Attitude Control Subsystem Design of the Stable and Highly Accurate Pointing Earth-imager A MSc Thesis By David Ju in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering at the Delft University of Technology Department of Space Engineering 5th October 2017 Supervisor Dr.ir. J.M. Kuiper Committee Members Dr. A. Cervone ir. B.C. Root Abbreviations ACS Attitude Control Subsystem ADCS Attitude Determination and Control Subsystem ARE Algebraic Ricatti Equation ATS Attitude Thruster Subsystem CMG Control Moment Gyro ConOps Concept of Operations COTS Commercial off the shelf EO Earth Observation FMS1 Full Major Spinup FMS2 Full Minor Spinup FOV Field of View IAGA International Association of Geomagnetism and Aeronomy IFOV Instantaneous Field of View IGRF12 International Geomagnetic Reference Field 12th generation LEO Low Earth Orbit LQR Linear Quadratic Regulator MEMS microelectromechanical system MSAFE Marshall Solar Activity Future Estimates (Model) MSFC Marshall Space Flight Center MT Magnetorquer MTF Modulation Transfer Function MW Momentum Wheel MWTS Momentum Wheel Torquing Subsystem NASA National Aeronautics and Space Administration NRLMSISE00 Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar Exosphere (2001 Model) PPL Precession Phase Lock PS Partial Spinup RW Reaction Wheel SHAPE Stable and Highly Accurate Pointing Earth-imager SMC Sliding Mode Control SMCS Sliding Mode Control Spinup SSO Sun Synchronous Orbit 2 TBD To Be Determined UTC Coordinated Universal Time VLEO Very Low Earth Orbit Nomenclature η Nutation Angle [deg] λ Longitude [deg] µ Pointing Error [rad] −7 -1 µ0 Vacuum Magnetic Permeability [4 π · 10 T m A ] 3 -2 µE Gravitational Parameter of Earth [398 600 km s ] ! Angular Body Rate Column Vector [rad s-1] Ωp Precession Frequency [rad/s] -1 !s Relative Rotor Angular Velocity Around the Spin Axis [rad s ] φ Latitude [deg] ρ Total Air Mass Density [kg m-3] -3 ρm Material Density [kg m ] τ External Torque [Nm] ξ Damper Displacement [m] A Wetted Surface Area [m2] a Semi-major Axis [km] B Magnetic Flux Density [T] b Initial Damper Mass Location to Center of Mass Column Vector [m] -1 cd Damping Coefficient [kg s m ] CD Drag Coefficient [-] FT Thrust [N] ga Spinup Torque [Nm] h Altitude [km] H Angular Momentum Column Vector [N m s] Hs Rotor Angular Momentum [N m s] I Mass Moment of Inertia Matrix [kg m2] 2 Is Rotor Moment of Inertia Around the Spin Axis [kg m ] -1 kd Spring Stiffness [kg m ] 3 m Mass [kg] 2 MA Dipole Moment Vector of the Magnetorquers [A m ] 22 2 ME Earth’s Magnetic Moment Vector [8 · 10 A m ] 2 MM Spacecraft Magnetic Moment Vector [A m ] md Damper Mass [kg] n Mean Motion [rad s-1] n Spin Axis Column Vector [-] p Linear Momentum Vector [kg m s-1] -1 pn Linear Momentum of Damper Mass [kg m s ] T Rotational Kinetic Energy [J] tm Maintenance Operation Time [s] tn Nominal Operation Time [s] 4 Abstract As technology improves, increasingly higher resolution payload can be achieved using Cubesats for Earth observation. The diffraction limit prevents the resolution to up to a few meters for these missions and are confined to Very Low Earth Orbits (VLEO). At these altitudes, strong disturbances act on the system, limiting its lifetime and the pointing capabilities of CubeSats. As a solution, the Department of Space Engineering at the Delft University of Technology has proposed a 6 unit CubeSat named the Stable and Highly Accurate Pointing Earth-imager (SHAPE) orbiting at a Sun synchronous VLEO which uses a momentum wheel to passively stabilize the system against the external environment within a competitive cost of less than 500 000 e. By utilizing the dual-spin stabilization concept, composed of a stable platform and a spinning rotor, it is expected to perform pointing missions of less than 1 degree. In this thesis, the SHAPE concept has been revisited and further developed based on the work of Kuiper and Dolkens to conduct whether these types of missions are feasible within the aspect of the Attitude Determination and Control Subsystem (ADCS). This thesis covers the base of this subsystem approached from a top-down methodology; designed from the final nominal mission mode to the detumbling mode on a system level. The ADCS design will consist of a momentum wheel which has been determined to have an angular momentum of 1 Nms. This value is based on a prediction of the worst-case atmospheric density of the next solar cycle. The design point, at which the momentum wheel has been sized, has been taken at 90% of SHAPE’s lifetime after several design iterations. Hereby, the last 10% of the mission has been partially forfeited with degraded performances due to the exponential increase in disturbances acting on the spacecraft at lower altitudes. As therefore, the mass and size of the momentum wheel has been reduced with 41% and 20%, respectively. To re-align the angular momentum vector within the 1 degree pointing requirement, a set of magnetorquers with a dipole moment of 0.5 Am2 has been chosen due to their low power consumption, mass, cost, and high reliability while capable of producing sufficient torque. Also, a damper is to be integrated as it provides the system asymptotic reduction of the transverse momenta, thus increasing the image quality without expenditure of additional power. To reach the nominal mission observation state, several momentum wheel spinup strategies have been investigated. Based on a trade-off between three spinup concepts, it was concluded that the major axis spinup is most suited. This type is initiated after the spacecraft as a whole has attained an angular momentum equivalent to that of the desired end value of the momentum wheel. Then, a constant rotor torque is applied, providing a momentum transfer from the platform to the rotor. The disadvantage of this spinup procedure is that the system’s solar panels are aligned parallel to the orbital plane, meaning that power cannot be generated and batteries are required during the spinup. Despite this, it was found that after completing the spinup, the transverse angular momenta was minimized to marginal values in contrast to the other spins. The inclusion of the passive damper during the major axis spin further improves the ability of reducing the transverse momentum as the damper’s dissipative energy property adds an asymptotic attraction at the point of lowest energy, located at the spin axis near the end of the spinup. The all-spun state is achieved using a set of thrusters. This choice was taken as the magnetorquers was found not to deliver sufficient torque. From the detumbling analysis, it was concluded that the magnetorquers are able to reduce the tumbling rates with magnitudes of up to 35 deg/s to mean motion values in less than an orbit using a static gain B-dot controller. Imperfections in the momentum wheel can cause static and dynamic imbalance, imparting internal disturbances to the system which affects the image quality detrimentally. Therefore, isolators are to be integrated within the momentum wheel suspension subsystem. If these disturbances can be negated using isolators, it can be expected that the pointing error will stay within one degree and attitude stability can be achieved at least until the design altitude of 280 km. However, the analysis and design of the isolators have yet to be done and thus the attainability of the pointing and image quality requirements are still inconclusive. 5 6 "Life is the sum of all your choices." - Albert Camus 7 8 Preface From my youth, I was always fascinated in rockets, planets and the universe (and also insects for which my curiosity to it has vanished). Pursuing science was very obvious. The interest of space and pursue to it were not during my lifetime. At my final years of high school, my carrier decision had to be made and was divided into either medicine or aerospace engineering; to help people or go into the direction of my own interest. This decision was tough, but I decided to pursue in aerospace engineering at Delft University of Technology mainly as a challenge. Halfway though my bachelor studies, aerospace engineering had not been motivating for me and pursuing this seemed to have been disappointing. Doubt was in my mind. This changed at the design synthesis exercise. Focusing more on the space and especially on the attitude control system of the spacecraft has awoken my fascination in space and has enlightened me to further pursue to do my master’s degree in space engineering. To keep thinking about what to do and what would have been if I have chosen a different path is a thought of futility as life is continuous and flowing in a single direction. Or as Albert Camus, a philosopher of the Absurd, has said; "You will never be happy if you continue to search for what happiness consists of. You will never live if you are looking for the meaning of life." I would like to thank my supervisor Hans Kuiper for the subject of SHAPE and his pragmatic approach towards engineering. This subject has greatly introduced me to spinning spacecraft (which I thought to be obsolete for satellites) and its intriguing complex rotational motions. Furthermore, I am especially grateful for my parents and brother for supporting me throughout my academic life with their love for which I dedicate this thesis to. 9 Contents 1 Introduction 17 2 System Objective 19 2.1 Case Study . 19 2.2 System Requirements . 20 2.3 Control Modes . 21 2.3.1 Control Mode Requirements . 22 2.3.2 Modulation Transfer Function Requirement . 24 2.4 Design Methodology .