Theoretical Exploration of Irrigation Control for Stem Water Potential through Model Predictive Control

Abstract

Irrigation takes considerable amount of water; however, in many cases up to half of it is wasted. Improving the efficiency of irrigation control, therefore, is an important task for sustainable water management. Most existing irrigation control systems are based on soil moisture level. In this work, we explore theoretically the use of continuous values stem water potential (SWP) as a basis for control. SWP is a more direct measure of plant water status than the soil moisture level. After linearizing and discretizing a nonlinear dynamic model of water dynamics in a plant, we develop a model predictive control (MPC) framework for regulating SWP. To prevent plants from suffering water stress, data-driven robust MPC (DDRMPC) which captures the uncertainty of weather forecast error is implemented. A case study based on almond tree is presented to characterize the effectiveness of the DDRMPC strategy relative to on-off control. Sensitivity analysis on the prediction horizon and penalty weights were performed to investigate the varying irrigation control decisions. For the case characterized, the analysis shows that controlling tree trunk water potential through DDRMPC can save 2.5% amount of water comparing to on-off control while maintaining zero violation.