In this project a cube was constructed with the intent for it to balance on one of its edges by regulating the speed of a reaction wheel. To be able to do this, a research was done to understand the mechanics of the system and to know what components were required for the project. A brushed DC motor was used with one reaction wheel on each end of its shaft, using the moment of inertia to convert the torque from the motor to an angular acceleration of the cube. A control system was implemented to regulate the speed of the motor depending on the angular offset of the cube. This control system was chosen to be a proportional–integral–derivative (PID) controller, and a number of different tuning methods were used to determine the parameters of said controller to create a stable system. Despite the different methods used, the cube did not successfully balance for a longer period of time. / Under detta projekt har en kub konstruerats med syfte att balansera på en av sina kanter genom att reglera hastigheten på ett reaktionshjul. En undersökning genomfördes för att få en bra förståelse för det mekaniska systemet samt för att ta reda på vilka komponenter som var väsentliga för projektet. En borstad likströmsmotor användes tillsammans med ett reaktionshjul på varsin sida av motorns drivande axel vars tröghetsmoment utnyttjades för att överföra momentet från motorn till en vinkelacceleration på kuben. En regulator implementerades för att styra hastigheten på reaktionshjulen beroende på vinkelavvikelsen från jämviktsläget. Regulatorn som valdes var en proportionell, integrerande och deriverande (PID) regulator och flera olika metoder användes för att bestämma regulatorns parametervärden som avgör dess egenskaper. Trots att olika metoder prövades lyckades inte kuben balansera under en längre period.

In todays society there are microprocessors in almost every new item that is produced for home use. They are all being connected and smart, and by that microcontrollers are playing an increasingly important role in peoples private life. In this thesis in mechatronics a controller will be implemented on an Arduino to make it possible for a cube to balance in upright position. The cube is in theory an inverted pendulum with one degree of freedom, and is intended to balance using an inertia wheel at the top of the structure. A PID regulator was used, and at the time this report was written, the right parameter values for the PID was not found. The cube is able to shift its position back and forth over the setpoint with support on each side to prevent it from falling. A bit more tuning is required to make it balance on its own / I dagens samhälle är det microprocessorer i nästan alla nya produkter som skapas för den privata marknaden. De är alla sammankopplade och smarta. I och med det spelar mikrokontrollers en allt större roll i människors dagliga liv. I den här rapporten inom mekatronik implementeras en regulator i en arduino för att balansera en kub stående på en kant. I teorin är en kub en inverterad pendel med en frihetsgrad och är tänkt att balansera med hjälp av ett reaktionshjul monterat överst på prototypen. En PID regulator användes och då denna rapporten skrevs hade rätt parametrar inte påträffats. Kuben klarar av att ändra position fram och tillbaka över referensläget då den blockeras från att ramla. För att den ska klara av att balansera av sig själv behöver regulatorn ställas in bättre.

Nesta dissertação, um tipo diferente de pêndulo invertido controlado por rodas de reação é apresentado. Sua principal diferença está em seu ponto de articulação, que é constituído por uma junta esférica que permite com que o pêndulo gire em torno de seus três eixos. Além disso, três rodas de reação são utilizadas para seu controle e estabilização. Primeiramente, um modelo do sistema é obtido a partir das equação de Euler-Lagrange, das leis de Newton e das leis de Kirchhoff. Em seguida, uma lei de controle que assegura a estabilização assintótica do sistema em um grande domínio é proposta. Por fim, simulações são realizadas para validar o controlador projetado. Esse sistema possui diversas características interessantes, tanto do ponto de vista teórico como do ponto de vista de pesquisa. Do ponto de vista teórico, o sistema é nãolinear e suas entradas são fortemente acopladas, o que torna particularmente adequado para o processo de projeto e implementação de diversas técnicas de estabilização. Do ponto de vista de pesquisa, são consideradas duas técnicas de controle não linear: linearização padrão e linearização exata. Para que o sistema seja robusto e não desperdice energia, essas duas leis de controle diferentes são comutadas para a obtencão de um número suficiente de domínio de estabilidade. / In this dissertation, a different kind of the reaction wheel pendulum is presented. The main difference is that its articulation point consists of a ball joint that allows the pendulum to rotate around its three axes. Furthermore, three reaction wheels are used for its control and stabilization. First, a model of the system is obtained from Euler-Lagrange equations, Newton laws and Kirchhoff laws. After that, a control law that assure asymptotic stabilization of the system in a large domain is proposed. Finally, simulations are performed to validate the designed controller. This system has several interesting features, both from a theoretical standpoint as from a research standpoint. From a theoretical standpoint, the system is nonlinear and its inputs are tightly coupled, making it particularly suitable for the design and implementation process of various stabilization techniques. From a research standpoint, two non-linear control techniques are considered: standard linearization and exact linearization. For the system to be robust and do not waste energy, these two different control laws are switched for obtaining a sufficiently large domain of stability.

Nesta dissertação, um tipo diferente de pêndulo invertido controlado por rodas de reação é apresentado. Sua principal diferença está em seu ponto de articulação, que é constituído por uma junta esférica que permite com que o pêndulo gire em torno de seus três eixos. Além disso, três rodas de reação são utilizadas para seu controle e estabilização. Primeiramente, um modelo do sistema é obtido a partir das equação de Euler-Lagrange, das leis de Newton e das leis de Kirchhoff. Em seguida, uma lei de controle que assegura a estabilização assintótica do sistema em um grande domínio é proposta. Por fim, simulações são realizadas para validar o controlador projetado. Esse sistema possui diversas características interessantes, tanto do ponto de vista teórico como do ponto de vista de pesquisa. Do ponto de vista teórico, o sistema é nãolinear e suas entradas são fortemente acopladas, o que torna particularmente adequado para o processo de projeto e implementação de diversas técnicas de estabilização. Do ponto de vista de pesquisa, são consideradas duas técnicas de controle não linear: linearização padrão e linearização exata. Para que o sistema seja robusto e não desperdice energia, essas duas leis de controle diferentes são comutadas para a obtencão de um número suficiente de domínio de estabilidade. / In this dissertation, a different kind of the reaction wheel pendulum is presented. The main difference is that its articulation point consists of a ball joint that allows the pendulum to rotate around its three axes. Furthermore, three reaction wheels are used for its control and stabilization. First, a model of the system is obtained from Euler-Lagrange equations, Newton laws and Kirchhoff laws. After that, a control law that assure asymptotic stabilization of the system in a large domain is proposed. Finally, simulations are performed to validate the designed controller. This system has several interesting features, both from a theoretical standpoint as from a research standpoint. From a theoretical standpoint, the system is nonlinear and its inputs are tightly coupled, making it particularly suitable for the design and implementation process of various stabilization techniques. From a research standpoint, two non-linear control techniques are considered: standard linearization and exact linearization. For the system to be robust and do not waste energy, these two different control laws are switched for obtaining a sufficiently large domain of stability.

Spacecrafts are generally equipped with high precision optical and other sensor payloads. The structures of most of the spacecrafts are light-weight, flexible and have low damping. Vibrations are often induced in the spacecraft body due to the presence of many disturbance sources such as momentum/reaction wheels, control thrusters used for attitude control and cryocoolers etc. Low damping leads to long decay time for vibrations hence during this period the spacecraft sensors cannot be used effectively. One possible solution is to isolate the precision sensor from the rest of the satellite and this strategy has been used for spaceborne telescopes and interferometers that have extremely precise positional and vibratory tolerances imposed on them in order to achieve scientific goals. Another strategy is to isolate the vibration source itself from the spacecraft body. This thesis deals with modelling, analysis and experimentation of a novel low frequency flexible space platform designed to serve as a mount for the disturbance source in order to insulate the source generated vibrations reaching critical areas of the structure. The novel space platform consisting of folded continuous beams, is light-weight and is capable of isolating vibration generated by sources such as reaction/momentum wheels. Finite element analysis of the platform is carried out for static and dynamic load cases. Simulation studies are carried out on flexible beam platform in order to firm up the design for passive vibration isolation. Modal analyses is done to simulate the response of each mode. Active control has been studied by embedding the platform’s beam elements with piezo actuators and sensors. The simulation results show that the space platform can effectively attenuate vibration and further improvement in vibration attenuation is possible with active control. Based on the analysis, a prototype low frequency platform has been designed and fabricated. An experimental validation has been done to test the usefulness of the low frequency platform to act as a mount for reaction wheels and to mitigate the vibration disturbances/effects transmitted from the reaction wheel assembly to structure. Measurements and tests have been conducted at varying wheel speeds to quantify and characterize the amount of isolation to the reaction wheel generated vibrations. The time and frequency domain analysis of test data clearly show that level of isolation is significant and an average of 13 dB of isolation is seen. The level of isolation is different for different isolators and it depends upon the isolator design and wheel speed. Forces and moments measured at the base for wheel with isolator and wheel without isolator clearly demonstrate and confirm a reduction in the disturbance levels of atleast one order. These isolators are further tested successfully for launch dynamic loads in order to confirm the design adequacy to sustain such loads. Results indicate that the flexible mounts of the type discussed in this thesis can be used for effective passive vibration isolation in spacecrafts with reaction/momentum wheels.