Feedback control of plant-soil autotoxicity via pulse-width modulation

Plant-soil negative feedback (PSNF) is the rise in soil of negative conditions for plant performance induced by the plants themselves, limiting the full potential yield and thus representing a loss for the agricultural industry. It has been recently shown that detrimental effects the PSNF has on the growth of plant's biomass can be mitigated by periodically intervening on the plant/soil system, for example by washing the soil. The periodic control inputs were computed by using an average model of the system and then applied in open-loop. In this paper we present two feedback control strategies, namely a PI and a MPC-based controllers, that, by adapting online the duty-cycle of the periodic control input, guarantee precise regulation of the biomass yield and at the same time robustness to unavoidable modeling errors and perturbations acting on the system. The performance of the proposed control strategies is then validated by means of extensive numerical simulations.