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Attitude Control of the CubeSail Solar Sailing Spacecraft Victoria Coverstone, Andy Pukniel University of Illinois at Urbana-Champaign Rod Burton, Dave Carroll CU Aerospace ISSS 2010 New York

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CubeSail Mission Overview Low cost solar sailing demonstration. Goal is to deploy 20 m 2 (80mm x 250m) of film between 2 nanosatellites. Deployment is to occur into a sun-synchronous terminator orbit above 800km altitude along the local vertical. Gravity-gradient aids in deployment and provides sail stiffening. Secondary payload opportunities are used to reduce cost. Validation of the dynamical and performance models and subsequent advancement of the TRL will likely lead to secondary demonstration followed by possible full-scale UltraSail experiment.

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Research Motivation Consider two reasons for slow emergence of solar sailing technology: Challenges associated with stowage and deployment of large sails and stiffening structure (booms, masts, stays, etc.) High risk combined with high launch costs associated with investment in a poorly-characterized technology.

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Technical Approach Stowage and deployment based on the UltraSail concept Sail material is stored in long strips wound onto motorized reels 3-axis stabilized satellite on each blade tip control the deployment and attitude Risk and cost reduction is achieved through IlliniSat-2 bus and secondary launch opportunities IliniSat-2 bus provides: Active 3-axis ACS achieved via magnetic torque actuation Deployable antenna and associated communication hardware C&DH capable of supporting wide range of payloads Power generation and management system Complete bus fits into 10x10x10cm volume IlliniSat-2 Bus Payload

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55 Operational Sequence

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Initial Detumbling and Stabilization Initial detumbling and stabilization is posed as a Linear Quadratic problem. Two operational modes: detumbling and tracking. Cost function depends on the mode and is either: the time to reduce angular body rates on all 3 axis below a threshold of 0.1 º/sec or the accumulated Euler angle error for values above 5º (figure below) Desired performance is achieved with GA-selected Q and R matrices.

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Attitude Control Simulator Matlab-based simulator is used to test performance. Satellite DynamicsLQRMagnetic Torquers + T GG T AD Duty Cycle Direction Torque Typical single run Euler angles and rates are shown below.

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Robustness Testing Results The attitude control simulator is run 1000 times with randomly varying ICs to ensure the selected penalty matrices are robust and the spacecraft can stabilize from any attitude and worst predicted rates of 5º/sec on all axis.

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Modeling of External Forces Solar Radiation Pressure force model includes effects of: Reflection, absorption, and re-radiation The non-ideal parameters are given as: Aerodynamic Drag force is calculated using the method of accommodation coefficients and includes variations due to: Angle of incidence of incoming molecules Major atmospheric constituents at altitude Surface coating material and surface temperature Semi-diffuse reflection model

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Aerodynamic Drag Results The Aerodynamic Drag force is computed for an undeformed sail in 2 ways: accommodation coefficient method classical method of constant coefficient of drag, C d, of 2.2 Interestingly, the classical method underestimates the magnitude of the force for all but high angles of incidence. In order to match the force computed using the accommodation coefficient method, C d must be varied between 0.9 and 2.9 in the classical equation.

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Steady-State Shape of the Sail Steady-state deformations of the sail are computed by including forces due to: Solar Radiation Pressure Aerodynamic Drag Gravity-Gradient The sail is assumed to be traveling in a sun-synchronous terminator orbit. Sail is oriented with its edge to the orbital velocity direction. Deviation away from the local vertical is ignored and only out-of-plane deflection is considered. The governing equations can be written as:

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Steady-State Shape of the Sail Deflections due to Solar Radiation Pressure are relatively small. Maximum out-of-plane deflection is approximately 18 m. Final angle away from the local vertical are approximately 15º.

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Out-of-plane deformations along the sail length for varying pitch angles

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Conclusions Optimization of Q and R matrices for the LQR controller with Genetic Algorithms provides good performance, robust results. Classical treatment of Aerodynamic Drag with constant coefficient of drag underestimates the force exerted on the sail. Equivalent coefficient of drag (specific to the CubeSail geometry and deployment orbit) varies between 0.9 and 2.9. Out-of-plane, steady-state sail deformation due to solar radiation pressure are relatively small as compared to the sail length.

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Future Work Steady-state shape of the sail with a linearly-varying pitch (twist) along its length is studied. Non-linear gravity-gradient deployment dynamics in the presence of aerodynamic drag and solar radiation pressure is examined.

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In-plane deformations along the sail length for varying pitch angles

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Tension along the sail length for varying pitch angles

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