The significance of crop co-states for receding horizon optimal control of greenhouse climate

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Abstract

While a tomato crop grows on the time-scale of weeks, the greenhouse climate changes on a time-scale of minutes. The economic optimal control problem of producing good quality crops against minimum input of resources is tackled by a two time-scale decomposition. First, the sub-problem associated to the slow crop evolution is solved off-line, leading to a seasonal pattern for the co-states of the amount of assimilates produced by photosynthesis, and the fruit and leaf weights. These co-states can be interpreted as the marginal prices of a unit of assimilate, leaf and fruit. Next, they are used in the goal function of an on-line receding horizon control (RHOC) of the greenhouse climate, thus balancing costs of heating and CO2-dosage against predicted benefits from harvesting, while profiting as much as possible from the available solar radiation. Simulations using the time-varying co-states are compared to experimental results obtained with fixed co-states. It appears that the on-line control is sensitive to the time evolution of the co-states, suggesting that it is advantageous to repeat the seasonal optimisation from time to time to adjust the co-states to the past weather and realised crop state. ? 2002 Elsevier Science Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)625-632
JournalControl Engineering Practice
Volume10
Issue number6
DOIs
Publication statusPublished - 2002

Fingerprint

Receding Horizon Control
Greenhouse
Greenhouses
Climate
Crops
Optimal Control
Time Scales
Fruit
Leaves
Fruits
Tomato
Solar Radiation
Photosynthesis
Climate Change
Harvesting
Weather
Balancing
Heating
Optimal Control Problem
Time-varying

Cite this

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title = "The significance of crop co-states for receding horizon optimal control of greenhouse climate",
abstract = "While a tomato crop grows on the time-scale of weeks, the greenhouse climate changes on a time-scale of minutes. The economic optimal control problem of producing good quality crops against minimum input of resources is tackled by a two time-scale decomposition. First, the sub-problem associated to the slow crop evolution is solved off-line, leading to a seasonal pattern for the co-states of the amount of assimilates produced by photosynthesis, and the fruit and leaf weights. These co-states can be interpreted as the marginal prices of a unit of assimilate, leaf and fruit. Next, they are used in the goal function of an on-line receding horizon control (RHOC) of the greenhouse climate, thus balancing costs of heating and CO2-dosage against predicted benefits from harvesting, while profiting as much as possible from the available solar radiation. Simulations using the time-varying co-states are compared to experimental results obtained with fixed co-states. It appears that the on-line control is sensitive to the time evolution of the co-states, suggesting that it is advantageous to repeat the seasonal optimisation from time to time to adjust the co-states to the past weather and realised crop state. ? 2002 Elsevier Science Ltd. All rights reserved.",
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The significance of crop co-states for receding horizon optimal control of greenhouse climate. / van Straten, G.; van Willigenburg, L.G.; Tap, R.F.

In: Control Engineering Practice, Vol. 10, No. 6, 2002, p. 625-632.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - While a tomato crop grows on the time-scale of weeks, the greenhouse climate changes on a time-scale of minutes. The economic optimal control problem of producing good quality crops against minimum input of resources is tackled by a two time-scale decomposition. First, the sub-problem associated to the slow crop evolution is solved off-line, leading to a seasonal pattern for the co-states of the amount of assimilates produced by photosynthesis, and the fruit and leaf weights. These co-states can be interpreted as the marginal prices of a unit of assimilate, leaf and fruit. Next, they are used in the goal function of an on-line receding horizon control (RHOC) of the greenhouse climate, thus balancing costs of heating and CO2-dosage against predicted benefits from harvesting, while profiting as much as possible from the available solar radiation. Simulations using the time-varying co-states are compared to experimental results obtained with fixed co-states. It appears that the on-line control is sensitive to the time evolution of the co-states, suggesting that it is advantageous to repeat the seasonal optimisation from time to time to adjust the co-states to the past weather and realised crop state. ? 2002 Elsevier Science Ltd. All rights reserved.

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