Une méthode orientée optimisation pour la réduction des erreurs d'application d'engrais par épandage centrifuge

[Departement_IRSTEA]EA [TR1_IRSTEA]TESAD / TECHPROPRECentrifugal spreaders are very popular for application of granular fertilizers. Nevertheless, their use raises issues about application accuracy. Indeed, they enable to distribute almost uniform deposits with regularly spaced parallel tramlines but lead to adverse environmental and economical effects when distances separating the successive tractor trajectories are not constant or if paths are not parallel between them. Moreover, irregular applications occur also for start and end of fields. The resulting over-applications mostly lead to an over nitrate enrichment and with ground lixiviation, can cause problems of excessive growth of algae in surface waters. This phenomenon known as eutrophication result then in numerous aquatic animals disappearances. In case of under-applications, productivity losses can be very important. To solve these issues, some works such as were done to find optimal paths followed by the spreader according to the transverse distribution. Unfortunately, these kinds of methods cannot be applied when tramlines are already imposed by other agricultural operations like sowing for example. Furthermore, the search for the best transverse distribution overlappings cannot reduce the application errors because it does not deal with the actual phenomenon occurring during spreading operation: spread patterns overlappings. Therefore, it is important to know how best arrange the placement and the shape of these spatial distributions during the spreading process in the presence of imposed paths. This adjustment should be continuously carried out for each GPS position of the applicator by changing its settings. The spread patterns have a model relying on the product of the mass flow rate by two gaussians which parameters are the medium radius and the medium angle. The medium radius corresponds to the distance between the spinning disc centre and the spread pattern centre, while the medium angle specifies the angle between the travel direction and the axis passing by the disc centre and the spread pattern one. From this model, this study discusses an optimization-based approach to compute optimal variables for uniform fertilizer application. A cost function reflecting the application errors is formalized and its discretization is carried out. In order to take into account the mechanical and dynamical limits of the machine, bound constraints on the decision parameters and their discrete time derivatives are introduced. Thanks to this procedure, the optimal parameters can then be afterwards used as reference variables for the control of the spreader in the future. Faced with a large scale problem owing to the applied discretization scheme, the spatial domain is divided into subdomains to handle each trajectory separately by considering the spreading symmetry properties. The resulting sub-problems are then solved by applying an augmented Lagrangian technique which permits to severely penalize unacceptable parameters. Besides, in view of the costly computational time caused by the cost function and gradients evaluations, we choose to implement also a L-BFGS technique shown to be efficient in this case. To illustrate the improvements given by using this approach, numerical simulations for a field with parallel and non parallel tramlines are presented. After optimization, the obtained results are very satisfying in comparison with absolute application errors reaching more than 100% when traditional settings are used