Anti Sloshing Control Law Design For Launchers Using A Model-Free Approach
Creators: name:  P. COCAUL 
name:   H. PIET-LAHANIER 
name:   M. GANET 
name:   S. BERTRAND 
name:   L. LEMAZURIER 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT DYNAMICS
GNC
AVIONICS
CONTROL
GUIDANCE

description: The performances of a launchers mission in terms of accuracy of trajectory following, energy consumption and reliability depend on the ability of the control design to reject or reduce perturbations. After separation of the first stage, short boosts of the upper stages thruster allow to reach the expected trajectory. Maneuvers are currently performed by orientating the nozzle which can lead to unknown propellant slosh dynamics and may affect the vehicle stability and controlability. Propellant sloshing is considered as one of the major sources of pertubations that should be accounted for in the design of the attitude control laws. In classical linear control law of a launcher stage, this perturbation is not represented in the dynamics model used for control synthesis. One relies on robust linear control to limit their impact on the launcher stability at the potential cost of higher conservatism. Gains in efficiency could be sought for by introducing a model of the dynamics of sloshing but this induced movement is proved to be difficult to represent. The main goal here is to find the best compromise between precision and robustness in a disturbed context with modeling of the nozzle movement and the disturbances due to the sloshing. Equivalent Mechanical Models such as spring-mass or pendulum are often used as they provide a fair compromise between accuracy of the representation and model complexity, but they may not reflect all the coupling dynamics at stake. Several approaches have been suggested to design a controller based on these models which avoids amplification of the fuels movement. As the model characteristics are usually partially unknown or could evolve during the trajectorys phases, adaptive solutions have been sought for to stabilize their evolution, and expand the operating range of the controller. In this paper, an adaptive approach is presented to derive an anti sloshing control strategy for a launchers second stage subject to short boosts in space. Our objective is to mitigate the impact of disturbing phenomena to preserve a level of performances similar to the one obtained for the nominal launcher model. We propose here a new control design based on the developments in the field of model-free control approach. The plant behavior in terms of input-output relationship is assumed to be well-approximated by a system of ordinary differential equations, e. g. a second-order equation between output y and input u. The implicit function theorem yields then that the equations can be synthesized in the form of y(n)=F+alpha u, where alpha is a non-physical constant parameter and F represents the structural information. The loop can be closed via an intelligent PID controller, or i-PID controller. The resulting control expresses as a linear function of the reference output trajectory\'s derivatives, a local approximation of F and a PID control on the tracking error. Model-Free Control allows to consider systems with a poor modeling knowledge and to handle perturbations and uncertainties as already illustrated in various applications but not yet for a launcher upper stages control. We aim at comparing the results obtained using Model-Free control with those obtained using a structured control law with observer. Stability criteria are introduced to qualify the behavior of the controlled launcher. Description of the methodology developed for efficient search of the parameters of the Model-Free control is also presented. The results obtained can be compared to those of more traditional methods which have certified results on launchers such as H? synthesis. A simulation demonstrates the improvement of the disturbance rejection with the ultra-local adaptive model of the model-free controller