The Reaction Wheel Pendulum (RWP) is an interesting nonlinear system. A prototypical control problem for the RWP is to stabilize it around the upright position starting from the bottom, which is generally divided into at least 2 phases: (1) Swing-up phase: where the pendulum is swung up and moves toward the upright position. (2) Stabilization phase: here, the pendulum is controlled to be balanced around the upright position. Previous studies mainly focused on an energy method in swing-up phase and a linearization method in stabilization phase. However, several limitations exist. The energy method in swing-up mode usually takes a long time to approach the upright position. Moreover, its trajectory is not controlled which prevents further extensions. The linearization method in the stabilization phase, can only work for a very small range of angles around the equilibrium point, limiting its applicability. In this thesis, we took the 2nd order state space model and solved it for a constant torque input generating the family of phase-plane trajectories (see Appendix A). Therefore, we are able to plan the motion of the reaction wheel pendulum in the phase plane and a sliding mode controller may be implemented around these trajectories. The control strategy presented here is divided into three phases. (1) In the swing up phase a switching torque controller is designed to oscillate the pendulum until the system’s energy is enough to drive the system to the upright position. Our approach is more generic than previous approaches; (2) In the catching phase a sliding surface is designed in the phase plane based on the zero torque trajectories, and a 2nd order sliding mode controller is implemented to drive the pendulum moving along the sliding surface, which improves the robustness compared to the previous method in which the controller switches to stabilization mode when it reaches a pre-defined region. (3) In the stabilization phase a 2nd order sliding mode integral controller is used to solve the balancing problem, which has the potential to stabilize the pendulum in a larger angular region when compared to the previous linearization methods. At last we combine the 3 phases together in a combined strategy. Both simulation results and experimental results are shown. The control unit is National Instruments CompactRIO 9014 with NI 9505 module for module driving and NI 9411 module for encoding. The Reaction Wheel Pendulum is built by Quanser Consulting Inc. and placed in UT’s Advanced Mechatronics Lab. / text

Among the various challenges involved in the development of CubeSats lies the attitude determination and control of the satellite. The importance of a properly functioning attitude determination and control system (ADCS) on any satellite is vital to the satisfaction of its mission objectives. Due to this importance, three-axis attitude control simulators are commonly used to test and validate spacecraft attitude control systems before flight. However, these systems are generally too large to successfully test the attitude control systems on-board CubeSat-class satellites. Due to their low cost and rapid development time, CubeSats have become an increasingly popular platform used in the study of space science and engineering research. As an increasing number of universities and industries take part in this new approach to small-satellite development, the demand to properly test, verify, and validate their attitude control systems will continue to increase. An approach to CubeSat attitude determination and control simulation is in development at the Virginia Tech Space Systems Simulation Laboratory. The final test setup will consist of an air bearing platform placed inside a square Helmholtz cage. The Helmholtz cage will provide an adjustable magnetic field to simulate that of a low earth orbit (LEO), and the spherical air bearing will simulate the frictionless environment of space. In conjunction, the two simulators will provide an inexpensive and adjustable system for testing any current, and future, CubeSat ADCS prior to flight. Using commercial off the shelf (COTS) components, the Virginia Tech CubeSat Attitude Control Simulator (CSACS), which is a low cost, lightweight air bearing testing platform, will be coupled with a 1.5-m-long square Helmholtz cage design in order to provide a simulated LEO environment for CubeSat ADCS validation. / Master of Science / The attitude determination and control subsystem is a vital component of a spacecraft. This subsystem provides the pointing accuracy and stabilization which allows a spacecraft to successfully perform its mission objectives. The cost and size of spacecraft are dependent on their specific applications; where some may fit in the palm of your hand, others may be the size of a school bus. However, no matter the size, all spacecraft contain some form of onboard attitude determination and control. This leads us to the introduction of a miniaturized class of spacecraft known as CubeSats. Their modular 10×10×10 cm cube structural design allows for both low cost and rapid development time, making CubeSats widely used for space science and engineering research in university settings. While CubeSats provide a low cost alternative to perform local, real-time measurements in orbit, it is still very important to validate the attitude determination and control subsystem before flight to minimize any risk of failure in orbit. Thus, the contents of this thesis will focus on the development, design, and testing of two separate spacecraft attitude determination and control simulation systems used to create an on-orbit environment in a laboratory setting in order to properly validate university-built CubeSats prior to flight.

In this work, a unicycle system with reaction wheel is presented, considering the construction, the modeling, the design and test of the controllers. Firstly, a mechanical model considering a tridimensional computer aided design (3D CAD) is built in order to assist the construction and, after that, the modeling using the Lagrange method. In this work, linear controllers are designed and, therefore, the linearization of the system is done by the Jacobian, that is, assuming small variations around the equilibrium point. In this situation, there is no coupling between the pitch and the roll angles, thus resembling two inverted pendulums. The prototype is constructed by attaching the electronic components, the battery, the wheels and the motors to a body, to make it fully autonomous. The positioning of the parts has to balanced in order to maintain the position of the center of mass along the vertical and horizontal axis of symmetry. Then, a linear control project is done to stabilize the plant using two techniques that are validated considering simulations of the nonlinear coupled system. Then, the techniques were tested in the built prototype. The first one consists of the optimal LQR control that, although it worked, presented some problems due to parametric uncertainties. Therefore, the H2 control is used via LMI in such a way that the project becomes similar to the LQR, but in this way it is possible to insert parametric uncertainties and find a controller with some degree of robustness to them. / Neste trabalho, é apresentado um sistema de um monociclo com roda de reação, mostrando desde a construção, passando pela modelagem até o projeto e teste dos controladores. Primeiramente, é feito o projeto mecânico por meio de um desenho assistido por computador tridimensional (3D CAD), para auxiliar a construção e, em seguida, a modelagem por meio do método de Lagrange. Naturalmente, o sistema é não linear e os ângulos de arfagem e rolamento são acoplados. Neste trabalho, controladores lineares são projetados e, portanto, a linearização do sistema é feita pelo Jacobiano, ou seja, assumindo pequenas variações em torno do ponto de equilíbrio. Nesta situação, o modelo desacopla os ângulos de arfagem e rolamento. O protótipo é construído fixando os componentes eletrônicos, a bateria, as rodas e os motores a um corpo, de forma a ser totalmente autônomo. O posicionamento das peças precisa ser equilibrado, de forma a manter a posição do centro de massa ao longo dos eixos de simetria vertical e horizontal. Em seguida, é feito um projeto de controle linear para estabilização da planta usando duas técnicas que são validadas via simulações do sistema não linear acoplado. Depois, as técnicas são testadas no protótipo construído. A primeira consiste do controle ótimo LQR que, apesar de ter funcionado, apresentou alguns problemas devidos a incertezas paramétricas. Logo, é usado o controle H2 via LMI, de tal forma que o projeto equivalha ao LQR, mas desta forma é possível inserir incertezas paramétricas e achar um controlador com algum grau de robustez a elas.

Applied System Identification for a Four Wheel Reaction Wheel Platform By Seth Franklyn Silva At the California Polytechnic State University, San Luis Obispo there is a four-wheel reaction wheel pyramidal simulator platform supported by an air-bearing. This simulator has the current capability to measure the wheel speeds and angular velocity of the platform, and with these measurements, the system identification process was used to obtain the mass properties of this simulator. A handling algorithm was developed to allow wireless data acquisition and command to the spacecraft simulator from a “ground” computer allowing the simulator to be free of induced torques due to wiring. The system identification algorithm using a least squares estimation scheme was tested on this simulator and compared to theoretical analysis. The resultant principle inertia about the z-axis from the experimental analysis was 3.5 percent off the theoretical, while the other inertias had an error of up to 187 percent. The error is explained as noise attributed to noise in the measurement, averaging inconsistencies, low bandwidth, and derivation of accelerations from measured data.

The Generic Nanosatellite Bus (GNB) is a spacecraft platform designed to accommodate the integration of diverse payloads in a common housing of supporting components. The development of the GNB at the Space Flight Laboratory (SFL) under the Canadian Advanced Nanospace eXperiment (CanX) program provides accelerated access to space while reducing non-recurring engineering (NRE) costs. The work presented herein details the development of the attitude determination and control subsystem (ADCS) of the GNB. Specific work on magnetorquer coil assembly, integration, and testing (AIT) and reaction wheel testing is included. The embedded software development and unit-level testing of the GNB sun sensors are discussed. The characterization of the AeroAstro star tracker is also a major focus, with procedures and results presented here. Hardware models were developed and incorporated into SFL's in-house high-fidelity attitude dynamics and control simulation environment. This work focuses on specific contributions to the CanX-3, CanX-4&5, and AISSat-1 nanosatellite missions.

The Generic Nanosatellite Bus (GNB) is a spacecraft platform designed to accommodate the integration of diverse payloads in a common housing of supporting components. The development of the GNB at the Space Flight Laboratory (SFL) under the Canadian Advanced Nanospace eXperiment (CanX) program provides accelerated access to space while reducing non-recurring engineering (NRE) costs. The work presented herein details the development of the attitude determination and control subsystem (ADCS) of the GNB. Specific work on magnetorquer coil assembly, integration, and testing (AIT) and reaction wheel testing is included. The embedded software development and unit-level testing of the GNB sun sensors are discussed. The characterization of the AeroAstro star tracker is also a major focus, with procedures and results presented here. Hardware models were developed and incorporated into SFL's in-house high-fidelity attitude dynamics and control simulation environment. This work focuses on specific contributions to the CanX-3, CanX-4&5, and AISSat-1 nanosatellite missions.

In this research, nonlinear attitude controllers are designed for a low earth orbit satellite intended to be used in observatory missions. The attitude is represented by the Modified Rodriguez Parameters (MRP) which is a minimal representation providing a fully invertible kinematics. As a difference from the classical satellite models existent in the literature, the model of this work incorporates the dynamics of the reaction wheel (actuator) including a brushless dc motor which is armature controlled. The total model has four group of state vectors which are the attitude, body rates, actuator torque and velocity. The main control approach of this research is developed by utilizing integrator back - stepping which provides a recursive stabilization methodology to the designer. For performance comparison, a second controller based on input output feedback linearization (IOFL) is presented. Both of the approaches produce a torque demand law and this is used for generating a desired reaction wheel velocity command. A reaction wheel controller uses the motor as the actuator and produces the necessary amount of the torque according to the desired wheel velocity command. In addition for the back - stepping based approach, a stability analysis against the external disturbance torques is also provided. Simulations are presented for validating the performance and robustness of the proposed controllers.

In this work, a unicycle system with reaction wheel is presented, considering the construction, the modeling, the design and test of the controllers. Firstly, a mechanical model considering a tridimensional computer aided design (3D CAD) is built in order to assist the construction and, after that, the modeling using the Lagrange method. In this work, linear controllers are designed and, therefore, the linearization of the system is done by the Jacobian, that is, assuming small variations around the equilibrium point. In this situation, there is no coupling between the pitch and the roll angles, thus resembling two inverted pendulums. The prototype is constructed by attaching the electronic components, the battery, the wheels and the motors to a body, to make it fully autonomous. The positioning of the parts has to balanced in order to maintain the position of the center of mass along the vertical and horizontal axis of symmetry. Then, a linear control project is done to stabilize the plant using two techniques that are validated considering simulations of the nonlinear coupled system. Then, the techniques were tested in the built prototype. The first one consists of the optimal LQR control that, although it worked, presented some problems due to parametric uncertainties. Therefore, the H2 control is used via LMI in such a way that the project becomes similar to the LQR, but in this way it is possible to insert parametric uncertainties and find a controller with some degree of robustness to them. / Neste trabalho, é apresentado um sistema de um monociclo com roda de reação, mostrando desde a construção, passando pela modelagem até o projeto e teste dos controladores. Primeiramente, é feito o projeto mecânico por meio de um desenho assistido por computador tridimensional (3D CAD), para auxiliar a construção e, em seguida, a modelagem por meio do método de Lagrange. Naturalmente, o sistema é não linear e os ângulos de arfagem e rolamento são acoplados. Neste trabalho, controladores lineares são projetados e, portanto, a linearização do sistema é feita pelo Jacobiano, ou seja, assumindo pequenas variações em torno do ponto de equilíbrio. Nesta situação, o modelo desacopla os ângulos de arfagem e rolamento. O protótipo é construído fixando os componentes eletrônicos, a bateria, as rodas e os motores a um corpo, de forma a ser totalmente autônomo. O posicionamento das peças precisa ser equilibrado, de forma a manter a posição do centro de massa ao longo dos eixos de simetria vertical e horizontal. Em seguida, é feito um projeto de controle linear para estabilização da planta usando duas técnicas que são validadas via simulações do sistema não linear acoplado. Depois, as técnicas são testadas no protótipo construído. A primeira consiste do controle ótimo LQR que, apesar de ter funcionado, apresentou alguns problemas devidos a incertezas paramétricas. Logo, é usado o controle H2 via LMI, de tal forma que o projeto equivalha ao LQR, mas desta forma é possível inserir incertezas paramétricas e achar um controlador com algum grau de robustez a elas.

The Pyramidal Reaction Wheel Platform, or PRWP, is used to simulate three-axis controls in a torque free space-like environment. The primary purpose of the system will be to evaluate the effects of conjoining sensors to maximize pointing accuracy. Furthermore, the system will incorporate a star tracker in conjunction with a Simulated Star Field (SSF) to better estimate the PRWP orientation. For the sake of this document, however, the goal is to implement a gyroscope, wheel rate sensors, and a make-shift accelerometer—to the PRWP—and integrate a controls algorithm such that three-axis controls are achieved for the PRWP. Three sensors were either better integrated into the system or added altogether. Tachometers were created as a form of hardware circuitry to measure each wheel rate with an accuracy of approximately 2.5 Hz (nearly 15 radians per second). The TAC board circuitry converted each motors encoder output into a speed by use of a frequency to voltage converter. Additionally, although three gyroscopes had been implemented previously, the system was better incorporated into the model such that it was directly transformed via a ROBOSTIX ADC converter before being relayed to SIMULINK via a Bluetooth link. The MEMS gyroscopes allowed for very accurate rate measurements—with a minimum resolution of approximately 0.25 radians per second. Finally, a makeshift accelerometer was incorporated into the system for the purpose of system identification. The accelerometer was incorporated into the system by utilizing a discrete time derivative of the gyroscope readings. However, thankfully a system of two accelerometers can be later utilized to achieve an accuracy of approximately 6 degrees per second-second in the x-axis and 2-3 degrees per second-second in the y- and z-axes. A controls test was performed where the starting location was qo=[0, 0, sqrt(2)/2, sqrt(2)/2] and the target location was qc=[0, 0, 0, 1]. At 80 seconds, the pointing accuracy was 70 degrees around the target and the system was unable to settle during the 80 second trial. The inaccuracy was because of the low frequency of operation of the system—1 Hz. Additionally, the platform reacts slowly to sensor readings and commands. The coupling of these issues causes the pointing accuracy to high. Furthermore, through experimental testing, the maximum wheel rate was found to be approximately 6400 RPM at a duty cycle of 50% at an 8000Hz PWM application due to the Pololu MD01B design limitations: low voltage range (up to 16V), low limit current limiter (5A), and high susceptibility to overheating for large currents.

Control theory can be used to make an unstable system stable. This thesis seeks to do this, where the system is a two DOF inverted pendulum with reaction wheels for stabilisation. The thesis also seeks to answer what is most important for making it stabilize for a longer period of time. It was decided that a state space controller was to be used with various sensors measuring the states. To be able to design a functioning demonstrator, a mathematical model of the system dynamics was developed. In the end the demonstrator proved to function as desired, being able to balance indefinitely. It was found that it is absolutely necessary to either give the controller a perfect set point or to implement an automatic set point. / Reglerteknik kan användas för att göra ostabila system stabila. Målet med detta projekt var att göra detta med ett system i form av en inverterad pendel med två frihetsgrader som balanseras med hjälp av två svänghjul. Projektet söker att besvara frågan om vad som är de viktigaste faktorerna för att få systemet att vara stabilt över en längre tid. En tillståndsåterkoppling användes som regulator vilket innebar att flera olika sensorer behövdes för att mäta de olika tillstånden. För att kunna konstruera en fungerande prototyp utvecklades en matematisk modell av systemet vilken användes för simulering av systemet. Till slut konstruerades en fungerade prototyp som till synes kunde balansera över oöverskådlig tid. En av de faktorer som visade sig påverka huruvida systemet uppnår stabilitet över längre tid var hur bra referenspunkt som gavs till regulatorn, det vill säga det tillstånd som regulatorn reglerar systemet mot. Det visade sig vara möjligt att implementera en självjusterande referenspunkt som gjorde systemet stabilt över tid.