Contribució a l'estudi dels exponents de Lyapunov per a sistemes bilineals i a l'analisi de les bifurcacions en el convertidor boost controlat amb superficies de lliscamente i histèresi.

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

The engagement of students using the virtual platform tools. A successful case in a required subject of 1st year in mathematics in engineering (UPC)

Fonaments matemàtics is a required 1st year subject in engineering career at the university EPSEVG (Universitat Politècnica de Catalunya) with approximately 270 students enrolled each semestre that traditionally it had a medium pass rate. Over the last 6 years we have introduced gradual changes in the teaching planning of it with the idea of achieving: 1) that students work throughout the course, 2) leveling knowledge and 3) reduce the number of students not presented to any exam. The changes have been implemented and corrected based on our feedback from students (engagement, grades, acceptance and survey assessments). The introduction of the calculator, laptops and tablets in everyday life and the use of the tools of the UPC virtual platform have been key. In this contribution, we present the strategies used and the good results obtained

Representation of a general composition of Dirac structures

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.Postprint (published version

Validation of a Orcaflex OBSEA's platform model

Peer Reviewe

Order reduction of a distributed parameter PEM fuel cell anode gas channel model

Distributed parameter modeling is required to accurately consider space variations, which are important regarding the performance and durability of the Proton Exchange Membrane Fuel Cells (PEMFC) [1-3]. However, the number of differential and algebraic equations (DAE) obtained from the discretization of a set of partial differential equations (PDE) is very large, and this not only slows down the numerical simulations, but also complicates the design of online model-based controllers. The inclusion of complex DAE models within model-based control schemes requires a previous simplification. A method to simplify complex models consists of reducing the order while preserving the relationship between certain input and output variables, determined from the control objectives. These Model Order Reduction (MOR) techniques have been extended to DAE systems [4]. This work focuses on obtaining an order reduced model, from a PEMFC anode gas channel PDE model, which incorporates the effects of distributed parameters that are relevant for the proper functioning and performance of PEMFC. The original model is an in-house MATLAB® code, flexible enough to manipulate the underlying model equations and apply MOR techniques. The obtained order-reduced model is suitable to perform numerical simulations and design efficient controllers for the original nonlinear PDE model.Postprint (published version

Experimental validation and modelling of electromagnetic kinetic harvester for oceans drifters

Harvesting the mechanical energy of ocean motion are finding different applications for offshore exploration and ocean monitoring. Because of the very low and varying frequency, from 0.1Hz to 2Hz, harvesting this energy has an important hurdle. In this paper, we provide a comprehensive study of a new idea to supply low power oceanic drifters using an electromagnetic vibration harvester. Therefore, this work presents a solution on how to generate power from low frequency driven electromagnetic energy harvester for an ocean drifter self-powered system. A prototype with a proposed electronic harvesting system is built and tested in a real medium, showing the results before concluding the articlePostprint (published version

Retirement Investing: A New Approach

This paper proposes a new approach to investing for retirement that takes advantage of recent market innovations and advances in finance theory to improve the risk/reward opportunities available to individual investors before and after retirement. The approach introduces three new elements: 1. It uses inflation-protected bonds to hedge a minimum standard of living after retirement; 2. It takes account of a person’s willingness to postpone retirement, and 3. It uses option “ladders” to lever growth in retirement income

Aprendre matemàtiques dissenyant

Matemàtiques per al disseny és una assignatura de l’EPSEVG (UPC). S’hi presenten els fonaments matemàtics del disseny industrial. Explicarem com hem incorporat la metodologia aprendre fent. A banda d’il·lustrar tots els conceptes amb objectes quotidians, basem l’aprenentatge en el treball per projectes. Això permet incorporar la creativitat dels estudiants i afavoreix la seva implicació. A més, hem usat les xarxes socials com a mitjà de comunicació.Postprint (published version

Real-time seismic data from the bottom sea

An anchored marine seismometer, acquiring real-time seismic data, has been built and tested. The system consists of an underwater seismometer, a surface buoy, and a mooring line that connects them. Inductive communication through the mooring line provides an inexpensive, reliable, and flexible solution. Prior to the deployment the dynamics of the system have been simulated numerically in order to find optimal materials, cables, buoys, and connections under critical marine conditions. The seismometer used is a high sensitivity triaxial broadband geophone able to measure low vibrational signals produced by the underwater seismic events. The power to operate the surface buoy is provided by solar panels. Additional batteries are needed for the underwater unit. In this paper we also present the first results and an earthquake detection of a prototype system that demonstrates the feasibility of this concept. The seismometer transmits continuous data at a rate of 1000 bps to a controller equipped with a radio link in the surface buoy. A GPS receiver on the surface buoy has been configured to perform accurate timestamps on the seismic data, which makes it possible to integrate the seismic data from these marine seismometers into the existing seismic network.Peer ReviewedPostprint (published version