Fig. 8 - Spin velocity evolution for the predictive algorithm. Initial condition =5º,
![](data:image/png;base64,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)
.
Desired reference =0º,
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.
Conclusions and Future Work
This article presented the work carried out to date under the ConSat project, in particular the implementation of an ADCS simulator and the development of an innovative attitude stabilisation and spin control algorithm.
It was shown that this algorithm is asymptotically stable. Simulation results
revealed good performance, when compared with the algorithms proposed in the literature. For restricted actuators the low computational demands suggest a possible implementation for the on board available computer resources. The reduced computational needs of the algorithm when used with restricted actuators suggest its use also with unrestricted actuators. Guaranteeing that the available set of control magnetic moments is perpendicular to the geomagnetic field can reduce the power needs, which is a critical factor for small satellites.
At present the attitude determination block of the
ADCS loop is being implemented, enabling the further testing of the control algorithms mentioned in section 4 as well as of different or new algorithms. This testing may lead to an improved ADC algorithm for PoSAT-1 and to further attitude control results for micro satellites. The same path used to attain an improved controller for PoSAT-1 can then be followed in the future with other micro and mini satellites.
Preliminary contacts have been made for upgrading the ADC software of PoSAT-1.
Acknowledgements
The ESF COSY Programme supported some of the work presented in this article. The authors would also like to acknowledge the support of INETI and Marconi.
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