This bachelor thesis at the Royal Institute of Technology in Stockholm, Sweden, aims to clarify how the minimum bandwidth of a stabilised mobile inverted pendulum is affected by the position of its center of mass and the frequency of measuring the state variables. The scope is to apply basic theories in automation control and electronic systems when designing the system. The mechatronical system in the experimental trials is constructed with the main components consisting of bipolar stepper motors, stepper motor drivers (DRV8825), potentiometer and Arduino UNO. The mobile pendulum in question consists of a cart on a rail with a potentiomoter and a rod mounted to it. In the experimental trials in this paper, three different radial positions of the center of mass are analysed with regards to the bandwidth of relevant measurements. A variety of PID parameters, for both the angle and position regulation, are the essential basis on which these stability trials are performed. The results are limited to the resolution of the potentiometer outputs, the length of the rail and the stiffness of the rod. The result is presented by comparisons between data of the greatest angles which are stabilised and the corresponding maximal latency of the angle corrections. These data concludes to that the minimum required bandwidth to sustain stability decreases for an increasing length between the center of mass and the point of rotation. / Denna kandidatexamensuppsats genomfördes på Kungliga Tekniska Högskolan, i Stockholm, Sverige, och har som mål att klargöra hur den minsta bandbredden för en stabiliserad inverterad pendel påverkas av positionen av dess tyngdpunkt samt nätfrekvensen av tillståndsvariablerna. Projektet omfattar grundläggande teorier om reglerteknik och elektriska system.  Det mekatroniska systemet som används i experimenten är uppbyggt av följande nyckelkomponenter: bipolära stegmotorer, stegmotordrivare (DRV8825), potentionmeter och Arduino UNO. Den mobila pendeln består av en stång och en potentiometer som är monterad på en vagn löpandes på en räls. I de utförda experimenten i denna rapport analyseras tre radiella positioner på masscentrum med hänsyn till bandbredden och relevanta mätningar. En reglering med olika PID parametrar, för både vinkel- och positionsreglering, är den kritiska process som lade grunden för analyserna av stabiliteten. Resultaten är begränsade av upplösningen hos potentiometerns utsignal, längden av rälsen och stångens styvhet.  Resultaten presenteras genom jämförelser mellan data för de största vinklarna som stabiliseras och de motsvarande maximala fördröjningarna. Sammanfattningsvis minskar den minst nödvändiga bandbredden för att upprätthålla stabilitet för ökande längder mellan pendelns tyngdpunkt och rotationspunkten.

En damm används i huvudsak för att magasinera vatten i energiutvinningssyfte. Dammen rör sig fram och tillbaka i ett säsongsmönster mestadels beroende på skillnader i utomhustemperatur och vattentemperaturen i magasinet. Det nordiska klimatet innebär risk för isläggning i magasinet, för vilken lasten är relativt outforskad. Denna rapport syftar till ett med multipla linjära regressionsmodeller samt dynamiska regressionsmodeller avgöra vilka variabler som förklarar en specifik svensk dammkonstruktions rörelse. Dammens rörelse mäts genom att mäta dammens förflyttning kontra berggrunden med data från dammens inverterade pendlar. Av särskilt intresse är att avgöra islastens påverkan på rörelsen. Resultaten visar att multipla linjära regressions-modeller inte fullständigt lyckas modellera dammens rörelse, då de har problem med autokorrelerade residualer. Detta hanteras med hjälp av autoregressiva regressionsmodeller där de initiala förklarande variablerna inkluderas, kallat dynamisk regression. Denna rapports resultat visar att de autoregressiva parametrarna fungerar mycket väl för att förklara pendlarna, men att även tid, temperatur, det hydrostatiska trycket samt istjocklek är användbara förklarande variabler. Istjockleken visar signifikant påverkan på 5 % signifikansnivå på två av de undersökta pendlarna, vilket är ett noterbart resultat. Författarna menar att rapportens resultat indikerar att det finns anledning att fortsätta forska kring islastens påverkan på dammkonstruktioner. / A dam is a structure mainly used for storing water and generating electricity. The structure of a dam moves in a season-based pattern, mainly because of the difference in temperature between the air on outside of the dam and the water on the inside. Due to the Nordic climate, occurrences of icing on the water in the basin is fairly frequent. The effects of ice on the structural load of the dam are relatively unexplored and are the subject to this bachelor’s thesis. The goal of this project is to evaluate which predictors are significant to the movement of the dam with multiple linear regression models and dynamic regressions. The movement is measured by inverted pendulums that register the dam’s movement compared to the foundation. It is of particular interest to determine if the ice load influences the movement of the dam. The multiple regression models used to explain the dam’s movement were all discarded due to autocorrelation in the residuals. This falsifies the models, since autocorrelation means that they don’t meet the needed assumptions. To counteract the autocorrelation, dynamic models with autoregressive terms were fitted. These models showed no problem with autocorrelation. The result from the dynamic models were successful and managed to significantly explain the movement of the dam. The autoregressive terms proved to be efficient explanatory variables. The dynamic regression models also show that the time, temperature, hydrostatic pressure and ice thickness variables are also useful explanatory variables. The ice thickness shows a significant effect at the 5 % significance level on two of the investigated pendulums. The report's results indicate that there is reason to continue research on the ice load impact on dam constructions.

A robot capable of balancing itself on two wheels has been built and programmed. While balancing, the robot keeps within a limited area. The robot has a face with two eyes and a mouth, consisting of LED-matrices, which switch between six different facial expressions. The robot is programmed using Arduino boards, one of which implements PID regulators to control the motors.

Le suivi de la déformation de la croûte terrestre durant la phase intersismique pour la recherche des transitoires nécessite des instruments précis capables d'opérer pour de très longues durées. Le projet ANR-LINES a visé le développement de trois nouveaux instruments : un sismomètre mono-axial, un inclinomètre hydrostatique à longue base et un inclinomètre de forage pendulaire. Ces trois instruments profitent d'un capteur interférométrique de déplacement à longues fibres optiques du type Fabry-Pérot Extrinsèque (EFFPI). Leurs architectures mécaniques et l'utilisation de longues fibres permettent à ces instruments géophysiques nouvellement fabriqués d'atteindre les objectifs fixés.Le premier objectif de cette étude est de proposer des méthodes adaptées à l'estimation de la phase du chemin optique dans les cavités Fabry-Pérot. Une modulation du courant de la diode laser, suivie par une démodulation homodyne du signal d'interférence et un filtre de Kalman permettent de déterminer la phase en temps réel. Les résultats sont convaincants pour des mesures de courtes durées mais exigent des solutions complémentaires pour se prémunir des effets de la variation des phénomènes environnementaux.Le capteur EFFPI intégré dans l'inclinomètre de forage LINES lui offre l'opportunité d'établir une mesure différentielle de l'oscillation de la masselotte pendulée grâce à trois cavités Fabry-Pérot. Le sismomètre LINES utilise lui aussi le capteur de déplacement EFFPI pour la mesure du déplacement de sa bobine. Une description de l'architecture mécanique de ces instruments et une analyse des phénomènes détectés (mouvements lents, marées, séismes, microséismes . . . ) font partie de cette thèse. / Monitoring crustal deformation during the interseismic phase when searching for earth transients requires precise instruments able to operate for very long periods. The ANR-LINES project aimed to develop three new instruments: a single-axis seismometer, a hydrostatic long base tiltmeter and a borehole pendulum tiltmeter. These three instruments benefit of an extrinsic Fabry-Pérot interferometer (EFFPI) with long optic fibers for displacement detections. Their mechanical architectures and their disposal of long fibers help these newly manufactured geophysical instruments complete their goals.The first objective of this study is to propose appropriate methods for estimating the phase of the optical path in the Fabry-Pérot cavities. A modulation of the laser diode current, followed by a homodyne demodulation of the interference signal and a Kalman filter, allow determining the phase in real time. The results are convincing while taking short periods measurements but require additional solutions for protection against environmental phenomena variations. The EFFPI sensor integrated in the LINES borehole tiltmeter gives it the opportunity to establish a differential measurement of the bob's oscillation thanks to three Fabry-Perot cavities. The LINES seismometer also uses the EFFPI displacement sensor to measure its coil's displacement. A description of the two instruments' mechanical structures and an analysis of the detected phenomena (slow movements, tides, earthquakes, microseisms . . . ) are part of this thesis.Keywords: Laser interferometry, wavelength modulation, synchronous homodyne demodulation, ellipse fitting, Kalman filter, temperature compensation, borehole tiltmeter, simple pendulum, differential measurements, slow drift, seismicobservations, seismometer.

La problématique du port de charges par l’Homme est l’objet de questionnements scientifiques depuis plus d’un siècle, notamment dans les armées où les soldats doivent remplir des objectifs opérationnels tout en emportant des équipements lourds, distribués de façon complexe autour de leur corps, et cela au cours d’efforts allant de quelques heures à plusieurs jours. Aussi, avec le développement des nouvelles technologies et l’arrivée des systèmes fantassins futurs sur le marché de la défense, cette problématique continue de se complexifier puisque la masse totale emportée tend encore à croître. Objectif général : Le but de ce travail de thèse était d’étudier l’impact biomécanique, métabolique et neuromusculaire du port d’un système fantassin moderne chez le soldat expérimenté. Plus précisément, une première recherche a été menée pour caractériser les effets aigus du port d’un tel équipement sur la biomécanique et le coût métabolique de la marche. Puis, une seconde recherche a été consacrée à l’étude des conséquences neuromusculaires et locomotrices d’une mission militaire (simulation sur le terrain) de durée « extrême » réalisée avec ce système fantassin moderne. Première partie : L’analyse de la marche sur tapis roulant dynamométrique a permis de montrer que le port du système fantassin en configurations de « combat » et de « marche d’approche » (principales configurations du théâtre militaire, représentant respectivement ~30 % et ~50 % de la masse corporelle des sujets) altérait le pattern spatio-temporel par rapport à la marche sans charge. Par ailleurs, le travail mécanique appliqué au centre de masse et le coût métabolique de la marche augmentaient parallèlement lors du port des deux configurations du système fantassin, ce qui résultait en un maintien du rendement locomoteur constant dans toutes les conditions testées. Le mécanisme de transfert d’énergie en pendule inversé (méthode Cavagna), permettant de minimiser les coûts mécanique et métabolique de transport, était également similaire dans toutes les conditions avec et sans charge. Enfin, bien que complexement organisés autour du corps du soldat, les équipements militaires n’induisaient pas d’effets mécaniques et métaboliques sensiblement plus importants que ceux rapportés lors du port de masses positionnées symétriquement autour de la taille ; ce mode de portage étant pourtant considéré comme l’un des plus optimisés, abstraction faite des techniques de portage sur la tête inadaptées au contexte militaire. Deuxième partie : La réalisation d’une mission simulée, incluant 21 h d’activités militaires sur le terrain et le port constant d’un système fantassin, résultait en une fatigue neuromusculaire (mesure des forces, électrostimulation et EMG) relativement modérée des muscles locomoteurs extenseurs du genou et fléchisseurs plantaires chez les soldats expérimentés inclus dans ce travail. Les origines de cette fatigue neuromusculaire étaient essentiellement périphériques, mais s’accompagnaient d’une fatigue subjective importante. Enfin, la réalisation de la mission, et donc la fatigue des muscles locomoteurs notamment associée à cette dernière, n’affectait pas sensiblement les paramètres mécaniques et métaboliques de la marche. Conclusion générale : Ce travail rapporte les premières données relatives aux effets biomécaniques, métaboliques et neuromusculaires du port d’un système fantassin moderne chez le soldat expérimenté, et ce par le biais d’une simulation opérationnelle visant à reproduire les conditions militaires / For more than a century, load carriage has been the source of many scientific questions and researches, especially in armies in which soldiers have to reach operational goals while carrying heavy loads complexly distributed around their body and this for some hours to several days. Moreover, with the development of new technologies and the advent of land warfare systems, this issue is becoming more complex since load continues to increase. General purpose: The aim of the present work was to investigate the biomechanical, metabolic and neuromuscular constraints imposed by the carriage of a modern land warfare system in experienced soldiers. Specifically, a first study was conducted to characterize the acute effects of land warfare equipments carriage on the biomechanics and energetics of walking. Moreover, a second research was performed to investigate the neuromuscular and locomotor consequences of an extreme-duration simulated military mission (performed in the field) involving the carriage of these specific equipments. First part: Walking analyses performed on an instrumented treadmill showed that the carriage of a land warfare system in two configurations made for “Battles” and “Road marches” (main configuration used in the field representing ~30% and ~50% of subject’s body mass, respectively) altered the walking pattern. Moreover, the mechanical work applied to the center of mass increased in parallel with the energy cost of walking during Battle and Road March configurations carriage, as shown by the constant locomotor efficiency in the three tested conditions. The inverted pendulum-like energy exchange (Cavagna’s standard method), allowing mechanical/metabolic energy saving, was also constant in all the unloaded and loaded conditions. Finally, even if the load was complexly distributed around soldiers’ body with this warfare system, this did not induce greater effects than those reported with loads carried symmetrically around the waist and close to the center of mass; which has yet been hypothesized to be the optimal method of load carriage from both mechanical and metabolic standpoints (except “original” methods such as head carrying that cannot be used in the military theater). Second part: Performing a 21-h simulated military mission with heavy land warfare system carriage induced relatively moderate neuromuscular alterations (isometric force measurement with electrical stimulation and EMG) for both knee extensors and plantar flexors locomotor muscle groups in experienced soldiers. Moreover, the origin of fatigue was essentially peripheral for both muscle groups but was concomitant with a large sensation of fatigue. Finally, the simulated mission, and notably the associated locomotor muscles fatigue, did not alter walking biomechanics and energetics. General conclusion: These results bring the first insight into the biomechanical, metabolic and neuromuscular consequences of modern land warfare system carriage in experienced soldiers, and this by a real-world approach aiming at simulating the military theater conditions

[pt] Esta tese apresenta o estudo dinâmico de três sistemas pendulares e de um sistema de corpo livre no espaço com 3 graus de liberdade. O primeiro sistema pendular consiste de um pêndulo acoplado ao centro de uma roda, que rola sem escorregar na direção horizontal, enquanto o segundo, se baseia num pêndulo simples, porém com comprimento variável, que ao mudar seu tamanho consegue ganhar/perder energia para aumentar/diminuir a amplitude de seu movimento e finalmente o terceiro está baseado num pêndulo duplo que, a despeito de restrições impostas ao movimento consegue inserir/retirar energia do sistema de forma similar ao segundo. O modelo de corpo livre no espaço está baseado na suspensão cardânica de um giroscópio e se utiliza de um modelo didático real de um giroscópio para observação das características dinâmicas. A partir destes exemplos estudou-se formas de controle não-linear para movimentar os sistemas de maneira a utilizar-se da mudança de posição interna do centro de massa para injetar e retirar energia dos sistemas. Foram gerados modelos matemáticos simulados no Simulink valendo-se do Matlab para análise, e geradas animações também com o Matlab para melhor observação dos efeitos. Em paralelo, para dois destes sistemas foram construídos em bancada experimentos para comprovação dos resultados numéricos, e os resultados são comparados em cada caso, analisando as diferenças. Ao final, todas as observações sobre os estudos foram analisadas, e comentários feitos baseados nos resultados, além de sugerir trabalhos futuros. / [en] This thesis presents the study of the dynamics of three pendulum systems and a 3DoF free body in space. The first pendular system is based on a simple pendulum coupled to the center of a wheel that translates horizontally without slip; while the second system is based on a simple pendulum, with variable length, which is able to acquire/lose energy to grow/diminish the amplitude of its movement; and finally the third one is based on a double pendulum that, in spite of movement restrictions, can as well inject/drop energy like the second system. The free body in space is based on a real gyroscope for didactical use, which is helpful for the observation of the dynamic characteristics of the motion. Using these examples a non-linear control was designed to drive the system by using the property that changing the internal position of the center of mass it is possible to inject or to subtract energy from the systems. Mathematical models were simulated with Simulik software, Matlab was used for the analysis, and animations were created also with Matlab for a better sight of the effects. In parallel, there were developed 2 test rig systems for verification of the numerical results. In the conclusions all the considerations about the study were analyzed, and comments made on the results, as well also future developments are suggested.

Ziel der Arbeit ist es, die instationären zeitlichen und räumlichen Bewegungsabläufe stark deformierbarer eindimensionaler Kontinua durch ein allgemeines mechanisch-mathematisches Modell unter Berücksichtigung ihrer Biege- und Torsionssteifigkeit zu beschreiben und zu dessen Lösung geeignete numerische Verfahren zu testen und auszuwählen. Die entwickelten Algorithmen werden auf Aufgabenstellungen aus der Raumfahrt-, Meeres- und Textiltechnik angewendet. / It is the aim of this thesis to describe the instationary motion of flexible one-dimensional continua by a general mechanical-mathematical model, when bending and torsional stiffness is not negligible, and to test and select appropriate numerical solution methods. The developed algorithms are used to solve problems from space, marine and textil engineering.

Ziel der Arbeit ist die anschauliche Demonstration der Leistungsfähigkeit von Hardware- Systemen zur Regelung instabiler Systeme am Beispiel des Inversen Pendels. Dabei handelt es sich um das Balancieren eines Stabes, einem Standard-Problem der Regelungstechnik. Es wird die Konzeption und Implementierung einer Hardware-Regelung in einem FPGA-Prototypenboard zur Realisierung dieser Aufgabe beschrieben. Die Regelung basiert mit LQR-Entwurf und Kalman-Filter auf klassischen Methoden der Regelungstechnik. Zur Demonstration der Regelung wurde ein mechanischer Aufbau vorgenommen, an dem die Funktionsfähigkeit des Inversen Pendels praktisch gezeigt wurde.

Syftet med projektet är att konstruera en inverterad pendel som sedan med hjälp av reglertekniska metoder ska stabiliseras. De linjära regulatorer som prövats är Proportionell, Integrerande och Deriverande (PID) -regulatorn och Linnear Quadratic Gaussian (LQG) -regulatorn som båda är populära och beprövade i industrin. PID-regulatorn är den absolut mest använda regulatorn medan LQG-regulatorn är mer raffinerad och i vissa avseenden en optimal regulator. Regulatorerna programmerades in i mikrokontrollern Arduino Nano som skickar signaler till en motordrivare som styr den stegmotor som ska balansera pendeln. Mycket av arbetet har handlat om att skapa en uppställning som tillåter goda förutsättningar för att pröva regulatorerna. I uppställningen finns delar som utformats i Computor-Aided design (CAD) -verktyget OpenSCAD och skrivits ut på en 3D-skrivare. Den givare vi använt för att mäta pendelns vinkel är en potentiometer infäst i dessa 3D-utskrivna delar. Motorn kunde styras till sin maximala kapacitet och en uppställning har skapats. Dock skulle en starkare motor och en mer robust uppställning möjliggöra en avsevärt bättre reglering. Regulatorerna klarade inte av att stabilisera systemet mer än ett fåtal sekunder, detta bland annat pågrund av tidsbrist till att justera regleringsvariablerna.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-17T17:42:26Z No. of bitstreams: 1 LEOPOLDO MAURÍCIO TAVARES BARBOSA - DISSERTAÇÃO PPGMAT 2007..pdf: 712644 bytes, checksum: 6b24483b48b038e23d4ace377b04ece5 (MD5) / Made available in DSpace on 2018-07-17T17:42:27Z (GMT). No. of bitstreams: 1 LEOPOLDO MAURÍCIO TAVARES BARBOSA - DISSERTAÇÃO PPGMAT 2007..pdf: 712644 bytes, checksum: 6b24483b48b038e23d4ace377b04ece5 (MD5) Previous issue date: 2007-10 / CNPq / Capes / Neste trabalho usamos métodos variacionais para mostrar a existência de solução fraca para dois tipos de problema. O primeiro trata-se de uma Equação Diferencial Ordinária. O segundo é referente ao sistema Hamiltoniano. *Para Visualisar as equações ou formulas originalmente escritas neste resumo recomendamos o downloado do arquivo completo. / In this work we use variational methods to show the existence of weak solutions for two types problems. The first, is related with a following Ordinary Differential Equations. The second is relating at the Hamiltonian Systems. *To see the equations or formulas originally written in this summary we recommend downloading the complete file.