guaranteed interval estimation, the interval width needs to be as small as possible.…”

Section: Motivation and Overviewmentioning

confidence: 99%

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

Schwartz

Krebs

Hohmann

2021

Sensors

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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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Section: Motivation and Overviewmentioning

confidence: 99%

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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“…Application scenarios in which interval observers have been applied successfully to dynamic systems in engineering as well as related fields such as computational biology are (without claim of completeness): vehicle lateral dynamics [12], state estimation of induction machines [25], control of the air-fuel ratio in direct injection combustion engines [5], state estimation in anaerobic digestion processes [1], exothermic fed-batch reactors [48], and other (bio-)technological processes with uncertain kinetics for growth of microorganisms and wastewater treatment [9,10], fault detection in flight control systems [8], as well as fault detection and estimation algorithms on the basis of Takagi-Sugeno models [32]. Although the summary above was mainly focused on finite-dimensional system models, also sets of PDEs such as the parabolic differential equation of heat conduction were investigated.…”

Section: Introductionmentioning

confidence: 99%

From Verified Parameter Identification to the Design of Interval Observers and Cooperativity-Preserving Controllers

Rauh

Kersten

2020

Acta Cybern

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One of the most important advantages of interval observers and the associated trajectory computation is their capability to provide estimates for a given dynamic system model in terms of guaranteed state bounds which are compatible with measured data subject to bounded uncertainty. However, the inevitable requirement for being able to produce such verified bounds is the knowledge about a dynamic system model in which possible uncertainties and inaccuracies are themselves represented by guaranteed bounds. For that reason, classical point-valued parameter identification schemes are often not sufficient or should, at least, be handled with sufficient care if safety critical applications are of interest. This paper provides an application-oriented description of the major steps leading from a control-oriented system model with an associated interval-valued parameter and disturbance identification to a verified design of interval observers which provide the basis for the development and implementation of cooperativity-preserving feedback controllers. Such combined control and observer structures allow for forecasting guaranteed lower and upper state bounds that can be determined by solving initial value problems for crisp-parameter models. As such, they replace the significantly more demanding task of computing tubes of reachable states by means of general-purpose interval methods. The corresponding computational steps for the cooperativity-preserving control and observer synthesis are described and visualized for the temperature control of a laboratory-scale test rig available at the Chair of Mechatronics at the University of Rostock.

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Interval observers for LPV systems and application to the guaranteed state estimation of an induction machine

Cited by 2 publications

References 9 publications

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

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

From Verified Parameter Identification to the Design of Interval Observers and Cooperativity-Preserving Controllers

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