# ESA GNC Conference Papers Repository

**Title:**

##### Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws

**Authors:**

**Presented at:**

**Full paper:**

**Abstract:**

During the development of a new attitude control system for ambitious satellite missions, the validation & verification phase represents a large part of the process. One difficulty is to detect worst case configurations. In such cases, when applicable, µ-analysis [1] offers a nice additional tool to be used before launching the Monte Carlo simulation campaign, but does not provide any quantification of the probability of occurrence of the identified worst-cases. A control system can then be invalidated on the basis of unlikely events. Probabilistic µ-analysis was introduced in this context 20 years ago to bridge the gap between the two techniques. It has been used for the first time in [2] in the challenging context of validation of launcher thrust vector control systems. But it appeared to be computationally very expensive. At that time indeed, no practical tool offering both good reliability and reasonable computational time was available, making this technique hardly usable in an industrial context. After the preliminary work of [3,4], strong improvements have been achieved by ONERA supported by ESA and CNES to develop the STOchastic Worst-case Analysis Toolbox (STOWAT). With the help of this new Matlab toolbox, probabilistic µ-analysis may now be considered as a very good candidate for integration in the aerospace V&V process in a near future, finding its place between Monte Carlo simulations useful for quantifying the probability of sufficiently frequent phenomena and worst-case ?-analysis relevant for detecting extremely rare events. Recently tested on a series of AOCS benchmarks of increasing complexity [5,6,7], the most recent version of the toolbox is now evaluated for the first time on a more challenging and realistic attitude control problem. The analysis focuses both on the normal mode (MNO) and on the orbit control mode (MCO) of the CNES MicroCarb mission [8,9]. The paper compares and discusses the results which have been obtained with different V&V techniques, critically assessing the advantages of the innovative method with respect to more classical procedures. [1] C. Roos. Systems Modeling, Analysis and Control (SMAC) toolbox: an insight into the robustness analysis library. Proceedings of the IEEE CACSD Conference, Hyderabad, India, 2013. [2] A. Marcos, S. Bennani, C. Roux. Stochastic µ-analysis for launcher thrust vector control systems. Proceedings of the EuroGNC Conference, Toulouse, France, 2015. [3] A. Falcoz, D. Alazard, C. Pittet. Probabilistic µ-analysis for system performances assessment. Proceedings of the 20th IFAC World Congress, Toulouse, France, 2017. [4] S. Thai, C. Roos, J.M. Biannic. Probabilistic µ-analysis for stability and H? performance verification. Proceedings of the ACC, Philadelphia, PA, USA, 2019. [5] J.M. Biannic, C. Roos, S. Bennani, F. Boquet, V. Preda, B. Girouart. Advanced probabilistic µ-analysis techniques for AOCS validation. European Journal of Control, 62 (2021), pp. 120-129. [6] C. Roos, J-M. Biannic, and H. Evain. A new step towards the integration of probabilistic µ in the aerospace V&V process. Proceedings of the EuroGNC Conference, Berlin, Germany, 2022. [7] F. Somers, S. Thai, C. Roos,[ J-M. Biannic, S. Bennani, V. Preda, and F. Sanfedino. Probabilistic gain, phase and disk margins with application to AOCS validation. Proceedings of the IFAC ROCOND Symposium, Kyoto, Japan, 2022. [8] Arnaud Varinois and al., MICROCARB: A micro-satellite for atmospheric CO2 monitoring, 4S 2016 [9] Genin, F. and Viaud, F. An innovative control law for Microcarb microsatellite, 32nd annual AAS Guidance and Control Conference, 2018