### Abstract

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.

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.

Original language | English |
---|---|

Pages (from-to) | 997-1006 |

Number of pages | 10 |

Journal | Acta Astronautica |

Volume | 69 |

Issue number | 11-12 |

Publication status | Published - 3 Aug 2011 |

### ASJC Scopus subject areas

- Aerospace Engineering
- Control and Systems Engineering

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## Cite this

Horri, N., Palmer, P., & Roberts, M. (2011). Design and validation of inverse optimisation software for the attitude control of microsatellites.

*Acta Astronautica*,*69*(11-12), 997-1006.