(372c) Adaptive Model Predictive Control for Optimal Irrigation Scheduling

In the quest for sustainable agriculture, precision irrigation is an important tool for conserving water resources while maintaining crop yields. This study introduces an adaptive model predictive control (MPC) framework that synergies with a crop simulator, namely decision support system for agrotechnology transfer (DSSAT), to optimize irrigation timing and amount for irrigated crops. DSSAT is a software application program that comprises crop simulation models for over 42 crops, which has gained wide acceptance and has been used to simulate various applications at different spatial and temporal scales (Jones et al. l, 2003). DSSAT does not have the capability of optimal irrigation scheduling in real-time as it is a simulator that requires not only soil and crop genetic information, but also daily weather data and detailed crop management (e.g., irrigation and fertilization) over the entire crop growth period. On the other hand, irrigation can be deemed as maintaining the soil moisture above a prespecified level by replenishing water in a timely and efficient manner (Shang et al., 2019). From this perspective, simple models that describe the soil water balance in the root zone have been utilized for model-based irrigation control (Delgoda et al., 2016; Guo & You, 2018). Our adaptive MPC framework is also derived from the soil water balance equation. However, we introduce an adaptive mechanism that continually modulates the soil moisture reference weights in the future trajectory in response to the updated weather conditions and uncertainties. The adaptive strategy ensures that MPC remains agile and responsive to the near-future environmental fluctuations, enhancing the system’s ability to optimize irrigation scheduling. In addition, existing MPC approaches in irrigation applications optimize crop yield with everyday irrigation, which is unrealistic for real applications. In contrast, our approach takes real application into consideration and only applies irrigation above certain thresholds. Finally, our approach considers both crop yield and water use efficiency (WUE) by maximizing a weighted sum of two key outcomes: the expected ratio of the achievable yield (Y^*) to the potential yield (Y­₀), and the expected efficiency of water use, quantified as the ratio of evapotranspiration (ETp) to the sum of irrigation (I*) and precipitation (PREC) as shown below:

max_w,i,I Λ•E(Y*/Y0)+(1-Λ)•∑^H_{i = 1}E(ETp/I*+PREC)_i Eq.(2)

The weighting factor λ balances the focus between yield maximization and WUE, allowing us to adaptively recalibrate set points in response to shifting weather patterns, ensuring both the sustainability of water resources and the maximization of agricultural outputs.

To demonstrate the effectiveness of the proposed adaptive MPC framework, we simulate the growth and water usage of maize (corn) in the Piracicaba region of Brazil, referencing soil properties, and management practices within the DSSAT system. We utilize 39 years of weather data, spanning from 1985 to 2023, sourced from NASA’s POWER (Prediction Of Worldwide Energy Resources) project. We compare the performance of the proposed adaptive MPC approach to the performance of the DSSAT built-in irrigation management strategy in terms of crop yield and WUE. We show that our approach can significantly improve both crop yield and WUE at the same time. We also demonstrate the robustness of the proposed method under different levels of weather forecast uncertainties.

Reference

• Jones, J. W., Hoogenboom, G., Porter, C. H., Boote, K. J., Batchelor, W. D., Hunt, L. A., ... & Ritchie, J. T. (2003). The DSSAT cropping system model. European journal of agronomy, 18(3-4), 235-265.
• Shang, C., Chen, W. H., Stroock, A. D., & You, F. (2019). Robust model predictive control of irrigation systems with active uncertainty learning and data analytics. IEEE transactions on control systems technology, 28(4), 1493-1504.
• Delgoda, D., Malano, H., Saleem, S. K., & Halgamuge, M. N. (2016). Irrigation control based on model predictive control (MPC): Formulation of theory and validation using weather forecast data and AQUACROP model. Environmental Modelling & Software, 78, 40–53.
• Guo, C., & You, F. (2018). A Data-Driven Real-Time Irrigation Control Method Based on Model Predictive Control. 2018 IEEE Conference on Decision and Control (CDC), 2599–2604.