Batlle Arnau, Carles
Total activity: 129
Expertise
Applied mathematics, Control and systems theory, Theoretical physics
h index
8
Professional category
University lecturer
Doctoral courses
Ciencias Físicas
University degree
Ciencias Físicas
Research group
ACES - Advanced Control of Energy Systems
Department
Department of Applied Mathematics IV
Institute
Institute of Industrial and Control Engineering (IOC)
School
Vilanova i la Geltrú School of Engineering (EPSEVG)
E-mail
carlesma4.upc.edu
Contact details
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Scientific and technological production
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1 to 50 of 129 results
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    Symmetries of the Free Schrodinger Equation in the Non-Commutative Plane  Open access

     Batlle Arnau, Carles; Gomis, Jaoquim; Kamimura, kiyoshi
    Symmetry, integrability and geometry: methods and applications
    Date of publication: 2014-01-01
    Journal article

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    We study all the symmetries of the free Schrodinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

    We study all the symmetries of the free Schrodinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

  • Study of the stability of a direct stator current controller for a doubly fed induction machine using the complex hurwitz test

     Doria Cerezo, Arnau; Bodson, Marc; Batlle Arnau, Carles; Ortega, Romeo
    IEEE transactions on control systems technology
    Date of publication: 2013-11
    Journal article

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    In this brief, a new control scheme is presented for the doubly fed induction machine (DFIM). The proposed control algorithm offers the advantages of proven stability and remarkable simplicity. In contrast to the classical vector control method, where the DFIM is represented in a stator-flux-oriented frame, a model with orientation of the stator voltage is adopted. This approach allows the decomposition of the active and reactive powers on the stator side and their regulation on the rotor side. A main contribution of this brief is the use of the Hurwitz test for polynomials with complex coefficients that has had little prior application in control theory. This results in a proof that a proportional-integral (PI) control regulating the stator currents ensures global stability for a feedback-linearized DFIM. The specific condition that the PI gains must satisfy is derived as a simple inequality. The PI controller has a particular structure that directly relates the $d$-component of the rotor voltages to the $q$-component of the stator currents and vice versa. The feedback linearization stage only uses the direct measurement of the rotor and stator currents and is thus easily implementable. Furthermore, it is also shown that the PI controller (without the feedback linearization terms) is also stable for a large range of control gains and does not require the knowledge of the machine parameters. Finally, the control system is validated in simulations and in experiments.

  • Analysis of conventionally controlled PEMFC based on a distributed parameter model

     Sarmiento Carnevali, Maria Laura; Serra Prat, Maria; Batlle Arnau, Carles
    Iberian Symposium on Hydrogen Fuel Cells and Advanced Batteries
    Presentation's date: 2013
    Presentation of work at congresses

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    Linear control of the yaw and rudder limitations for Cormoran AUV  Open access

     Gonzalez Agudelo, Julian; Masmitja Rusiñol, Ivan; Batlle Arnau, Carles; Gomariz Castro, Spartacus; Llorens Garcia, Ariadna
    International Workshop on Marine Technology
    Presentation's date: 2013-10-11
    Presentation of work at congresses

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    This work presents a detailed situation about the linear control design for the yaw in the Cormoran autonomous underwater vehicle (AUV). The development includes the physical limitations of the rudder that involve more constraints for the control that has a limited action and implies to reduce the gain loop of the controller. The whole system is simulated in simulink and three different controls (P, PD, PID) are compared.

  • Cascade sliding mode-PID controller for a coupled-inductor boost converter

     Carrero Candelas, Niliana Andreina; Batlle Arnau, Carles; Fossas Colet, Enric
    IEEE Conference on Decision and Control
    Presentation's date: 2013-12
    Presentation of work at congresses

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    In this paper, a coupled-inductor Boost converter is modelled as a piece-wise complementarity system and controlled by means of two loops: a sliding mode control inner loop and an experimentally tuned PID outer loop control. The aim of the closed loop system is to regulate the output voltage of the coupled-inductor Boost converter. The control is carried out using the piece-wise complementarity model of the converter, which takes into account its hybrid dynamic. In addition, the performance and the effectiveness of the feedback control is validated through computer simulations using MATLAB and Psim.

    In this paper, a coupled-inductor Boost converter is modelled as a piece-wise complementarity system and controlled by means of two loops: a sliding mode control inner loop and an experimentally tuned PID outer loop control. The aim of the closed loop system is to regulate the output voltage of the coupled-inductor Boost converter. The control is carried out using the piece-wise complementarity model of the converter, which takes into account its hybrid dynamic. In addition, the performance and the effectiveness of the feedback control is validated through computer simulations using MATLAB and Psim.

  • Mathematical model of the Guanay II AUV

     Gonzalez Agudelo, Julian; Masmitja Rusiñol, Ivan; Gomariz Castro, Spartacus; Batlle Arnau, Carles; Sarria Gandul, David; Del Rio Fernandez, Joaquin
    OCEANS MTS/IEEE
    Presentation's date: 2013-06-12
    Presentation of work at congresses

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    This work presents a mathematical study to obtain the coefficients that define the dynamics of an autonomous underwater vehicle (AUV), the Guanay II vehicle, with 3 degrees of freedom. This dynamics is given by several forces and moments (hydrostatic, hydrodynamic, added masses and propellers), which largely depend on the vehicle geometry. The Guanay II AUV has been designed following a Myring profile, which improves the hydrodynamics of the vehicle but also yields a tractable mathematical model. The model describes the geometric characteristics of the vehicle and the disposition of the thrusters and has backward movement capacity. The model has been tested by means of simulations and a prototype has been validated in real navigation.

    This work presents a mathematical study to obtain the coefficients that define the dynamics of an autonomous underwater vehicle (AUV), the Guanay II vehicle, with 3 degrees of freedom. This dynamics is given by several forces and moments (hydrostatic, hydrodynamic, added masses and propellers), which largely depend on the vehicle geometry. The Guanay II AUV has been designed following a Myring profile,which improves the hydrodynamics of the vehicle but also yields a tractable mathematical model. The model describes the geometric characteristics of the vehicle and the disposition of the thrusters and has backward movement capacity. The model has been tested by means of simulations and a prototype has been validated in real navigation.

  • Observation of the internal states of a PEMFC anode gas channel

     Luna Pacho, Julio Alberto; Batlle Arnau, Carles; Kunusch, Cristian; Riera Colomer, Jordi; Sarmiento Carnevali, Maria Laura; Serra Prat, Maria
    Jornadas de Automática
    Presentation's date: 2013
    Presentation of work at congresses

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    In this work a non-linear, model-based state observer is developed. Dynamics of the system described by a distributed parameter, partial differential equations model. Forward and backward discretization of the model to take advantage of the boundary conditions. Simulation results are presented to show the performance of the observer. Comparison between the linear and nonlinear approaches of the observers.

  • Desarrollo de sistemas de control para la mejora de la eficiencia y la vida útil en sistemas basados en pilas de combustible PEM

     Sarmiento Carnevali, Maria Laura; Kunusch, Cristian; Husar, Attila Peter; Riera Colomer, Jordi; Batlle Arnau, Carles; Strahl, Stephan; Massana Hugas, Immaculada; Simo Mezquita, Ester; Creemers, Tom Lambert; Serra Prat, Maria
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  • Modeling a coupled-inductor boost converter in the complementarity framework

     Carrero Candelas, Niliana Andreina; Batlle Arnau, Carles; Fossas Colet, Enric
    European Symposium on Computer Modeling and Simulation
    Presentation's date: 2012-11-16
    Presentation of work at congresses

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    We consider the modeling of switching circuits, consisting of passive elements, independent sources, which are subject both to externally induced switches (time events) and to state events. We focus on the use of the complementarity formalism for obtaining such hybrid (actually piecewise linear)models, assuming idealized current-voltage characteristics of the diodes and switches. In particular, a coupled-inductor Boost converter is modelled as a piece-wise complementarity system. We obtained also a discrete-time model which may be used for design and simulation purposes. In order to show the good performance of the model obtained, it is compared with the model of the converter obtained from the PSIM simulation software.

    We consider the modeling of switching circuits, consisting of passive elements, independent sources, which are subject both to externally induced switches (time events) and to state events. We focus on the use of the complementarity formalism for obtaining such hybrid (actually piecewise linear) models, assuming idealized current- voltage characteristics of the diodes and switches. In particular, a coupled-inductor Boost converter is modelled as a piece-wise complementarity system. We obtained also a discrete-time model which may be used for design and simulation purposes. In order to show the good performance of the model obtained, it is compared with the model of the converter obtained from the PSIM simulation software.

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    Distributed parameter model simulation tool for PEM fuel cells  Open access

     Sarmiento Carnevali, Maria Laura; Serra Prat, Maria; Batlle Arnau, Carles
    Congreso Nacional de Pilas de Combustible
    Presentation's date: 2012
    Presentation of work at congresses

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    In this work, a simulation tool for proton exchange membrane fuel cells (PEMFC) has been developed, based on a distributed parameter model. The tool is designed to perform studies of time and space variations in the direction of the gas channels. Results for steady-state and dynamic simulations for a single cell of one channel are presented and analyzed. Considered variables are concentrations of reactants, pressures, temperatures, humidification, membrane water content, current density, among others that have significant effects on the performance and durability of PEMFC.

    En este trabajo se ha desarrollado una herramienta de simulación para pilas de combustible tipo PEM, basada en un modelo de parámetros distribuidos. La herramienta está diseñada para realizar estudios de variaciones espaciales y temporales a lo largo de los canales de alimentación de reactantes. El trabajo muestra y analiza los resultados de simulación de una monocelda monocanal. Las variables estudiadas son las concentraciones de los reactantes, presiones, temperaturas, humidificación, contenido de agua de la membrana, corriente, entre otras que influyen significativamente sobre el rendimiento y durabilidad de las pilas PEM.

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    Representation of a general composition of Dirac structures  Open access

     Batlle Arnau, Carles; Massana Hugas, Immaculada; Simo Mezquita, Ester
    IEEE Conference on Decision and Control and European Control Conference
    Presentation's date: 2011-12-14
    Presentation of work at congresses

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    We provide explicit representations for the Dirac structure obtained from an arbitrary number of component Dirac structures coupled by means of another interconnecting Dirac structure. Our work generalizes the results in [1] in two aspects. First, the interconnecting structure is not limited to the simple feedback case considered there, and this opens new possibilities for designing control systems. Second, the number of simultaneously interconnected systems is not limited to two, which allows for extra flexibility in modeling, particularly in the case of electrical networks. Several relevant particular cases are presented, and the application to the interconnection of port- Hamiltonian systems is discussed by means of an example.

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    De la mecánica clásica y las leyes de Kirchhoff a los sistemas hamiltonianos con puertos  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau
    La Gaceta de la Real Sociedad Matemática Española
    Date of publication: 2010
    Journal article

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    En este artículo exponemos los orígenes conceptuales de la teoría PHS (port-Hamiltonian systems), empezando por las leyes de Kirchhoff y enlazando con las ecuaciones de la mecánica clásica, para acabar con la estructura geométrica subyacente a todo el formalismo, conocida como estructura de Dirac, y con los métodos de control asociados. Concluimos con un apunte de las generalizaciones y desarrollos más recientes.

    Postprint (author’s final draft)

  • Passivity-based control of a wound-rotor synchronous motor

     Doria Cerezo, Arnau; Batlle Arnau, Carles; Espinosa Pérez, Gerardo
    IET control theory and applications
    Date of publication: 2010-10
    Journal article

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  • Corrigendum to 'On the control of non-linear processes: an IDA-PBC approach' (H. Ramírez et al., Journal of Process Control 19 (1) (2009) 405¿414)

     Batlle Arnau, Carles; Ortega, Romeo; Sbarbaro, Daniel; Ramírez, Héctor
    Journal of process control
    Date of publication: 2010-01
    Journal article

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    In a recent paper [1], the Interconnection and Damping Assignment Passivity-based Control (IDA-PBC) method [2] is studied in the case when the key matching equation is not satisfied. The paper proposes to fix a desired storage function and to design a scaling matrix, which is obtained solving an algebraic Lyapunov equation, in such a way that the linearized dynamics of the closed-loop system is stable – without the need to solve the matching equation. Unfortunately, the derivations in [1] are incorrect, invalidating the results of the paper, in particular, Proposition 1. To explain the problems encountered in [1], in the present note we first re-derive the closed-loop dynamics of a system controlled using the IDA-PBC method in the case when the matching condition is not satisfied, that is, Eq. (11) in [1]. This computations are carried-out following a route, which is slightly different from the one used in [1], that we believe is more general and straightforward. Then, we indicate the points that invalidate Proposition 1.

  • Propulsor híbrido para vehículo urbano liviano

     Muñoz Aguilar, Raul Santiago; Roqueiro, Nestor; Griño Cubero, Roberto; Fossas Colet, Enric; Doria Cerezo, Arnau; Batlle Arnau, Carles; Riera Colomer, Jordi; Olm Miras, Josep Maria; Pagano, Daniel Juan; Valencia da Luz, Mauricio; Oliveira, Amir; Nicolazzi, Lauro; de Souza Vieira, Rodrigo; Gaudenzi Faria, Marcelo; de Lima, Sigmar; de Souza Campos, David
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  • ACES CONTROL AVANÇAT DE SISTEMES D'ENERGIA

     Serra Prat, Maria; Olm Miras, Josep Maria; Riera Colomer, Jordi; Biel Sole, Domingo; Batlle Arnau, Carles; Griño Cubero, Roberto; Doria Cerezo, Arnau; Costa Castelló, Ramon; Sarmiento Carnevali, Maria Laura; Franch Bullich, Jaime; Fossas Colet, Enric
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  • ALGORITMOS PARA LA REDUCCIÓN DE ORDEN Y CONTROL DE SISTEMAS INTERCONECTADOS DE GRAN DIMENSIÓN

     Ras Sabido, Antoni; Massana Hugas, Immaculada; Simo Mezquita, Ester; Fossas Colet, Enric; Franch Bullich, Jaime; Prat Farran, Joana d'Arc; Riego Pérez, Albert; Batlle Arnau, Carles
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  • Port-Based Modeling in Different Domains

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date of publication: 2009-08-19
    Book chapter

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  • Simultaneous interconnection and damping assignment passivity-based control: the induction machine case study

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Espinosa-Perez, Gerardo; Ortega, Romeo
    International journal of control
    Date of publication: 2009-02
    Journal article

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  • Bond graph models of electromechanical systems: the AC generator case

     Batlle Arnau, Carles; Doria Cerezo, Arnau
    14th International Symposium on Industrial Electronics
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  • Simultaneous IDA-passivity-based control of a wound rotor synchronous motor

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Espinosa, G
    47th IEEE Conference on Decision and Control
    Presentation's date: 2008-12-10
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  • Bidirectional power flow control of a power converter using passive Hamiltonian techniques

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    International journal of circuit theory and applications
    Date of publication: 2008-10
    Journal article

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  • MODELING AND NUMERICAL STUDY OF NONSMOOTH DYNAMICAL SYSTEMS. Applications to Mechanical and Power Electronics Systems  Open access

     MERILLAS SANTOS, IVAN
    Defense's date: 2007-02-22
    Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
    Theses

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    This thesis is concerned with the modeling and numerical study of nonsmooth dynamical systems (NSDS). The first part of the thesis deals with the modeling of some DC-DC power converters using the complementarity formalism. This mathematical theoretical framework allows us to ensure existence and uniqueness of solutions in a "natural" and synthetic way. Specifically, it works pretty well in power electronic converters because it incorporates generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM are stated and simulation results, showing a variety of behaviours, such as persistent or re-entering GDCM, are also presented. Furthermore, the analysis and simulation of a parallel resonant converter (PRC), which has four diodes, illustrate the convenience of the complementarity formalism to simulate electrical systems with a large number of ideal diodes. We also present the simulation of a boost converter with a sliding mode control, even though a general control theory for complementarity systems is not still developed.In the second part of the thesis we focus on the bifurcation analysis in NSDS, and in particular, we have studied different mechanical systems which involve impacts and dry-friction. It is known that nonsmooth or discontinuous dynamical systems can exhibit the bifurcations also exhibited by smooth systems. In addition to these, there are also some novel transitions so-called discontinuity-induced bifurcations (DIBs) which are unique to these systems. We have investigated the complex behaviour occurring in an impacting mechanical system. DIBs such as corner impact bifurcations and transitions from complete to uncomplete chattering motions have been analysed in detail. Another type of DIBs recently classified are the so-called sliding bifurcations. Such bifurcations are a characteristic feature of so-called Filippov systems. We present detailed examples of all the different sliding bifurcation scenarios in a dry friction oscillator using a measured friction characteristic firstly introduced by Popp. Furthermore, a codimension-two degenerate switching-sliding bifurcation is displayed. In this case of degenerate switching-sliding bifurcation two curves of codimension-one sliding bifurcations, crossing-sliding and adding-sliding, branch out from the codimension-two point. Also, a cusp smooth codimension-two bifurcation is shown and coexistence of periodic orbits in the region between both fold codimension-one curves is studied.We have also investigated the dynamic behaviour of the two-block Burridge model for earthquake simulations. Previous numerical studies investigated by Ruina verified that, with a friction force of Coulomb type, the system presents only periodic behaviour. We show that chaotic regions can be observed in a symmetric configuration even if a Coulomb friction is considered with the relaxation of one of the assumptions assumed in the seismological literature. Furthermore, we have studied the behaviour of the system with asymmetric configuration. Different periodic solutions and regions of chaos can be observed varying the asymmetry of the system. With respect to the bifurcation point of view, we have analysed several smooth bifurcations (smooth and DIBs) observed in this system.Chapter 6 of this thesis presents the SICONOS software platform dedicated to simulation of NSDS. We give an overview of the SICONOS software and the way NSDS are modeled and simulated within the platform. Routines for analysis (stability, bifurcations, invariant manifolds,.) of NSDS implemented in the platform are explained in detail. To conclude this part, several representative samples are shown in order to illustrate the SICONOS platform abilities.Conclusion and some open problems are presented in the last chapter.

  • Estructuras de Dirac: discretización y reducción de orden de modelos.

     Batlle Arnau, Carles; Fossas Colet, Enric
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  • A stator voltage oriented PI controller for the doubly-fed induction machine

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Ortega, R
    American Control Conference
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  • Modeling, simulation and control of a doubly-fed induction machine controlled by a back-to back converter

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Gesellschaft Für Angewandte MAthematik und Mechanik
    Presentation of work at congresses

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  • Simultaneous Interconnection and Damping Assignment Passivity-Based Control: Two Practical Examples

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Espinosa, G; Ortega, R
    Lecture notes in control and information sciences
    Date of publication: 2007-10
    Journal article

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  • Modeling, simulation and control of doubly-fed induction machine controlled by Back-to-Back converter  Open access

     Doria Cerezo, Arnau
    Defense's date: 2006-10-18
    Institute of Industrial and Control Engineering (IOC), Universitat Politècnica de Catalunya
    Theses

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    Aquesta Tesi estudia el control d'un sistema complex, un sistema d'emmagatzement d'energia cinètica, incloent les seves especificacions de control, modelat, disseny de controladors, simulacions, muntatge i validació experimental.Primerament, s'estudia l'interconnexió i control dels sistemes electromecànics. Es presenta el formalisme Hamiltonià (PCHS) en general, i després particularitzant en els sistemes electromecànics, inclòs els sistemes d'estructura variable (VSS).L'IDA-PBC (Interconnection and damping assignment-passivity based control) és una tècnica de control basat en els PCHS. En aquesta Tesi s'estudien el problemes que apareixen en controlar, per IDA-PBC, sortides de grau relatiu u quan el paràmetres nominals del controlador són incerts. Per evitar-los es proposa introduir una acció integral que pot ésser interpretada dins l'estructura Hamiltoniana.En aquesta Tesi també es presenten dues modificacions que permeten millorar el rang d'aplicacions de la tècnica IDA-PBC. Primer, es demostra que el fet de descomposar la tècnica de l'IDA-PBC en deformar la funció d'energia i una injecció de fregament, redueix el conjunt de sistemes que es poden estabilitzar mitjançant aquest mètode. Per evitar aquest problema, es proposa fer simultàniament els dos passos donant lloc a l'anomenat SIDA-PBC. Per altre costat, el mètode IDA-PBC requereix el coneixement de la funció energia (o Hamiltonià). Això representa un problema perquè, en general, el punt d'equilibri depèn de paràmetres incerts. En aquest treball es desenvolupa una metodologia per seleccionar l'estructura Hamiltoniana que redueix aquesta dependència dels paràmetres. Aquesta tècnica permet millorar la robustesa dels les sortides d'ordre relatiu superior a u.El sistema d'emmagatzement d'energia cinètica consisteix en una màquina d'inducció doblament alimentada (DFIM) amb un volant d'inèrcia, controlada pel rotor per un convertidor de potència back-to-back (B2B). L'objectiu és gestionar el flux d'energia entre la DFIM i una càrrega local connectada a la xarxa, commutant entre diferents punts de funcionament. Per això es planteja una gestió de l'energia, basada en la velocitat òptima de la DFIM.Pel què fa al control de la DFIM, es proposa un nou esquema de control que ofereix importants avantatges, i que és considerablement més senzill que el mètode clàssic, el vector control. Aquest nou controlador permet una fàcil descomposició de les potències activa i reactiva de l'estator, i el seu control a través de les tensions de rotor. Aquest disseny s'obté aplicant el procediment que millora la robustesa de l'IDA-PBC.S'han estudiat d'altres controladors, com el vector control clàssic. També a partir de la tècnica IDA-PBC, on l'equació en derivades parcials que apareix en aplicar el mètode es pot resoldre fixant l'energia en llaç tancat, i afegint nous termes a la matriu d'interconnexió. Per obtenir un controlador definit globalment s'afegeix un terme de fregament depenent dels estats, que desacobla la part elèctrica i mecànica del sistema. Finalment, també es prova que mitjançant el SIDA-PBC es pot modelar l'energia total (elèctrica i mecànica) de la DFIM. Tots aquest controladors han estat simulats i comparats. El controlador robust IDA-PBC s'ha validat experimentalment amb uns resultats satisfactoris. A la Tesi també es presenta un controlador que permet el flux bidireccional de potència pel B2B. L'estudi de la dinàmica zero adverteix que les tècniques de control estàndard no garanties en l'estabilitat en ambdós direccions, i per això s'utilitza un controlador IDA-PBC. Pel disseny s'utilitza un model basat en GSSA (generalized state space averaging), on es descomposa i es trunca el sistema per determinades freqüències, i que permet expresar els objectius de control (tensió constant al bus de contínua i factor de potència unitari) com un problema de regulació. Les simulacions i els resultats experimentals validen, tant la llei de control, com les simplificacions efectuades.Els controladors proposats i validats experimentalment són usats, finalment, per implementar la gestió de potència del sistema d'emmegatzement d'energia cinètica. Els resultats confirmen el bon comportament del sistema i dels controladors IDA-PBC proposats.

    This Thesis studies a complex multidomain system, the Flywheel Energy Storage System, including the control objectives specification, modeling, control design, simulation, experimental setup assembling and experimental validation stages.The port interconnection and control of electromechanical systems is studied. The port Hamiltonian formalism is presented in general, and particularized for generalized electromechanical systems, including variable structure systems (VSS).Interconnection and damping assignment-passivity based control (IDA-PBC) is a well known technique for port Hamiltonian systems (PCHS). In this Thesis we point out the kind of problems that can appear in the closed-loop structure obtained by IDA-PBC methodsfor relative degree one outputs, when nominal values are used in a system with uncertain parameters. To correct this, we introduce an integral control, which can be cast into the Hamiltonian framework.This Thesis also presents two new approaches which improve the range of applicability of the IDA-PBC technique. First, we show that the standard two-stage procedure used in IDA-PBC consisting of splitting the control action into the sum of energy-shaping and damping injection terms is not without loss of generality, and effectively reduces the set of systems that can be stabilized with IDA-PBC. To overcome this problem we suggest to carry out simultaneously both stages and refer to this variation of the method as SIDA-PBC.Secondly, we present an improvement of the IDA-PBC technique. The IDA-PBC method requires the knowledge of the full energy (or Hamiltonian) function. This is a problem because, in general, the equilibrium point which is to be regulated depends on uncertain parameters. We show how select the target port-Hamiltonian structure so that this dependence is reduced. This new approach allows to improve the robustness for higher relative degree outputs.The Flywheel Energy Storage System consists of a doubly-fed induction machine (DFIM), controlled through the rotor voltage by a power electronics subsystem (a back-to-back AC/AC converter (B2B)), and coupled to flywheel. The control objective is to optimally regulate the power flow between the DFIM and a local load connected to the grid, and this is achieved by commuting between different steady-state regimes. A police management based on the optimal speed for the DFIM is proposed.In this Thesis we propose a new control scheme for the DFIM that offers significant advantages, and is considerably simpler, than the classical vector control method. This controller allows an easy decomposition of the active and reactive powers on the stator side and their regulation, acting on the rotor voltage, via stator current control. This design was obtained applying the new robust IDA-PBC procedure.Other controllers are also designed along the dissertation. The classical vector control is studied. We also apply the classic IDA-PBC technique. It is shown that the partial differential equation that appears in this method can be circumvented by fixing the desired closed-loop total energy and adding new terms to the interconnection structure. Furthermore, to obtain a globally defined control law we introduce a state--dependent damping term that has the nice interpretation of effectively decoupling the electrical and mechanical parts of the system. This results in a globally convergent controller parameterized by two degrees of freedom. Finally, we also prove that with SIDA-PBC we can shape the total energy of the full (electrical and mechanical) dynamics of the DFIM. These different controllers (vector control, IDA-PBC, SIDA-PBC and robust IDA-PBC) are simulated and compared. The IDA-PBC robust controller is also experimentally tested and shown to work satisfactorily.A controller able to achieve bidirectional power flow for the B2B converter is presented. Standard techniques cannot be used since it is shown that no single output yields a stable zero dynamics for power flowing both ways. The controller is computed using standard IDA-PBC techniques for a suitable generalized state space averaging truncation of the system, which transforms the control objectives, namely constant output voltage dc-bus and unity input power factor, into a regulation problem. Simulation and experimental results for the full system confirm the correctness of the simplifications introduced to obtain the controller.The proposed and tested controllers for the DFIM and the B2B are used to implement the power management policy. These results show a good performance of the flywheel energy storage system and also validate the IDA-PBC technique, with the proposed improvements.

  • Contribució a l'estudi dels exponents de lyapunov per a sistemes bilineals i a l'anàlisi de les bifurcacions en el convertidor boost controlat amb superfícies de lliscament i histèresi  Open access

     Massana Hugas, Immaculada
    Defense's date: 2006-10-31
    Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
    Theses

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    Després d'un capítol d'introducció (capítol 2) on es definieixen i s'expliquen les característiques i els fenòmens més importants dels sistemes dinàmics, aquest treball el podríem dividir bàsicament en dues parts. La primera d'elles és la que està desenvolupada en el capítol 3. En aquest capítol es recorda un dels mètodes numèrics més interessant, tan des del punt de vista numèric com des del punt de vista teòric, per calcular els exponents de Lyapunov. És el mètode que està basat en la descomposició QR de l'aplicació tangent que s'obté a l'estudiar l'evolució dinàmica de la diferència entre dues òrbites inicialment properes. S'ha aplicat el mètode als sistemes bilineals en general i s'han obtingut resultats específics pel convertidor buck. En concret, s'han escrit les equacions diferencials que han de complir els exponents de Lyapunov del convertidor buck, a partir de la descomposició QR de l'aplicació tangent obtinguda a partir d'una trajectòria de referència. S'han resolt numèricament les esmentades equacions i s'ha calculat l'exponent de Lyapunov més gran (LLE) per a un rang de valors del paràmetre de bifurcació i s'han resolt analíticament quan la trajectòria de referència és periòdica, tan si és estable com si és inestable. Quan l'òrbita periòdica és l'atractor dominant, el resultat analític coincideix amb el valor obtingut per integració numèrica. Els resultats també es corresponen amb el què prèviament es coneix a la literatura sobre la part real dels exponents de Floquet de les òrbites periòdiques del convertidor buck.La segona part del treball és la que està desenvolupada en els capítols 4 i 5. En ells s'ha estudiat la dinàmica del convertidor boost controlat amb una superfície de lliscament. En el capítol 4 s'ha estudiat la dinàmica de lliscament ideal del convertidor boost. S'han trobat les regions de lliscament en funció del paràmetre Vref i s'ha estudiat el caràcter del punt d'equilibri d'aquesta dinàmica ideal en funció també d'aquest paràmetre. Ja que aquest control significaria que el sistema commuta amb freqüència infinita, a efectes pràctics, s'haintroduït una banda d'histèresi. Aleshores s'ha analitzat la dinàmica del sistema en funció d'un altre paràmetre, Vg, el qual forma part de l'expressió del punt d'equilibri que presenta el convertidor en una de les seves configuracions quan aquest treballa en mode de conducció contínua (MCC). S'ha comprovat que en funció de la posició d'aquest punt d'equilibri, PE=(V_g,V_g/R), respecte la banda d'histèresi, la dinàmica o bé té un cicle límit que pot ser o no atractor, o un punt d'equilibri globalment estable o ambdues coses alhora.Finalment, en el capítol 5, s'ha intoduït un control integral i una tercera variable (variable error) al convertidor boost amb control de lliscament i amb banda d'histèresi. Les trajectòries són ara de $R^3$ i la dinàmica resultant és molt més complicada, havent-hi la possibilitat de la presència de caos. S'han trobat numèricament òrbites 1 i 2 periòdiques en funció del paràmetre de bifurcació $V_{ref}$ tan en MCC com en MCD i s'han trobat exemples de bifurcacions típiques dels sistemes suficientment diferenciables, com el desdoblament de període, i d'altres bifurcacions relativament noves a la literatura com són les que es produeixen per un canvi de mode de conducció, de MCC a MCD o a la inversa, o les que es presenten en sistemes non-smooth (que no són infinitament diferenciables a tot l'espai d'estats) com són les bifurcacions "border collision", etc.

    After an introductory chapter (Chapter 2), where we define and explain the concepts and characteristics of dynamical systems relevant to our work, the rest of the thesis can be divided into two parts. The first part comprises Chapter 3, where we review the most interesting, both from the computational and theoretical points ofview, numerical method to compute the Lyapunov exponents, based on the QR decomposition of the tangent map with respect to a reference trajectory. We apply it to a general class of bilinear systems.Specific results have been obtained for the buck converter. Indeed, we have written the diferential equations for the Lyapunov exponents of the buck converter which arise from the QR decomposition, and we have numerically solved the equations and computed the largest Lyapunov exponent for a range of values of the bifurcation parameter; analytical results have been obtained when the reference trajectory is a periodic one, either stable or unstable. When a periodic orbit is the dominant attractor, the analytical result coincides with the value obtained by numerical integration. The results also agree with what was previously known in the literature about the real part of the Floquet exponents of the periodics orbits of the buck converter. The second part of this work is developed in chapters 4 and 5. We have studied the dynamics of the boost converter with a sliding surface control. In Chapter 4, we have studied the dynamics of ideal sliding of the boost converter, and described the sliding regions as a function of the parameter /Vref/, and the character (stable or unstable) of the equilibrium poin of the ideal sliding dynamics with respect the same parameter has been determined. Because the chosen control implies that the dynamics of the system switches with infinity frequency, we have introduced a hysteris band for numericalcomputation purposes. We have also analysed the dynamics of the system with respect another parameter, /Vg/, which sets one of the coordinates of the equilibrium point of the boost converter in one of its configurations, when working in continuous conduction mode (CCM). It is found out that the position of this equilibrium point, /PE=(Vg,Vg/R),/ with respect to the hysteresis band, determines whether the dynamics develops a limit cicle, attractive or not, or a global equilibrium, or both. Finally, in Chapter 5, we have introduced an integral control and a third variable (an error variable) into the system described in the previous chapter. Due to the extra dimension, the resulting dynamic is more complicated. In particular, the possibility of chaotic phenomena now arises. We have computed numerically trajectories of period one and two while varying the parameter /Vref/, either in CCM or in discontinuous conduction mode (DCM). We have also found examples of a known class of bifurcations for smooth systems, namely period doubling bifurcation, although some examples of new types ofbifurcations related to the transition from CCM to DCM or vice versa, like those which happen in non-smooth systems, as border collision bifurcations, have also been observed.

  • A robustly stable PI controller for the doubly-fed induction machine

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Ortega, R
    The 32nd Annual Conference of the IEEE Industrial Electronic Society
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  • Energy-based modelling and control of a multi-domain energy storage and management system

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric; Ortega, R
    5th Vienna Symposium on Mathematical Modelling
    Presentation of work at congresses

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  • Simultaneous Interconnection and damping assignment passivity-based control: two practical examples

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Espinosa, G; Ortega, R
    3rd Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
    Presentation of work at congresses

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  • Energy-based modelling and simulation of the interconnection of a back-to-back converter and a doubly-fed induction machine

     Batlle Arnau, Carles; Doria Cerezo, Arnau
    American Control Conference
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  • Access to the full text
    Robust Hamiltonian passive control for higher relative degree outputs  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date: 2006-09
    Report

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    We present an improvement of the well-know Interconnection and Damping Assignment-Passivity-based Control (IDA-PBC) technique. The IDA-PBC method is based on the Port –controlled Hamiltonian Systems description and requires the knowledge of the full energy (or Hamiltonian) function. This is a problem because, in general, the equilibrium point which is to be regulated depends on uncertain parameters. In this paper, we show how select the target port-Hamiltonian structure so that this dependence is reduced. This new approach allows to improve the robustness for higher relative degree outputs, and, for illustration purposes, is applied to a simple academic nonlinear system

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    Experiments on generation and conversion  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric; Ortega, R
    Date: 2006-04
    Report

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    Experimental results of the flywheel energy storage systems are presented. This report finalizes the work of the UPC in the context of the GeoPlex European Project. This document contains only the experimental results of the system, while the associated theoretical results and simulations are presented in previous works. The experimental results validates the policy management, the port Hamiltonian models and the developed controllers using the IDA-PBC approach along the project

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    Report on theorerical results of power generation and conversion  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date: 2006-04
    Report

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    Experimental results of a new controller able to support bidirectional power flow in a full-bridge rectifier with boost-like topology are obtained. The controller is computed using port Hamiltonian passivity techniques for a suitable generalized state space averaging truncation system, which transforms the control objectives, namely constant output voltage dc-bus and unity input power factor, into a regulation problem. Simulation results for the full system show the essential correctness of the simplifications introduced to obtain the controller, although some small experimental discrepancies point to several aspects that need further improvement.

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    Experimental results on an IDA-PBC controller for a full-bridge boost converter  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date: 2006-04
    Report

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    Experimental results of a new controller able to support bidirectional power flow in a full-bridge rectifier with boost-like topology are obtained. The controller is computed using port Hamiltonian passivity techniques for a suitable generalized state space averaging truncation system, which transforms the control objectives, namely constant output voltage dc-bus and unity input power factor, into a regulation problem. Simulation results for the full system show the essential correctness of the simplifications introduced to obtain the controller, although some small experimental discrepancies point to several aspects that need further improvement.

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    Improving the robustness of hamiltonian passive control  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date: 2006-03
    Report

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    Interconnection and damping assignment passivity based control (IDA-PBC) is a well know technique for port Hamiltonian dissipative systems (PHDS). In this paper we point out the kind of problems that can appear in the closed-loop structure obtained by IDA-PBC methods for relative degree one outputs, when nominal values are used in a system with uncertain parameters. In particular, we show that, in general, the positive semidefiniteness of dissipation matrix breaks down, at least, in a neighborhood of the desired regulation point, preventing thus the use of LaSalle’s theorem. Nevertheless, we present an example where the closed-loop system regulates to a fixed point, albeit different from the desired one. To correct this, we introduce an integral control, which can be cast into Hamiltonian framework. Numerical simulations for our example show that the closed-loop system regulates to the desired point, although a rich dynamical behaviour is obtained when the feedback parameters are varied.

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    GeoPlex experimental setup: generator and converter  Open access

     Doria Cerezo, Arnau; Batlle Arnau, Carles; Fossas Colet, Enric
    Date: 2006-01
    Report

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    The experimental setup of the Flywhell Energy Storage System is presented. The system is made of a doubly-fed induction machine coupled to a flywheel and a back-to-back converter

  • Reconocimiento y financiación del grupo Control Avanzado de Sistemas

     Griño Cubero, Roberto; Fossas Colet, Enric; Batlle Arnau, Carles; Olm Miras, Josep Maria; Doria Cerezo, Arnau
    Participation in a competitive project

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  • IDA-PBC controller for a bidirectional power flow full-bridge rectifier

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    European Control Conference
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  • Generalized state space averaging for port controlled hamiltonian systems

     Batlle Arnau, Carles; Fossas Colet, Enric; Griño Cubero, Roberto; Martínez, S
    16th World Congress of the International Federation on Automatic Control
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  • Generalized state space averaging for port controlled hamiltonian systems

     Batlle Arnau, Carles
    16th World Congress of the International Federation on Automatic Control
    Presentation's date: 2005-07-07
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  • Generalized Discontinuous Conduction Modes in the Complementarity Formalism

     Batlle Arnau, Carles; Fossas Colet, Enric; Merillas, I; Miralles De La Asuncion, Alicia
    IEEE transactions on circuits and systems II: express briefs
    Date of publication: 2005-08
    Journal article

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    Analysis and control of an hybrid system: a doubly-fed induction machine and a back-to-back converter  Open access

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date: 2005-09
    Report

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    This report describes the port interconnection of two subsystems: a power elec- tronics subsystem (a back-to-back AC/AC converter (B2B), coupled to a phase of the power grid), and an electromechanical subsystem (a doubly-fed induction ma- chine (DFIM), coupled mechanically to a flywheel and electrically to the power grid and to a local varying load). The B2B is a variable structure system (VSS), due to the presence of control-actuated switches; however, from a modelling and simula- tion, as well as a control-design, point of view, it is sensible to consider modulated transformers instead of the pairs of complementary switches. The port-Hamiltonian models of both subsystems are presented and, using a power-preserving interconnec- tion, the Hamiltonian description of the whole system is obtained. Using passivity- based controllers computed in the Hamiltonian formalism for both subsystems, a closed loop Hamiltonian system is presented; simulations are run to test the cor- rectness and e-ciency of the Hamiltonian network modelling approach used in this work.

  • Hybrid model of a doubly-fed induction machine and a back-to-back converter

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Fossas Colet, Enric
    Date: 2005-03
    Report

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  • Modeling and control of electromechanical systems

     Batlle Arnau, Carles; Doria Cerezo, Arnau
    Date: 2005-07
    Report

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  • Power Flow Control of a Doubly-Fed Induction Machine Coupled to a Flywheel

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Ortega, R
    European journal of control
    Date of publication: 2005-08
    Journal article

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  • Diseño y control del sistema de acondicionamiento de energía eléctrica para pilas de combustible.

     Griño Cubero, Roberto; Malo Barragan, Shane Leonardo; Olm Miras, Josep Maria; Costa Castelló, Ramon; Doria Cerezo, Arnau; Fossas Colet, Enric; Batlle Arnau, Carles
    Participation in a competitive project

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  • Power flow control of a doubly-fed induction machine coupled to a flywheel

     Batlle Arnau, Carles; Doria Cerezo, Arnau; Ortega, R
    IEEE Conference on Control Applications
    Presentation's date: 2004-09-02
    Presentation of work at congresses

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