A B-Dot Acquisition Controller for the RADARSAT Spacecraft

B-Dot is an extremely simple control law sometimes used for despinning satellites. It relies on magnetic coils or torque rods as control actuators. The control law is based on the measurement of the rate of change of body-fixed magnetometer signals. Using only a magnetometer and a magnetic moment generator, the B-Dot controller despins the spacecraft relative to the Earth's magnetic field vector. When the spacecraft carries a constant speed momentum wheel, B-Dot control will precess the wheel spin axis to the orbit normal. The Canadian Space Agency's RADARSAT spacecraft is an Earth pointing, momentum bias system in a sun synchronous, dawn/dusk orbit. Its uses a passive Safehold Mode, relying on the momentum bias to maintain the spacecraft in a power positive state. This spacecraft presents an ideal opportunity for using B-Dot as an Sun Acquisition controller. It is an active controller, but it requires only magnetometers, magnetic torquers, and a momentum wheel, and the control law is very simple. This paper consists of two sections. The first presents a brief primer concerning a variety of magnetic controllers. The second section documents analysis and simulation results for the performance of the RADARSAT system using a B-Dot sun acquisition controller. Introduction We will be discussing an attitude control concept which has been frequently applied to low Earth orbit spacecraft, usually for despinning or unloading unwanted spacecraft angular momentum. A key ingredient in the B-Dot controller is the rate of change of magnetic field vector components as measured by on-board, body-fixed sensors called magnetometers. "B" is commonly used to denote the Earth's magnetic field, and the associated rate of change dB//dt, is often written B. Thus, the term "B-Dot." The actuators used in such systems are magnetic coils or torque rods. Both types of actuators produce magnetic moments which interact with the Earth's magnetic field to generate external torques on the spacecraft. The effect is calculated by the expression T = M x B. In SI units, the torque, T, in N-m equals the cross product of the magnetic moment, I_4, in amp-m 2 with the magnetic field, B, in tesla. With air core magnetic coils, the magnetic moment is simply the current through the coil, measured in amperes, times the area of the coil in m 2 times the number of loops in the coil. Torque rods, on the other hand, are usually long and slender, with many turns of wire wound on a cylindrical rod made of highly permeable material. The magnetic properties of the solid core dramatically amplify the magnetic moment produced by the current loops at the expense of additional weight. Section 1: A Brief Survey of Magnetic Controllers. 1.1 B-Dot Control In general, B-Dot control laws command, on a per-axis basis, a magnetic moment whose sign is opposite to that of the rate of change of the magnetic field along that axis. 1.1.1 B-Dot Proportional Control For a typical spacecraft axis, we set M x = -k B x for a magnetometer and a torquer aligned with the X-axis of the spacecraft, where k is a positive constant, M x is the commanded dipole for the X-axis torquer, and B x is the component of the Earth's magnetic field along the X-axis.