The problem of distinguishability of state space models

Avdeenko, Tatiana; Kargin, S.A.

doi:10.1109/apeie.2000.913094

Cited by 6 publications

(6 citation statements)

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“…Methods for generating the exhaustive summary include the transfer function or Laplace transform approach (Bellman and Åström (1970)) and the similarity transformation approach (Avdeenko and Kargin (2000)) for linear systems, as well as the timepower series or Taylor series approach (Pohjanpalo (1978)), generating-series approach (Raksanyi et al (1985); Walter and Pronzato (1996)) and local state isomorphism approach (Evans et al (2004)) for nonlinear systems. For nonlinear but rational models differential algebra has been used in Meshkat et al (2018).…”

Section: Methods For Distinguishability Analysismentioning

confidence: 99%

“…While the definitions of equivalence treat both models interchangeably, terms related to (in)distinguishability are sometimes used in a directed way: Model M (•) is said to be structurally indistinguishable (s.i.d.) from M (•) if for almost any admissible p there is at least one equivalent p (Raksanyi et al (1985); Avdeenko and Kargin (2000)). In this case M (•) is called the generating model, while M (•) is the model to be built (Walter et al (1984)).…”

Section: Definitionsmentioning

confidence: 99%

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Distinguishability study of 3-mass models for electromechanical motion systems

Wielitzka

Helmke

Perner

et al. 2020

IJMIC

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Physically motivated models of electromechanical motion systems are required in several applications related to control design and auto-tracking, model-based fault detection, feed-forward, and simply interpretation. However, attempts to create such models automatically via structure and parameter identification struggle with ambiguities regarding the correct internal structure of the model. Designing a reasonable set of candidate models is difficult, because it is not known which models are distinguishable and which are not. This paper gives a simple to use necessary condition for indistinguishability of multiple mass models as they are used to model the control-relevant features of motion systems. In an automated way models are generated that can be created by considering elasticities at different positions in the mechanical structures. The condition is applied to these models for the case of three masses. In three examples it is shown that the criterion simplifies the subsequent structure and parameter identification considerably by reducing the number of possible models. For higher numbers of masses, however, it would become intractable.

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Section: Methods For Distinguishability Analysismentioning

confidence: 99%

Section: Definitionsmentioning

confidence: 99%

Distinguishability study of 3-mass models for electromechanical motion systems

Wielitzka

Helmke

Perner

et al. 2020

IJMIC

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“…Definitions of indistinguishability are not reviewed but can be found in Vajda (1981); Walter et al (1984); Godfrey and Chapman (1989); Chapman and Godfrey (1989); Avdeenko and Kargin (2000); Rosa and Silvestre (2011). Here, the term structural indistinguishability is understood as follows: Two model structures M (•) and M (•) with parameter values p 0 ∈ Ω and p0 ∈ Ω and the same number of inputs and outputs are called equivalent if the corresponding system outputs are identical for all admissible input trajectories.…”

Section: Introductionmentioning

confidence: 99%

Model selection for servo control systems

Tantau¹,

Perner²,

Wielitzka³

2021

IJMA

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Physically motivated models of electromechanical motion systems are required in several applications related to control design, model-based fault detection and simply interpretation. Often, however, the high effort of modelling prohibits these model-based methods in industrial applications. Therefore, all approaches of automatic modelling / model selection are naturally appealing. An intuitive approach is to identify the parameters of several model candidates and to select the one with the best fit on unseen data. A shortcoming of this approach is that the chosen model may be one with high complexity in which some of the physically interpretable parameters are not practically identifiable and uncertain. Also, ambiguities in selecting the model structure would not be disguised resulting in false confidence in a chosen model. Designing a reasonable set of candidate models requires that distinguishability of models can be checked prior to the identification procedure.This paper proposes a strategy for frequency domain model selection. The resulting model is tailored to ensure practical identifiability of all parameters for the given excitation. The analysis is based on local sensitivity calculated for the frequency domain cost function. Also, the paper describes distinguishability analysis of candidate models utilizing transfer function coefficients and Markov parameters. Model selection and distinguishability analysis are applied to a class of models as they are commonly used to describe servo control systems. It is shown in experiments on an industrial stacker crane that model selection works with little user interaction, except from defining normalized hyperparameters and ensuring that the resulting model is sound. Distinguishability is analysed systematically for all models that result from rearranging actuator, sensor and spring-damper elements along a chain of discrete masses. It can be proved or disproved for almost all combinations of potential models.

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“…This paper is concerned with the property of distinguishability between the uncertain systems S 1 and S 2 . Most distinguishability problems are discussed for LTI systems without uncertainties (Avdeenko and Kargin (2000), Cocquempot et al (2004), Grewal and Glover (1976), Lou and Si (2009), Lou and Yang (2011) and such studies have applications in Fault Detection and Isolation (FDI) (Bayoudh et al (2008), Cocquempot et al (2004)), and in active mode detection in switched affine systems (Domlan et al (2007), Hakem et al (2010)). But it is well known that to describe a system with a linear model, approximations have generally to be made leading to uncertainties in the parameters of the linear model.…”

Section: Introductionmentioning

confidence: 99%