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Proceedings ArticleDOI

Discretization of Linear Fractional Representations of LPV systems

TL;DR: The proposed and existing methods are compared and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling, and criteria to choose appropriate sampling times with respect to the investigated methods are presented.
Abstract: Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing discretization approaches for LFRs suffer from disadvantages like alternation of dynamics, complexity, etc. To overcome the disadvantages, novel discretization methods are derived. These approaches are compared to existing techniques and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling.

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Citations
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Proceedings ArticleDOI
01 Dec 2013
TL;DR: This document proposes the nonlinear control of an industrial three-degrees-of-freedom (3-DOF) robotic manipulator as a benchmark problem for controller synthesis methods, that are applicable to complex plants, but can provide implementation with low complexity.
Abstract: This document proposes the nonlinear control of an industrial three-degrees-of-freedom (3-DOF) robotic manipulator as a benchmark problem for controller synthesis methods, that are applicable to complex plants, but can provide implementation with low complexity. Full details on the nonlinear model of the industrial robotic manipulator Thermo CRS A465 are provided. Furthermore, a solution is presented by considering linear parameter-varying (LPV) controller synthesis based on a reduced parameter set. Stability and performance guarantees are rendered void as the plant's parameter dependency is first approximated by means of principle component analysis. The guarantees are recovered by tools which have previously been reported.

18 citations


Cites methods from "Discretization of Linear Fractional..."

  • ...Implementation Complexity For implementation, the LPV controllers are discretized using the Tustin approximation [17] and a sampling time of Ts = 1 ms....

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Dissertation
26 Nov 2010
TL;DR: In this article, the authors propose a procedure systematique de transformation d'un systeme non-lineaire en le recrivant sous une forme multimodele, en evitant quelques inconvenients majoreurs.
Abstract: Cette these traite de l'analyse et de la synthese de multimodeles pour la simplification de modeles, l'estimation d'etat et le diagnostic des systemes non lineaires caracterises par une ou plusieurs echelles de temps. Ces travaux visent, dans un premier temps, a developper une procedure systematique de transformation d'un systeme non-lineaire en le recrivant sous une forme multimodele, en evitant quelques inconvenients majeurs : la transformation est realisee sans perte d'information, le choix de differents points de fonctionnement n'est plus necessaire, le choix de variables de premisse est realise d'une facon systematique. De plus, la methode offre le choix entre differents multimodeles. Ce degre de liberte sera utilise pour faciliter les etudes de controlabilite, d'observabilite et d'analyse de stabilite. Dans un deuxieme temps, l'obtention de la forme a perturbations singulieres d'un systeme non lineaire est proposee, en eliminant quelques contraintes structurelles et en rendant l'identification et la separation des echelles de temps independante de la structure du modele. Dans un troisieme temps, la synthese de plusieurs observateurs robustes vis-a-vis des perturbations, des erreurs de modelisation et des entrees inconnues a ete realisee afin de reconstruire l'etat et l'entree inconnue du systeme. La difficulte de cette etude provient du fait que le multimodele utilise depend de variables de premisse non mesurables, situation qui n'est pas intensivement etudiee, alors qu'elle est naturellement issue de l'approche par transformation systeme non lineaire - multimodele. Ensuite, le diagnostic de defauts de systemes est realise au moyen de bancs d'observateur a entrees inconnues permettant la generation et la structuration de residus indicateurs de defauts. Finalement, tous les travaux proposes sont appliques au modele d'une station d'epuration, Activated Sludge Model No.1, qui est largement utilise dans le domaine du traitement des eaux usees.

17 citations

Journal ArticleDOI
TL;DR: Not only can heading control be achieved in the proposed approach to coordinate the headings of motions in a network, but also spacing control for circular motion is achievable to design the spacing between neighboring nodes.
Abstract: Decentralized collective motion coordination is fundamental in systems as diverse as mobile sensor networks, swarm robotics, autonomous vehicles, and animal groups. In motion coordination, to conform to the discontinuous message exchange that can only be conducted at discrete-time instants, existing approaches addressing motion coordination usually perform continuous control design followed by discretization-based implementation. This two-stage strategy, however, can be problematic since discretization can harm or even destabilize the controller designed in the continuous-time domain. Inspired by pulse-based interaction in flashing fireflies and firing neurons, we propose an integrated communication and control approach for the motion coordination. The approach circumvents discretization and can guarantee the original control design performance in final implementation. Its communication only employs simple and identical pulses, which significantly reduces processing latency and communication delay compared with conventional packet-based communications. Not only can heading control be achieved in the proposed approach to coordinate the headings (orientations) of motions in a network, but also spacing control for circular motion is achievable to design the spacing between neighboring nodes (e.g., vehicles or robots).

15 citations


Cites background from "Discretization of Linear Fractional..."

  • ...This is a great advantage over existing approaches using a continuous-domain control design followed by discretization-based implementation, which can harm or even destabilize the originally designed controller [12] (cf....

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  • ...To make things worse, discretization can harm or even destabilize the controller designed in the continuoustime domain [12] (cf....

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Journal ArticleDOI
TL;DR: In this paper, the combination of an analytic and an experimental approach is used to identify an LPV model of a 2-DoF flexible surgical robotic manipulator, which is more precisely estimated by applying a dedicated Hoo-norm-based technique to yield a final parameter dependent model written as a linear fractional representation.

11 citations


Cites background from "Discretization of Linear Fractional..."

  • ...…matrices (A,B,C,D) are rational functions of measurable time-varying signals contained by the vector p(t) ∈ P ⊆ R np and called the scheduling variables, where P = {p ∈ R np | p i ≤ pi ≤ pi, ∀i ∈ {1, · · · , np}}, is the so-called “scheduling space” (Tóth et al., 2012) which is a compact set....

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  • ...In the LPV framework, the system matrices (A,B,C,D) are rational functions of measurable time-varying signals contained by the vector p(t) ∈ P ⊆ R np and called the scheduling variables, where P = {p ∈ R np | p i ≤ pi ≤ pi, ∀i ∈ {1, · · · , np}}, is the so-called “scheduling space” (Tóth et al., 2012) which is a compact set....

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Journal ArticleDOI
TL;DR: The sampled-data filter synthesis conditions are formulated in terms of linear matrix inequality optimisation problems and the viability of the proposed design method to cope with variable sampling rates is illustrated through numerical examples, where reliable estimation of the LPV system outputs is achieved.
Abstract: In this paper, we address the sampled-data filter design problem for continuous-time linear parameter-varying (LPV) systems. The filtering error system obtained from augmenting a continuous-time LPV system and the sampled-data filter is a hybrid system. The sampled-data filter design objective is to ensure the error system stability and a prescribed level of the induced energy-to-energy gain (or norm) from the disturbance input to the estimation error. To this purpose, we employ a lifting method to derive an equivalent discrete-time LPV representation for the continuous-time LPV system. In the present study, the sampled-data filter synthesis conditions are formulated in terms of linear matrix inequality optimisation problems. The viability of the proposed design method to cope with variable sampling rates is illustrated through numerical examples, where reliable estimation of the LPV system outputs is achieved.

10 citations

References
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Journal ArticleDOI

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

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"Discretization of Linear Fractional..." refers methods in this paper

  • ...Full zero-order hold approaches A commonly used approach, like in [4], [5], is to apply ZOHs and sampling on all signals of (1a-b) (see Figure 1b)....

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  • ...Basically the available methods use Zero-Order Hold (ZOH) and First-Order Hold (1OH) approaches to restrict the variations of the signals of the LFR in the sample interval which results in a DT description of the dynamics [4], [5], [6], [7], [8], [9], [10], [11]....

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TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
Abstract: This paper will very briefly review the history of the relationship between modern optimal control and robust control. The latter is commonly viewed as having arisen in reaction to certain perceived inadequacies of the former. More recently, the distinction has effectively disappeared. Once-controversial notions of robust control have become thoroughly mainstream, and optimal control methods permeate robust control theory. This has been especially true in H-infinity theory, the primary focus of this paper.

6,945 citations


"Discretization of Linear Fractional..." refers background in this paper

  • ..., [3])...

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  • ...The main reason is that stability and performance requirements can be more conveniently expressed in CT, like in a mixed sensitivity setting [3]....

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  • ..., [1]–[3]), often require LPV models in a linear fractional representation (LFR), as depicted in Fig....

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Journal Article

4,506 citations

01 Jan 2002

4,202 citations


"Discretization of Linear Fractional..." refers methods in this paper

  • ...In Section VI a numerical example is given for the comparison of the approaches....

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Book
01 Jan 1991
TL;DR: In this paper, the authors present the solution of stiff differential equations and differential-algebraic systems (differential equations with constraints) and discuss their application in physics, chemistry, biology, control engineering, electrical network analysis, and computer programs.
Abstract: The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.

4,045 citations