Browsing by Subject "Formation Flying"
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Item Dynamics and real-time optimal control of satellite attitude and satellite formation systems(Texas A&M University, 2006-10-30) Yan, HuiIn this dissertation the solutions of the dynamics and real-time optimal control of magnetic attitude control and formation flying systems are presented. In magnetic attitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with a pseudospectral algorithm are examined. The time-optimal magnetic control is bang-bang and the optimal slew time is about 232.7 seconds. The start time occurs when the maneuver is symmetric about the maximum field strength. For real-time computations, all the tested samples converge to optimal solutions or feasible solutions. We find the average computation time is about 0.45 seconds with the warm start and 19 seconds with the cold start, which is a great potential for real-time computations. Three-axis magnetic attitude stabilization is achieved by using a pseudospectral control law via the receding horizon control for satellites in eccentric low Earth orbits. The solutions from the pseudospectral control law are in excellent agreement with those obtained from the Riccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitude motion is in the steady state. Approximate models are often used for the study of relative motion of formation flying satellites. A modeling error index is introduced for evaluating and comparing the accuracy of various theories of the relative motion of satellites in order to determine the effect of modeling errors on the various theories. The numerical results show the sequence of the index from high to low should be Hill's equation, non- J2, small eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach and the Yan-Alfriend nonlinear method having the lowest index and equivalent performance. A higher order state transition matrix is developed using unit sphere approach in the mean elements space. Based on the state transition matrix analytical control laws for formation flying maintenance and reconfiguration are proposed using low-thrust and impulsive scheme. The control laws are easily derived with high accuracy. Numerical solutions show the control law works well in real-time computations.Item Modelling and control of satellite formations(Texas A&M University, 2004-09-30) Vaddi, Veera Venkata Sesha SaiFormation 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.Item Satellite Formation Design in Orbits of High Eccentricity for Missions with Performance Criteria Specified over a Region of Interest(2012-10-15) Roscoe, ChristopherSeveral methods are presented for the design of satellite formations for science missions in high-eccentricity reference orbits with quantifiable performance criteria specified throughout only a portion the orbit, called the Region of Interest (RoI). A modified form of the traditional average along-track drift minimization condition is introduced to account for the fact that performance criteria are only specified within the RoI, and a robust formation design algorithm (FDA) is defined to improve performance in the presence of formation initialization errors. Initial differential mean orbital elements are taken as the design variables and the Gim-Alfriend state transition matrix (G-A STM) is used for relative motion propagation. Using mean elements and the G-A STM allows for explicit inclusion of J2 perturbation effects in the design process. The methods are applied to the complete formation design problem of the NASA Magnetospheric Multiscale (MMS) mission and results are verified using the NASA General Mission Analysis Tool (GMAT). Since satellite formations in high-eccentricity orbits will spend long times at high altitude, third-body perturbations are an important design consideration as well. A detailed analytical analysis of third-body perturbation effects on satellite formations is also performed and averaged dynamics are derived for the particular case of the lunar perturbation. Numerical results of the lunar perturbation analysis are obtained for the example application of the MMS mission and verified in GMAT.