Torque equilibrium attitudes for the Space Station
All spacecraft orbiting in a low earth orbit (LEO) experience external torques due to environmental effects. Examples of these torques include those induced by aerodynamic, gravity-gradient, and solar forces. It is the gravity-gradient and aerodynamic torques that produce the greatest disturbances to the attitude of a spacecraft in LEO, and large asymmetric spacecraft, such as the space station, are affected to a greater degree because the magnitude of the torques will, in general, be larger in proportion to the moments of inertia. If left unchecked, these torques would cause the attitude of the space station to oscillate in a complex manner and the resulting motion would destroy the micro-gravity environment as well as prohibit the orbiter from docking. The application of control torques will maintain the proper attitude, but the controllers have limited momentum capacity. When any controller reaches its limit, propellant must then be used while the device is reset to a zero or negatively-biased momentum state. Consequently, the rate at which momentum is accumulated is a significant factor in the amount of propellant used and the frequency of resupply necessary to operate the station. A torque profile in which the area curve for a positive torque is not equal to the area under the curve for a negative torque is 'biased,' and the consequent momentum build-up about that axis is defined as secular momentum because it continues to grow with time. Conversely, when the areas are equal, the momentum is cyclic and bounded. A Torque Equilibrium Attitude (TEA) is thus defined as an attitude at which the external torques 'balance' each other as much as possible, and which will result in lower momentum growth in the controllers. Ideally, the positive and negative external moments experienced by a spacecraft at the TEA would exactly cancel each other out and small cyclic control torques would be required only for precise attitude control. Over time, the only momentum build-up in the controllers would be due to electro-mechanical losses within the device. However, the atmospheric torques are proportional to the density of the atmosphere and the density varies with the orbital position, time of day, time of year, and the solar cycle. In addition, there are unmodeled disturbances and uncertainties in the mass and inertias. Therefore, there is no constant attitude that will completely balance the environmental torques and the dynamic TEA cannot be solved in closed form. The objective of this research was to determine a method to calculate a dynamic TEA such that the rate of momentum build-up in the controllers would be minimized and to implement this method in the MATRIX(x) simulation software by Integrated Systems, Inc.