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Modelling Dynamic Behaviour of Photosynthesis Using a Simple Black Box Model Structure
Copyright@ IFAC Modelling and Control in Agriculture, Horticulture and Post-Harvest Processing, Wageningen, The Netherlands, 2000
MODELLING DYNAMIC BEHAVIOUR OF PHOTOSYNTHESIS USING A SIMPLE BLACK BOX MODEL STRUCTURE
C. BooDeD), O. JODiauxI, K. JaDsseDsI, D. Berckmans l , R. Lemeu.-2, A. Kharoubi 2 aDd H. PieD 2 Laboratory for Agricultural Buildings Research Katholieke Universiteit Leuven Kardinaal Mercierlaan 92, B-3001 Heverlee, Belgium 2 Laboratory of Plant Ecology University of Gent Coupure Links 653, B-9000 Gent, Belgium J
Abstract: The objective of the research reported in this paper is to model the dynamic response of photosynthesis on plant level. First. the influence of light. air temperature and air humidity on the plant's photosynthesis was investigated separately. From these data. a general model for the photosynthesis was created and validated with validation measurements. containing time variations in air temperature. humidity and light-dark alterations at the same time. Photosynthesis was modelled with ranging from 81 % to 99%. The obtained model will be used in an upscaling from modelling leaf to plant photosynthesis. This is the next step in developing an on-line adaptive model based climate controller. Copyright © 2000 1FAC
r
Keywords: ARMA parameter estimation. bio control. dynamic modelling. plants. response measurement
1.
The modelling of plant responses in relationship with the physical environment can be divided into two parts: the modelling of the microclimate out of the global process control inputs (e.g. inlet temperature. ventilation rate. heat supply. etc.) and the modelling of the plant's responses out of the microclimate. Today. optimised bioprocess controls can technically be realised by application of modem hard- and software and mathematical identification techniques Research made it possible to control the microenvironment around a living organism by means of the macrocIimate inputs as temperature and overall ventilation rate (Berckmans. et al.. 1992). Dynamic models of plant responses can be incorporated in climate controllers.
INTRODUCTION
In controlling bioprocesses in horticulture. it is tried to optimise the microclimate by means of expensive greenhouses. equipment and control systems. In practice these investments do not always yield the predicted production and managing results (Hashimoto. et al.. 1982; Ceulemans. 1985). From this point of view. there is a lack of knowledge concerning the dynamic relation between variations of the microclimate and dynamic plant responses (Hashimoto. et al .• 1985; Kim and Verma. 1991). In order to obtain better environment and bioprocess control (e.g. plants in horticulture) it is necessary to have more insight in the response of the organism to dynamic variations of its microenvironment. The microenvironment is the environment closely surrounding an organism and consists of physical. chemical and biological factors that affect them. Each of these factors varies in time and space. Understanding how organisms respond to these dynamic changes in their microenvironment is an essential part of all environmental related problems. Most models being developed to explain this relationship are descriptive (deterministic) and too complex to be used for control purposes (Young and Lees. 1996; Van Pee and Berckmans. 1999).
The objective of this research is to model plant responses to variations of the climate factors dynamically and to scale the model up from leaf level to plant level. taking into account 3-D gradients of the climate. In a first stage the response of leaf temperature to 3-D temperature and light-dark alterations has been modelled dynamically (Van Pee. et al.. 1998; Boonen. et al.. 1999). In this paper it is tried to model photosynthesis to variations in temperature. humidity and light intensity (PAR). 113
Kim, J. and S.B. Verma (1991). Modelling canopy photosynthesis scaling up from a leaf to a canopy in a temperate grassland ecosystem. Agricultural and Forest Meteorology. 57. 187-208. Kilppers. M. (1988). Water vapour and carbon dioxide exchange of leaves as affected by Acta different environmental conditions. Horticulturae, 229. 85-112. Ljung, L. (1987). System Identification: Theory for the user. Prentice Hall. New Jersey. Pasian, c.c. and 1.H. Lieth (1989). Analysis of the response of net photosynthesis of rose leaves of varying ages to photosynthetically active radiation and temperature. Journal for American Horticultural Science, 114,581-586. Pearcy, R.W., K. Osteryoung. H. Calkin and W. Calkin (1985). Photosynthetic responses to dynamic light environment by Hawaiian trees. Plant Physiology, 79, 896-902. Van Pee, M., K. Janssens. D. Berckmans and R. Lemeur (1998). Dynamic measurement and modelling of climate gradients around a plant for microenvironment control. Acta Horticulturae, 456. 399-406. Van Pee, M. and D. Berckmans (1999). Quality of modelling plant responses for environment control purposes. Computers and Electronics in Agriculture, 22, 209-219. Young, P.C. (1993). Concise Encyclopaedia of Environmental Systems. Pergamon Press, Oxford. Young, P.c. and M.J. Lees (1996). Simplicity out of complexity in glasshouse climate modelling. Acta Horticulturae, 406, 15-28.
The research described in this paper was done with a new experimental set-up. It is clear that the photosynthetic response to light-dark alterations is large enough to measure and model. However, if a model for the response of photosynthesis due to step changes in air temperature and relative humidity is to be made, more attention has to be given to improving the signal/noise ratio of the infrared gas analyser (IRGA). This can be done by decreasing the ventilation rate (more net photosynthesis will be obtained) or by upgrading the IRGA to a more accurate measurement system. More input variables such as CO2 concentration, ventilation rate, etc. should be performed in the future for a more detailed evaluation of the suitability of this modelling approach for developing modelbased climate control algorithms.
ACKNOWLEDGEMENTS We would like to acknowledge the Fund for Scientific Research - Flanders (Belgium) and the Katholieke Universiteit Leuven for funding this research.
REFERENCES Berckmans, D., M. De Moor and B. De Moor (1992). A new approach to modelling and control the energy and mass transfer in a three-dimensional imperfectly mixed ventilation space. Proc. of Roomvent '92: Air distribution in rooms (Aalborg, Denmark). Vol. 1, pp. 399-416. Boonen, c., O. Joniaux, K. Janssens, D. Berckmans, R. Lemeur and A. Kharoubi (1999). Relationship between leaf temperature and the threedimensional distribution of air temperature around a tomato plant. 1999 ASAElCSAE-SCGR Annual International Meeting, 18-21 July 1999, Toronto, Ontario Canada. Paper No. 994126. Ceulemans, R. (1985). Plant growth optimisation by photosynthetic monitoring. Acta Horticulturae, 174,309-312. Grantz. D.A. (1990). Plant response to atmospheric humidity. Plant, Cell and Environment. 13. 667679. Gross. L.J. and B.F. Chabot (1979). Time course of photosynthetic response to changes in incident light energy. Plant Physiology. 63.1033-1038. Hashimoto, Y., T. Morimoto and S. Funade (1982). Identification of water deficiency and photosynthesis in short-term plant growth under random variation of the environment. Proc. 6th IFAC symposium on system identification and parameters estimation, pp. 1559-1564. Hashimoto, Y., T. Morimoto and T. Fukuyama (1985). Some speaking plant approach to the synthesis of control system in the greenhouse. Acta Horticulturae. 174, 219-226.
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MODELLING DYNAMIC BEHAVIOUR OF PHOTOSYNTHESIS USING A SIMPLE BLACK BOX MODEL STRUCTURE
C. BooDeD), O. JODiauxI, K. JaDsseDsI, D. Berckmans l , R. Lemeu.-2, A. Kharoubi 2 aDd H. PieD 2 Laboratory for Agricultural Buildings Research Katholieke Universiteit Leuven Kardinaal Mercierlaan 92, B-3001 Heverlee, Belgium 2 Laboratory of Plant Ecology University of Gent Coupure Links 653, B-9000 Gent, Belgium J
Abstract: The objective of the research reported in this paper is to model the dynamic response of photosynthesis on plant level. First. the influence of light. air temperature and air humidity on the plant's photosynthesis was investigated separately. From these data. a general model for the photosynthesis was created and validated with validation measurements. containing time variations in air temperature. humidity and light-dark alterations at the same time. Photosynthesis was modelled with ranging from 81 % to 99%. The obtained model will be used in an upscaling from modelling leaf to plant photosynthesis. This is the next step in developing an on-line adaptive model based climate controller. Copyright © 2000 1FAC
r
Keywords: ARMA parameter estimation. bio control. dynamic modelling. plants. response measurement
1.
The modelling of plant responses in relationship with the physical environment can be divided into two parts: the modelling of the microclimate out of the global process control inputs (e.g. inlet temperature. ventilation rate. heat supply. etc.) and the modelling of the plant's responses out of the microclimate. Today. optimised bioprocess controls can technically be realised by application of modem hard- and software and mathematical identification techniques Research made it possible to control the microenvironment around a living organism by means of the macrocIimate inputs as temperature and overall ventilation rate (Berckmans. et al.. 1992). Dynamic models of plant responses can be incorporated in climate controllers.
INTRODUCTION
In controlling bioprocesses in horticulture. it is tried to optimise the microclimate by means of expensive greenhouses. equipment and control systems. In practice these investments do not always yield the predicted production and managing results (Hashimoto. et al.. 1982; Ceulemans. 1985). From this point of view. there is a lack of knowledge concerning the dynamic relation between variations of the microclimate and dynamic plant responses (Hashimoto. et al .• 1985; Kim and Verma. 1991). In order to obtain better environment and bioprocess control (e.g. plants in horticulture) it is necessary to have more insight in the response of the organism to dynamic variations of its microenvironment. The microenvironment is the environment closely surrounding an organism and consists of physical. chemical and biological factors that affect them. Each of these factors varies in time and space. Understanding how organisms respond to these dynamic changes in their microenvironment is an essential part of all environmental related problems. Most models being developed to explain this relationship are descriptive (deterministic) and too complex to be used for control purposes (Young and Lees. 1996; Van Pee and Berckmans. 1999).
The objective of this research is to model plant responses to variations of the climate factors dynamically and to scale the model up from leaf level to plant level. taking into account 3-D gradients of the climate. In a first stage the response of leaf temperature to 3-D temperature and light-dark alterations has been modelled dynamically (Van Pee. et al.. 1998; Boonen. et al.. 1999). In this paper it is tried to model photosynthesis to variations in temperature. humidity and light intensity (PAR). 113
Kim, J. and S.B. Verma (1991). Modelling canopy photosynthesis scaling up from a leaf to a canopy in a temperate grassland ecosystem. Agricultural and Forest Meteorology. 57. 187-208. Kilppers. M. (1988). Water vapour and carbon dioxide exchange of leaves as affected by Acta different environmental conditions. Horticulturae, 229. 85-112. Ljung, L. (1987). System Identification: Theory for the user. Prentice Hall. New Jersey. Pasian, c.c. and 1.H. Lieth (1989). Analysis of the response of net photosynthesis of rose leaves of varying ages to photosynthetically active radiation and temperature. Journal for American Horticultural Science, 114,581-586. Pearcy, R.W., K. Osteryoung. H. Calkin and W. Calkin (1985). Photosynthetic responses to dynamic light environment by Hawaiian trees. Plant Physiology, 79, 896-902. Van Pee, M., K. Janssens. D. Berckmans and R. Lemeur (1998). Dynamic measurement and modelling of climate gradients around a plant for microenvironment control. Acta Horticulturae, 456. 399-406. Van Pee, M. and D. Berckmans (1999). Quality of modelling plant responses for environment control purposes. Computers and Electronics in Agriculture, 22, 209-219. Young, P.C. (1993). Concise Encyclopaedia of Environmental Systems. Pergamon Press, Oxford. Young, P.c. and M.J. Lees (1996). Simplicity out of complexity in glasshouse climate modelling. Acta Horticulturae, 406, 15-28.
The research described in this paper was done with a new experimental set-up. It is clear that the photosynthetic response to light-dark alterations is large enough to measure and model. However, if a model for the response of photosynthesis due to step changes in air temperature and relative humidity is to be made, more attention has to be given to improving the signal/noise ratio of the infrared gas analyser (IRGA). This can be done by decreasing the ventilation rate (more net photosynthesis will be obtained) or by upgrading the IRGA to a more accurate measurement system. More input variables such as CO2 concentration, ventilation rate, etc. should be performed in the future for a more detailed evaluation of the suitability of this modelling approach for developing modelbased climate control algorithms.
ACKNOWLEDGEMENTS We would like to acknowledge the Fund for Scientific Research - Flanders (Belgium) and the Katholieke Universiteit Leuven for funding this research.
REFERENCES Berckmans, D., M. De Moor and B. De Moor (1992). A new approach to modelling and control the energy and mass transfer in a three-dimensional imperfectly mixed ventilation space. Proc. of Roomvent '92: Air distribution in rooms (Aalborg, Denmark). Vol. 1, pp. 399-416. Boonen, c., O. Joniaux, K. Janssens, D. Berckmans, R. Lemeur and A. Kharoubi (1999). Relationship between leaf temperature and the threedimensional distribution of air temperature around a tomato plant. 1999 ASAElCSAE-SCGR Annual International Meeting, 18-21 July 1999, Toronto, Ontario Canada. Paper No. 994126. Ceulemans, R. (1985). Plant growth optimisation by photosynthetic monitoring. Acta Horticulturae, 174,309-312. Grantz. D.A. (1990). Plant response to atmospheric humidity. Plant, Cell and Environment. 13. 667679. Gross. L.J. and B.F. Chabot (1979). Time course of photosynthetic response to changes in incident light energy. Plant Physiology. 63.1033-1038. Hashimoto, Y., T. Morimoto and S. Funade (1982). Identification of water deficiency and photosynthesis in short-term plant growth under random variation of the environment. Proc. 6th IFAC symposium on system identification and parameters estimation, pp. 1559-1564. Hashimoto, Y., T. Morimoto and T. Fukuyama (1985). Some speaking plant approach to the synthesis of control system in the greenhouse. Acta Horticulturae. 174, 219-226.
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