Non-collocated sliding mode control of partial differential equations for soil irrigation. (January 2019) - Challapa Molina, Nataly Ines; V.S. Cunha, José Paulo
Highlights: Sliding mode control (SMC) is developed to regulate the water content in the soil. The movement of water in the soil is modeled by the Richards partial differential equation (PDE). The proposed SMC can be also applied to other parabolic PDEs, such as the diffusion and heat equations. The non-collocated sensor and actuator SMC of PDEs is considered. Non-standard sliding manifolds are proposed. Abstract: In this paper, sliding mode control (SMC) is developed to regulate the water content in the soil. The movement of water in the soil is modeled by the Richards equation, which is a parabolic partial differential equation (PDE). The non-collocated SMC of PDEs is considered, that is, where the sensor and the actuator are at different positions. Two control objectives are considered: the mean water content control, and the water content control at a specified depth. For these purposes, non-standard sliding manifolds are proposed. The existence of the sliding mode in this control system is proved using a Lyapunov function, and the stability properties are analyzed using a frequency stability criterion. Simulation results indicate the excellent transient performance and the complete rejection of external disturbances caused by water evaporation, outperforming on–off and PI controllers.