Commande de systèmes linéaires sous contraintes fréquentielles et temporelles – Application au lanceur flexible

Doctoral thesis English OPEN
Chambon , Emmanuel;
(2016)
  • Publisher: HAL CCSD
  • Subject: SYSTEME LINEAIRE | [ PHYS.PHYS.PHYS-SPACE-PH ] Physics [physics]/Physics [physics]/Space Physics [physics.space-ph] | CONTROLE SOUS CONTRAINTES DE SORTIE | SYSTEME INCERTAIN | OBSERVATEUR PAR INTERVALLES | UNCERTAIN SYSTEMS | STRUCTURED CONTROLLER DESIGN | INTERVAL OBSERVER | LINEAR SYSTEMS | [PHYS.PHYS.PHYS-SPACE-PH]Physics [physics]/Physics [physics]/Space Physics [physics.space-ph] | OUTPUT-CONSTRAINED CONTROL | SYNTHESE DE CONTROLEUR STRUCTURE

In modern control design problems, both frequency- and time-domain requirements are usually considered such that the resulting control law satisfies the specifications. Novel non-smooth optimisation techniques can be used to achieve multiple frequency-domain specificati... View more
  • References (17)
    17 references, page 1 of 2

    1 Constrained control of linear systems 3 1.1 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Atmospheric control of a flexible launch vehicle . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Theoretical resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Linear OIST formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2 OIST saturations overlap mitigation and closed-loop stability analysis . . . . 9 1.3.3 OIST extension for Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.4 Application to simplified models of the launch vehicle . . . . . . . . . . . . . . . . . . 10 1.3.5 Non-smooth optimization-based approach to linear interval observer design 10 1.4 Dissertation outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    Multi-models multi-objectives robust structured controller design 15

    2.1 Introduction to robust control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Linear systems theory prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.2 Relevant notations for robust control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.3 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.4 H∞-based approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    2.2 Multi-models multi-objectives structured controller design approach . . . . . . . . . . . . 22 2.2.1 Considered multi-models multi-objectives synthesis problem . . . . . . . . . . . . . 22 2.2.2 Final formulation as an optimization problem . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    2.3 Introduction to observer-based controllers with Youla parameter augmentation . . . 25 2.3.1 Choosing an observer-based structure for the controller . . . . . . . . . . . . . . . . . 25 2.3.2 Presentation of the observer-based structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.3 Conclusions on the augmented observer-based structure . . . . . . . . . . . . . . . . . 28

    2.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    3 Introduction to OIST 31 3.1 Notations and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 Motivations for a new approach to output-constrained control . . . . . . . . . . . . . . . . . . 32 3.2.1 An example: non-linear crane control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.2 State of the art of output-constrained control . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.3 A new approach to the output-constrained control problem . . . . . . . . . . . . . . 38 3.3 Output to input saturation transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.1 Considered class of non-linear systems and constraints . . . . . . . . . . . . . . . . . . 39 3.3.2 Output constraint to input saturation problem formulation . . . . . . . . . . . . . . 40 3.3.3 Proposed transformation (OIST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3.4 A solution to the output-constrained problem using OIST . . . . . . . . . . . . . . . 42 3.3.5 Remarks on the proposed approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4 Illustration on the crane problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    5 Extension of OIST to the incomplete measurements and uncertain cases 85 5.1 Motivations for an extension of OIST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2 Extended problem statement: taking robustness into account . . . . . . . . . . . . . . . . . . 86 5.2.1 Extension of the considered class of linear systems . . . . . . . . . . . . . . . . . . . . . 87 5.2.2 Extended OIST problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.3 OIST extension for Robustness (OISTeR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.3.1 Interval observer of the closed-loop and differentiability issues . . . . . . . . . . . 90 5.3.2 Simultaneous structured controller/time-invariant SCT synthesis . . . . . . . . . 94 5.3.3 Description of the OIST extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.4 Conclusions on the OIST extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.4.1 Second-order LTI system with incomplete state measurements . . . . . . . . . . . 101 5.4.2 Second-order uncertain cooperative LTI system . . . . . . . . . . . . . . . . . . . . . . . . 106

    5.5 Comments on the extension and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    Control Design. Automatica, vol. 60, no. 7, pages 1857-1869, 2015.

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