Effective procedure for the optimization of the linear controller in an industrial drive for a nonlinear mechanism

Il progetto di tesi è incentrato sull’ottimizzazione del procedimento di taratura dei regolatori lineari degli anelli di controllo di posizione e velocità presenti negli azionamenti usati industrialmente su macchine automatiche, specialmente quando il carico è ad inerzia variabile in dipendenza dalla posizione, dunque non lineare, come ad esempio un quadrilatero articolato. Il lavoro è stato svolto in collaborazione con l’azienda G.D S.p.A. ed il meccanismo di prova è realmente utilizzato nelle macchine automatiche per il packaging di sigarette. L’ottimizzazione si basa sulla simulazione in ambiente Matlab/Simulink dell’intero sistema di controllo, cioè comprensivo del modello Simulink degli anelli di controllo del drive, inclusa la dinamica elettrica del motore, e del modello Simscape del meccanismo, perciò una prima necessaria fase del lavoro è stata la validazione di tali modelli affinché fossero sufficientemente fedeli al comportamento reale. Il secondo passo è stato fornire una prima taratura di tentativo che fungesse da punto di partenza per l’algoritmo di ottimizzazione, abbiamo fatto ciò linearizzando il modello meccanico con l’inerzia minima e utilizzando il metodo delle formule di inversione per determinare i parametri di controllo. Già questa taratura, seppur conservativa, ha portato ad un miglioramento delle performance del sistema rispetto alla taratura empirica comunemente fatta in ambito industriale. Infine, abbiamo lanciato l’algoritmo di ottimizzazione definendo opportunamente la funzione di costo, ed il risultato è stato decisamente positivo, portando ad un miglioramento medio del massimo errore di inseguimento di circa il 25%, ma anche oltre il 30% in alcuni casi.

On the Wick product and Wong-Zakai approximations.

This thesis is a compilation of 6 papers that the author has written together with Alberto Lanconelli (chapters 3, 5 and 8) and Hyun-Jung Kim (ch 7). The logic thread that link all these chapters together is the interest to analyze and approximate the solutions of certain stochastic differential equations using the so called Wick product as the basic tool. In the first chapter we present arguably the most important achievement of this thesis; namely the generalization to multiple dimensions of a Wick-Wong-Zakai approximation theorem proposed by Hu and Oksendal. By exploiting the relationship between the Wick product and the Malliavin derivative we propose an original reduction method which allows us to approximate semi-linear systems of stochastic differential equations of the Itô type. Furthermore in chapter 4 we present a non-trivial extension of the aforementioned results to the case in which the system of stochastic differential equations are driven by a multi-dimensional fraction Brownian motion with Hurst parameter bigger than 1/2. In chapter 5 we employ our approach and present a “short time” approximation for the solution of the Zakai equation from non-linear filtering theory and provide an estimation of the speed of convergence. In chapters 6 and 7 we study some properties of the unique mild solution for the Stochastic Heat Equation driven by spatial white noise of the Wick-Skorohod type. In particular by means of our reduction method we obtain an alternative derivation of the Feynman-Kac representation for the solution, we find its optimal Hölder regularity in time and space and present a Feynman-Kac-type closed form for its spatial derivative. Chapter 8 treats a somewhat different topic; in particular we investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of semi-linear stochastic differential equations describing a predator-prey model perturbed by Gaussian noise.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.

A comprehensive study on robotic manipulation of deformable linear objects

There are many deformable objects such as papers, clothes, ropes in a person’s living space. To have a robot working in automating the daily tasks it is important that the robot works with these deformable objects. Manipulation of deformable objects is a challenging task for robots because these objects have an infinite-dimensional configuration space and are expensive to model, making real-time monitoring, planning and control difficult. It forms a particularly important field of robotics with relevant applications in different sectors such as medicine, food handling, manufacturing, and household chores. In this report, there is a clear review of the approaches used and are currently in use along with future developments to achieve this task. My research is more focused on the last 10 years, where I have systematically reviewed many articles to have a clear understanding of developments in this field. The main contribution is to show the whole landscape of this concept and provide a broad view of how it has evolved. I also explained my research methodology by following my analysis from the past to the present along with my thoughts for the future.

New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

Caracterização da área foliar de Merremia aegyptia

O conhecimento da área foliar de plantas daninhas pode auxiliar o estudo das relações de interferência entre elas e as culturas agrícolas. O objetivo desta pesquisa foi determinar uma equação matemática que estime a área foliar de Merremia aegyptia, a partir da relação entre as dimensões lineares dos limbos foliares. Folhas da espécie foram coletadas de diferentes locais na Universidade Estadual Paulista, Jaboticabal, Brasil, medindo-se o comprimento (C), a largura máxima (L) e a área foliar de três tipos de folíolos. Foram estimadas equações lineares (Y = a*X) para cada tipo de folíolo. A área foliar da espécie pode ser estimada pelo somatório das áreas dos limbos foliares de cada tipo de folíolo, por meio da equação AFest = 0,547470(X) + 1,145298(Y) + 1,244146(Z), em que X indica C*L do folíolo principal e Y e Z indicam C*L médios dos folíolos primário e secundário, respectivamente.

PRACTICAL LAND GRADING BASED ON LEAST SQUARES.

Practical methods for land grading design of a plane surface for rectangular and irregularly shaped fields based on a least squares analysis are presented. The least squares procedure leads to a system of three linear equations with three unknowns for determination of the best-fit plane. The equations can be solved by determinants (Cramer's rule) using a procedure capable of solution by many programmable calculators. The detailed computational process for determining the equation of the plane and a simple method to find the centroid location of an irregular field are also given. An illustrative example and design instructions are included to demonstrate the application of the design procedure.

Über die Linearität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen

Über die Liniarität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. In meiner Arbeit beschäftige ich mich mit Darstellungen der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. Mein Ansatz hierbei ist, die Teichmüllersche Modulgruppe in eine p-adische Liegruppe einzubetten. Sei nun F die von zwei Elementen erzeugte freie Gruppe und Aut(F) die Automorphismengruppe von F. Inhalt des ersten Kapitels ist es nun zu zeigen, daß folgende Aussagen äquivalent sind: - Die Teichmüllersche Modulgruppe des Torus mit zwei Punktierungen ist linear, - Aut(F)ist linear, - F besitzt eine p-Kongruenzstruktur, deren Folgen- glieder von Aut(F) festgehalten werden, also charak- teristisch sind. Im zweiten Kapitel wird unter anderem gezeigt, daß es eine Einbettung einer Untergruppe endlichen Indexes der Aut(F) in die Automorphismengruppe einer einfachen p-adischen Liegruppe gibt. Bisher ist unbekannt, ob die Buraudarstellung treu ist.In dieser Arbeit wird ein unendliches, lineares Gleichungssystem, dessen Lösungen gerade die Koeffizienten der Wörter des Kernes der Buraudarstellung sind, vorgestellt.Im dritten Kapitel wird mit den Methoden des 1.Kapitels gezeigt, daß der Torus mit zwei Punktierungen genau dann linear ist, wenn die Teichmüllersche Modulgruppe der Sphäre mit 5 Punktierungen es auch ist. Bekanntlich ist die 4. Braidgruppe linear. Nun ist aber die 4. Braidgruppe letztlich die Teichmüllersche Modulgruppe der abgeschlossenen Kreisscheibe mit 5 Punktierungen. Wenn man nun deren Randpunkte miteinander identifiziert und anschließend wegläßt, erhält man die 5-fach punktiereSphäre.Mit der eben beschriebenen Abbildung kann man zeigen, daß die Teichmüllersche Modulgruppe der fünffach punktierten Sphäre linear ist.

Modelo computacional para avaliação do desempenho hidrodinâmico de embarcações de planeio em águas calmas.

Em geral, uma embarcação de planeio é projetada para atingir elevados níveis de velocidade. Esse atributo de desempenho está diretamente relacionado ao porte da embarcação e à potência instalada em sua planta propulsiva. Tradicionalmente, durante o projeto de uma embarcação, as análises de desempenho são realizadas através de resultados de embarcações já existentes, retirados de séries sistemáticas ou de embarcações já desenvolvidas pelo estaleiro e/ou projetista. Além disso, a determinação dos atributos de desempenho pode ser feita através de métodos empíricos e/ou estatísticos, onde a embarcação é representada através de seus parâmetros geométricos principais; ou a partir de testes em modelos em escala reduzida ou protótipos. No caso específico de embarcações de planeio, o custo dos testes em escala reduzida é muito elevado em relação ao custo de projeto. Isso faz com que a maioria dos projetistas não opte por ensaios experimentais das novas embarcações em desenvolvimento. Ao longo dos últimos anos, o método de Savitsky foi largamente utilizado para se realizar estimativas de potência instalada de uma embarcação de planeio. Esse método utiliza um conjunto de equações semi-empíricas para determinar os esforços atuantes na embarcação, a partir dos quais é possível determinar a posição de equilíbrio de operação e a força propulsora necessária para navegar em uma dada velocidade. O método de Savitsky é muito utilizado nas fases iniciais de projeto, onde a geometria do casco ainda não foi totalmente definida, pois utiliza apenas as características geométricas principais da embarcação para realização das estimativas de esforços. À medida que se avança nas etapas de projeto, aumenta o detalhamento necessário das estimativas de desempenho. Para a realização, por exemplo, do projeto estrutural é necessária uma estimativa do campo de pressão atuante no fundo do casco, o qual não pode ser determinado pelo método de Savitsky. O método computacional implementado nesta dissertação, tem o objetivo de determinar as características do escoamento e o campo de pressão atuante no casco de uma embarcação de planeio navegando em águas calmas. O escoamento é determinado através de um problema de valor de contorno, no qual a superfície molhada no casco é considerada um corpo esbelto. Devido ao uso da teoria de corpo esbelto o problema pode ser tratado, separadamente, em cada seção, onde as condições de contorno são forçadamente respeitadas através de uma distribuição de vórtices.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential

In this work we consider the effect of a spatially dependent mass over the solution of the Klein-Gordon equation in 1 + 1 dimensions, particularly the case of inversely linear scalar potential, which usually presents problems of divergence of the ground-state wave function at the origin, and possible nonexistence of the even-parity wave functions. Here we study this problem, showing that for a certain dependence of the mass with respect to the coordinate, this problem disappears. (c) 2006 Elsevier B.V. All rights reserved.

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.