Formation flying is a new paradigm in space mission design, aimed at replacing large satellites with multiple small satellites. Some of the proposed benefits of formation flying satellites are: (i) Reduced mission costs and (ii) Multi mission capabilities, achieved through the reconfiguration of formations. This dissertation addresses the problems of initiatialization, maintenance and reconfiguration of satellite formations in Earth orbits. Achieving the objectives of maintenance and reconfiguration, with the least amount of fuel is the key to the success of the mission. Therefore, understanding and utilizing the dynamics of relative motion, is of significant importance. The simplest known model for the relative motion between two satellites is described using the Hill-Clohessy-Wiltshire(HCW) equations. The HCW equations offer periodic solutions that are of particular interest to formation flying. However, these solutions may not be realistic. In this dissertation, bounded relative orbit solutions are obtained, for models, more sophisticated than that given by the HCW equations. The effect of the nonlinear terms, eccentricity of the reference orbit, and the oblate Earth perturbation, are analyzed in this dissertation, as a perturbation to the HCW solutions. A methodology is presented to obtain initial conditions for formation establishment that leads to minimal maintenance effort. A controller is required to stabilize the desired relative orbit solutions in the presence of disturbances and against initial condition errors. The tradeoff between stability and fuel optimality has been analyzed for different controllers. An innovative controller which drives the dynamics of relative motion to control-free natural solutions by matching the periods of the two satellites has been developed under the assumption of spherical Earth. A disturbance accommodating controller which significantly brings down the fuel consumption has been designed and implemented on a full fledged oblate Earth simulation. A formation rotation concept is introduced and implemented to homogenize the fuel consumption among different satellites in a formation. To achieve the various mission objectives it is necessary for a formation to reconfigure itself periodically. An analytical impulsive control scheme has been developed for this purpose. This control scheme has the distinct advantage of not requiring extensive online optimization and the cost incurred compares well with the cost incurred by the optimal schemes.

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<div> <div> <div> <p>A control methodology to design and establish spacecraft formations is presented. The intuitive design of complex spacecraft formation geometry is achieved by utilizing two different sets of relative orbital elements derived from a linearization of the dynamics. These sets provide strong insights into the shape, size, and orientation of the relative trajectory and facilitate the design of relative orbits in addition to relative positions. An artificial potential function (APF) composed of an attractive potential for goal seeking and a repulsive potential for obstacle avoidance is constructed. The derivation of a control law from this APF results in a computationally efficient algorithm able to fully control the relative position and velocity of the spacecraft and therefore to establish spacecraft formations. The autonomous selection of some of the design parameters of the model based on fuel minimization considerations is described. An assessment of the formation establishment accuracy is conducted for different orbital perturbation as well as various degrees of thrust errors and state uncertainties. Then, the performance of the control algorithm is demonstrated with the numerical simulation of four different scenarios. The first scenario is the design and establishment of a 10-spacecraft triangular lattice, followed by the establishment of a 37-spacecraft formation composed of two hexagonal lattices on two different relative planes. The control method is used to illustrate proximity operations with the visual inspection of an on-orbit structure in the third scenario. Finally, a formation composed of four spacecraft arranged in a tetrahedron is presented.<br></p> </div> </div> </div>

The goal of this thesis is to use the Cal Poly Spacecraft Attitude Dynamics Simulator to provide proof of concept of two adaptive control theories developed by former Cal Poly students: Nonlinear Direct Model Reference Adaptive Control and Adaptive Output Feedback Control. The Spacecraft Attitude Dynamics Simulator is a student-built air bearing spacecraft simulator controlled by four reaction wheels in a pyramidal arrangement. Tests were performed to determine the effectiveness of the two adaptive control theories under nominal operating conditions, a “plug-and-play” spacecraft scenario, and under simulated actuator damage. Proof of concept of the adaptive control theories applied to attitude control of a spacecraft is provided. The adaptive control theories are shown to attain similar or improved performance over a Full State Feedback controller. However, the measurement capabilities of the simulator need to be improved before strong comparisons between the adaptive controllers and Full State Feedback can be achieved.

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Most present day spacecrafts have large interconnected solar panels. The dynamic behavior of the spacecraft in orbit can be modeled as a free rigid mass with flexible elements attached to it. The natural frequencies of such spacecrafts with deployed solar panels are very low. The low values of the natural frequencies pose difficulties for maneuvering the spacecraft. The control torque required to maneuver the spacecraft is influenced by the flexibility of the solar arrays. The control torque sets up transient oscillations in the flexible solar panels which in turn induces disturbances in the rigid satellite body and the payload within. Therefore the payload operations can be carried out only after the disturbances die out. For any reduction of the above disturbances it is necessary to understand the dynamic behavior of such systems to an applied torque. The present work first studies the nature of the disturbances. The influence of structural parameters on these disturbances is then investigated. Finally, the use of passive damping treatment using viscoelastic material is investigated for the reduction of the disturbances. In order to understand the nature of vibrations induced in the flexible appendages of a satellite during maneuvers, we model the maneuver loads in terms of applied angular acceleration as well as varying torque. The transient decay of the disturbance of the rigid element is characterized by the dynamic characteristics of the flexible panels or appendages. It is shown that by changing the stiffness of the panel the response of the rigid element can be modified. A simple model consisting of an Euler-Bernoulli beam attached to a free mass is next considered. The influence of various parameters of the EulerBernoulli beam in mitigating vibration and thereby the disturbance in the rigid mass is investigated. As the response of the rigid system mounted with the large flexible panels are influenced by the dynamics of the flexible panels, reduction of these disturbances can be achieved by reducing the vibration in the flexible panels. Therefore application of viscoelastic materials for passive damping treatment is investigated. The loss factor of a structure is significantly improved by using constrained viscoelastic layer damping treatment. However providing a constrained layer damping treatment on the entire structure is very inefficient in terms of the additional mass involved. Therefore damping material is applied at suitable optimal locations. In previous studies reported in literature, modal strain energy distribution in the viscoelastic material as well as the base structure is used as a tool to arrive at the optimum location for the damping treatment. It is shown in this study that such locations selected are not the optimum. A new approach is proposed in this study by which both the above shortcomings are overcome. It is shown that use of a parameter that is the ratio of the strain in the viscoelastic material to the angle of flexure is a more reliable measure in arriving at optimal locations for the application of constrained viscoelastic layers. The method considers the deformations in the viscoelastic material and it is shown that significant values of loss factors are achieved by providing material in a small region alone. We also show that loss factor can be improved by providing damping material near the interface region. The loss factor can be further improved by incorporating spacers by using spacer material having higher extensional modulus. Also shown is the fact that loss factor is unaffected by the shear modulus of the spacer material. Experiments have been conducted to validate these results. In a related study we consider honeycomb type flexible structures since in most of the spacecraft applications honeycomb sandwich constructions are employed. But loss factors of sandwich panels with constrained layer damping treatment are seldom discussed in the literature. Use of viscoelastic layers to improve the loss factors of the honeycomb sandwich beams is explored. The results show that the loss factors are enhanced by increasing the inplane stiffness of the constraining layer. These conclusions too are validated by experimental results. Finally a typical satellite with flexible solar panels is considered, and the use of the viscoelastic material for improving the damping is demonstrated.

The Cal Poly Spacecraft Simulator is currently being developed for future testing and verifying theoretical control applications. This paper details the effort to balance the platform and remove undesired external torque from the system using System Identification technique developed by Patrick Healy. Since the relationship between the input and output of the system is linear, the least square method is proposed to identify the mass properties and location of center of mass of the system. The tests use four sine wave generators that are out of phase with different amplitudes as the inputs to excite various structural modes of the system. The outputs, angular rates of the platform, are measured by the newly implemented LN-200 Inertial Measurement Unit that helps reducing the measurement noise. Two test cases of 90o yaw rotations with the identified inertia were performed and validated against the computer simulation model; and the result shows that the test cases trajectories followed closely with the computer simulation model.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.