Abstract
This paper presents a receding horizon optimal control (RHOC) method with an economic objective function for balancing the cost of resources ( resource use × cost ) with income through yield ( yield × product price ). This paper considers the two elements that determine the income through yield. The first element is yield and associated fruit development. A new, computationally viable, approach to model the income through yield is proposed and its prediction accuracy with respect to the original model is evaluated. The new approach employs a model that predicts at each time step, the future income through yield based on the assimilates partitioned to the fruits at the current time step. Simulations suggest that the assumptions made to arrive at the model for the new approach, do not significantly affect the accuracy of the predictions. The second element considered in this paper is the product price and the uncertainty inherent in its forecasts. Historical product price data are used to generate artificial product price forecasts. An uncertainty analysis, in combination with the artificial product price forecasts, showed that the product price forecast error does not considerably affect the optimised control strategy. Season-wide simulations with RHOC suggest that the product price forecast error does not considerably affect the value of the economic objective function. • A computationally viable approach to model the income through yield is proposed. • The new approach to model income through yield allows for RHOC with a short horizon. • Historical product price data are used to create artificial product price forecasts. • Product price forecast errors do not considerably affect the control strategy.
Highlights
The Netherlands is one of the biggest exporters of vegetables in the world, which, comes at a price
In Subsection 2.2, the approach proposed in Kuijpers et al (2021) and Seginer et al (2018) is generalised to arrive at a fundamentally different way to model fruit development which enables the use of SRHOC
One of the main contributions of this paper is the development of a fruit development model which can be used in combination with a computationally viable short receding horizon optimal controller
Summary
The Netherlands is one of the biggest exporters of vegetables in the world, which, comes at a price. In 2018, the Dutch horticultural industry consumed 100:5 PJ of energy, of which only 7:4 PJ was produced in a sustainable manner. This use of energy resulted in a CO2 emission of 5:7 Mt (Velden & Smit, 2019). The Dutch horticultural industry signed an agreement with the Dutch government to decrease the CO2 emission and its environmental footprint. Automatic control of the greenhouse is likely to contribute to achieving the goals set in the Dutch agreement and may lead to a more sustainable cultivation worldwide (van Straten & van Henten, 2010). Various applications of automatic control to the greenhouse system have been presented in the literature.
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