Design and validation of inverse optimisation software for the attitude control of microsatellites

The capabilities of microsatellite attitude control hardware have considerably evolved
during the last two decades. However, three axis attitude control software is still
predominantly based on the conservative use of standard flight proven PD type
controllers, which are known to be limited in terms of rapidity for a prescribed level
of energy consumption. Microsatellites are therefore typically not as agile as they could
be. This conservatism is due to the complexity of implementing global numerical
optimisation techniques to satellite attitude control. In this paper, we consider the
model of a low earth orbiting microsatellite with a four wheel configuration, where the
speed of one of the wheels is kept constant to provide a momentum bias and guarantee
gyroscopic stiffness to disturbances. A geometric optimal control approach is presented,
which circumvents the tedious tasks of numerically solving online the nonlinear
optimisation problem. The approach is based on the design of suboptimal phase space
trajectories. The phase space trajectory of a standard linear controller, typically a PD
law with gyro-compensation, is used as a benchmark. The proposed inverse optimal
control technique is then used to enforce higher convergence rate constraints than the
benchmark law, without increasing the total energy consumption. The convergence rate
of a Lyapunov function under the effect of the optimal controller outperforms the
convergence rate of the same function under PD control and keeps increasing until a
design settling time limit is reached. Guidelines are given for the tuning of the
controller. The optimal attitude control algorithms are validated on a microsatellite
software simulator in collaboration with the space company Surrey Satellite Technology
Limited (SSTL). The software simulator incorporates a precise model of the effects of
estimation errors, noise, external disturbances, sampling and actuator dynamics. The
software is similar to the flight software of typical Surrey microsatellites. The proposed
techniques are characterised by low implementation complexity because the difficulty
is confined to the theoretical design stage. Settling time is significantly enhanced for the
same level of energy consumed as the PD type law, which was used as a benchmark
without loss of generality.