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Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case
Copyright [1999] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approac
A unified strategy for windup prevention in control systems with multiple saturating actuators
Thesis (MScEng)--University of Stellenbosch, 2000.ENGLISH ABSTRACT: A unified method is proposed to treat saturation in both Multi-Input-Multi-Output MIMO
and Single-Input-Single-Output controllers. This method offers superior performance over
existing MIM 0 anti-saturation schemes.
The anti-saturation problem is posed as a linear programming problem. A practical and
efficient implementation of the algorithm is developed by transforming the problem into its
dual linear programming form. The problem, in dual form, is then solved using the dual
simplex method rather than the primal simplex method. The nature of the problem when
expressed in dual form and the properties of the dual simplex method are harmonised to
guarantee an initial basic feasible solution and an optimal bounded final solution in a finite,
predictable and minimal number of iterations.
The resultant controller never saturates, hence cannot windup. Furthermore the resultant
controller always applies the optimal control effort to the plant to minimise the error signal
input as follows:
• The controller is governed such that while the future free response combined with the
present forced response of the controller results in no saturation limits being exceeded,
now or at some time in the future, the normal linear response of the controller prevails.
• When the future free response combined with the present forced response of the controller
will result in a saturation limit being reached, now or at some time in the future,
the present time input signal into the controller is optimally governed to prevent the
saturation limit from being exceeded at any future time.AFRIKAANSE OPSOMMING: 'n Metode word voorgestel waarmee versadiging in enkel-inset enkel-uitset en meer-inset meeruitset
(MIMU) stelsels beheer kan word. Die metode presteer beter as ander huidige teenversadiging-
maatreels vir (MIMU) beheerders.
Die teen-versadigings-probleem word as 'n lineere programmeringsprobleem herformuleer. 'n
Praktiese en effektiewe implementering van die algoritme word verkry deur die probleem na
die duale vorm te transformeer. Die probleem, in duale vorm, word opgelos met die duale
simplex metode, in plaas van die direkte metode. Die eienskappe van hierdie formulering is 'n
gewaarborgde, aanvanklike, bereikbare oplossing en 'n optimale, begrensde, finale oplossing in
'n eindige, voorspelbare en minimum aantal stappe.
Die uiteindelike beheerder versadig nooit nie, en wen gevolglik nie op nie. Die beheerder wend
altyd die optimale aanleg-inset aan om die foutsein te minimeer soos volg:
• Wanneer die nul-inset gedrag saam met die huidige inset-gedrag geen beperkings nou
of in die toekoms saloorskry nie, word geen beperkende aksie geneem nie, en tree die
beheerder dus lineer op.
• Sodra die toekomstige nul-inset gedrag saam met die huidige inset-gedrag, nou of later
versadiging sou veroorsaak, word die huidige inset tot die beheerder optimaal begrens
om latere versadiging te voorkom
Constrained control using convex optimization
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1997.Includes bibliographical references (p. 113-121).by John Marc Shewchun.M.S
Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen
Durch die Nichtbeachtung der immer vorhandenen Stellbegrenzungen bei der Auslegung eines Reglers kann es während des Betriebs zu einem unerwünschten Fehlverhalten des Regelkreises - dem sogenannten Windup - kommen. Diese Arbeit beschäftigt sich mit der Entwicklung und dem systematischen Entwurf von Anti-Windup-Maßnahmen, die in Kombination mit einem zuvor ausgelegten Regler einen sicheren und effizienten Betrieb des Regelkreises trotz vorhandener Stellbegrenzungen gewährleisten. Es werden lineare und nichtlineare modellbasierte Anti-Windup-Methoden behandelt. Neben einer Stabilitätsgarantie für den Regelkreis und einer hohen Regelgüte liegt der Fokus auf einem einfach durchführbaren Entwurf mit möglichst wenigen vom Anwender zu wählenden Parametern. Letzteres wird durch eine auf konvexer Optimierung basierende Parametrierung des Anti-Windup erreicht