# Precision pointing H_{∞} control design for absolute, window-, and stability-time errors

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## Abstract

Achieving precision pointing performance plays a decisive role in future space missions. Pointing performance is specified by a set of requirements consisting of absolute, window- and stability-time errors. The European Cooperation for Space Standardization categorizes this set in the following pointing performance error indices: absolute performance error (APE), mean performance error (MPE), relative performance error (RPE), performance drift error (PDE) and performance reproducibility error (PRE). The analysis of pointing error indices in time-simulations is straightforward as error data time-series can be described by standard statistics. However, for design purposes there exists no method that can directly and systematically handle control loop performance in terms of window- and stability-time pointing error indices. In this article we extend the standard multi-objective *H*_{2}/*H*_{∞} control problem to explicitly take into account requirements on pointing error index performance. The main topic, however, is the derivation of a control design approach that subjects the closed-loop control system to only one matrix criterion, the *H*_{∞}-norm. Therefore an optimization is set up to map pointing error index requirements into closed-loop specifications. The advantage of this approach is that the derived closed-loop specifications serve as indicators for the direct identification of design drivers, limits of performance and eventually systematic design trade-offs. Unlike in multi-objective *H*_{2}/*H*_{∞} control design approaches, this can be done even before controller synthesis, and thus independently of the specified control problem feasibility. Moreover, the derived approach enables control design in the H_{∞} closed-loop shaping framework. Thus, various design objectives including pointing performance and robustness can be treated with one matrix criterion.

### Keywords

Pointing performance Window-time error Stability-time error ECSS Precision pointing*H*

_{inf}-control Closed-loop shaping Multi-objective

*H*

_{2}/

*H*

_{inf}control Mixed

*H*

_{2}/

*H*

_{inf}control

## Notes

### Acknowledgments

The results obtained and presented in this article have been developed under the ESA Network/Partnering Initiative with the title “Precision Pointing Control Design Under Agility Constraints“. Partners are the Institute of Flight Mechanics and Control of Universität Stuttgart, AOCS/GNC and Flight Dynamics Department of Astrium Satellites, Germany, and the Control Systems Division of ESA/ESTEC.

### References

- 1.Winkler, S., Cirillo, F., Ergenzinger, K., Ott, T., Wilhelm, R., Zaunick, E.: High-precision attitude determination and control of the EUCLID spacecraft: challenges and solutions. In: 8th International ESA Conference on Guidance, Navigation and Control Systems, Karlovy Vary (2011)Google Scholar
- 2.Schull, U., Knigge, T.: Geo-Oculus: A Mission for Real-Time Monitoring through High Resolution Imaging from Geostationary Orbit. EUMETSAT Meteorological Satellite Conference, Darmstadt (2008)Google Scholar
- 3.ECSS. “Pointing Performance Standard ECSS-E-ST-60-10C”, ESA-ESTEC Requirements and Standards Division (2008)Google Scholar
- 4.Lucke, R.L., Sirlin, S.W.: San Martin A.M.: New definition of pointing stability: AC and DC effects. J. Astron. Sci.
**40**(4), 557–576 (1992)Google Scholar - 5.Pittelkau, M.E.: Pointing error definitions, metrics, and algorithms. Am. Astron. Soc. AAS
**03–559**, 901 (2003)Google Scholar - 6.Scherer C.W.: Mixed H
_{2}/H_{∞}control. In: Isidori, A. (ed.) Trends in Control: A European Perspective. Springer, Berlin, pp. 173–216 (1995)Google Scholar - 7.Scherer C.W.: An efficient solution to multi-objective control problems with LMI objectives. Syst. Control Lett.
**40**(1), 43–57 (2000)Google Scholar - 8.Wong, E., Breckenridge, W.: An attitude control design for the Cassini spacecraft. In: AIAA Guidance, Navigation and Control Conference, Baltimore (1996)Google Scholar
- 9.Kia, T., Bayard, D.S., Tolivar, F.: A Precision Pointing Control System for the Space Infrared Telescope Facility (SIRTF). Jet Propulsion Laboratory Technical Report, Pasadena (1997)Google Scholar
- 10.Bayard, D.S.: High-precision three-axis pointing and control. Encyclopedia of Aerospace Engineering. Wiley, New York (2010)Google Scholar
- 11.Magarottot, E., et al.:
*H*_{2}/*H*_{∞}Control design: LMI techniques for space applications. In: IEEE International Conference on Control Applications, Trieste (1998)Google Scholar - 12.Frapard, B., Griseri, G., Guyot, P.: Industrial use of
*H*_{∞}optimisation for high performance laser communication pointing system: the SILEX application. Automatisierungstechnik**53**(10) 503–512 (2005)Google Scholar - 13.Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design. Wiley, New York (2005)Google Scholar
- 14.Zhou, K., Doyle, J., Glover, K.: Robust and Optimal Control. Prentice-Hall, Englewood-Cliffs (1996)Google Scholar
- 15.Fichter, W., Schleicher, A., Bennani, S., Wu, S.: Closed-loop performance and limitations of the LISA pathfinder drag-free control system. In: AIAA Guidance Navigation and Control Conference (2007)Google Scholar
- 16.Bayard, D.S.: A state-space approach to computing spacecraft pointing jitter. AIAA J. Guid. Control Dyn.
**27**(3) (2004)Google Scholar - 17.Stein, G., Doyle, J.: Beyond singular values and loop shapes. AIAA J. Guid. Control
**14**(1) (1991)Google Scholar - 18.Boyd, S.P., Barratt, C.H.: Linear Controller Design: Limits of Performance. Prentice-Hall, Englewood-Cliffs (1991)Google Scholar
- 19.ESA Engineering Standardization Board. Pointing Error Engineering Handbook ESSB-HB-E-003, ESA-ESTEC Requirements & Standards Division (2011)Google Scholar
- 20.Ott, T., Benoit, A., Van den Braembussche, P., Fichter, W.: ESA pointing error engineering handbook. In: 8th International ESA Conference on Guidance, Navigation and Control Systems, Karlovy Vary (2011)Google Scholar
- 21.MATLAB
^{®}. Robust Control Toolbox, MathWorks (2011)Google Scholar - 22.Christen, U.: Engineering Aspects of H
_{∞}Control. Swiss Federal Institute of Technology, Zürich (1996)Google Scholar - 23.Bendat, J.S., Piersol, A.G.: Random Data-Analysis and Measurement Procedures, 3rd edn. Wiley, Chichester (2000)Google Scholar
- 24.Ruth, M., Lebsock, K., Dennehy, C.: What’s new is what’s old: use of Bode’s integral theorem (circa 1945) to provide insight for 21st century spacecraft attitude control system design tuning. In: AIAA Guidance, Navigation, and Control Conference (2010)Google Scholar
- 25.Boyd, S.P., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)Google Scholar
- 26.Ott, T.: Robust Precision Pointing Control Design for Satellites with Small-Angle Agility Constraints, PhD Thesis, Institute of Flight Mechanics and Control, University of Stuttgart (to be published)Google Scholar
- 27.MATLAB
^{®}. Optimization Toolbox User’s Guide, MathWorks (2011)Google Scholar - 28.Saage, R., Ross, R., Schleicher, A., Fichter, W.: Controller design method for drag-free systems with micro-propulsion constraints. In: AIAA Guidance Navigation and Control Conference, Toronto (2010)Google Scholar