Minimum control authority of a system of actuators with applications to Gravity Probe-B

The forcing capabilities of systems composed of many actuators are analyzed in this paper. Multi-actuator systems can generate higher forces in some directions than in others. Techniques are developed to find the force in the weakest direction. This corresponds to the worst case output and is defined as the 'minimum control authority'. The minimum control authority is a function of three things: the actuator configuration, the actuator controller and the way in which the output of the system is limited. The following three output limits are studied: 1) fuel flow rate, 2) power and 3) actuator output. The three corresponding actuator controllers are derived. These controllers generate the desired force while minimizing either fuel flow rate, power or actuator output. It is shown that using the optimal controller can substantially increase the minimum control authority. For example the minimum control authority of a system limited by actuator output can be increased by 40% if the controller minimizes actuator output instead of power. The techniques for calculating the minimum control authority are applied to the Gravity Probe-B spacecraft thruster system. This example shows that the minimum control authority is a useful design tool. It can be used to design the individual actuators, choose an actuator configuration, choose an actuator controller and study redundancy.