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access icon free Affine linear parameter-varying embedding of non-linear models with improved accuracy and minimal overbounding

  • Author(s): Arash Sadeghzadeh 1 ; Bardia Sharif 2 ; Roland Tóth 1, 3
    • View affiliations
  • Source: Volume 14, Issue 20, 27 December 2020, p. 3363 – 3373
    DOI:  10.1049/iet-cta.2020.0474 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 14/04/2020, Accepted 29/09/2020, Revised 11/09/2020, Published 03/12/2020

In this study, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behaviour of non-linear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and the minimisation of the conservativeness of the resulting embedding. The LPV state-space model is synthesised with affine scheduling dependency, while the scheduling variables themselves are non-linear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the non-linear system model and also it can be used to minimise the complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a three degrees of freedom (3DOF) control moment gyroscope is converted by the proposed method to an LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.

Inspec keywords: nonlinear control systems; linear systems; gyroscopes; state-space methods; control system synthesis; scheduling

Other keywords: approximative embedding; LPV model; scheduling variables; gain-scheduled controller; low scheduling complexity; resulting embedding; linear parameter-varying state-space models; model accuracy; LPV state-space model; complete embedding; minimal overbounding; input variables; first-principle motion model; nonlinear models; affine scheduling dependency; nonlinear system model; trade-off between scheduling complexity; automated generation; affine linear parameter-varying embedding; nonlinear systems; existing LPV embeddings; nonlinear functions

Subjects: Control system analysis and synthesis methods; Nonlinear control systems; Linear control systems

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