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J. agric. Engng Res. (2001) 78 (4), 407}413

doi:10.1006/jaer.2000.0647, available online at http://www.idealibrary.com on

SE*Structures and Environment

A Strategy for Greenhouse Climate Control, Part I: Model Development

M. Trigui; S. Barrington; L. Gauthier

Department of Agricultural and Biosystems Engineering, Faculty of Agricultural and Environmental Studies, Macdonald Campus of McGillUniversity, 21 111 Lakeshore Road, Sainte Anne-de-Bellevue, Que&bec Canada H9X 3V9; e-mail of corresonding author:

barrington@macdonald.mcgill.caDe&partement des Sols et de Ge&nie Agroalimentaire, Faculte& des sciences de l'agriculture et de l'alimentation, Universite& Laval, Cite& Universitaire,

Que&bec Canada G1K 7P4

(Received 11 September 1998; accepted in revised form 6 September 2000; published online 23 January 2001)

This paper presents an algorithm developed to predict the dynamic ambient greenhouse air conditions which

optimize net pro"ts for the production of a greenhouse tomato crop. Pro"ts are equated to the crop yield value

less the energy costs for heating and dehumidi"cation and the CO

injection cost. The climatic conditions

considered are CO

level, temperature, relative humidity and incident radiation. These are varied dynamically

for every time interval spanning the harvesting period.

The algorithm has two sub-programs. For sets of selected internal climatic parameters, the "rst calculates

crop yield, and the second calculates energy costs (heating and dehumidi"cation) with reference to predicted

exterior climatic conditions (solar radiation, temperature, wind velocity and relative humidity). These twoalgorithms are then used to predict the particular set of climatic parameters, adjusted for each time interval over

the harvesting period, that will maximize the crop yield value less the energy costs.

2001 Silsoe Research Institute

1. Introduction

In North America, greenhouse production has

increased steadily despite high-energy costs (Statistics

Canada, 1995). By increasing the air tightness of modern

greenhouse structures for reduced energy use, problemsof high relative humidity have occurred. However, this

air tightness has also provided an opportunity to develop

and use computer programs to optimize the climate

inside greenhouses. The objective of this project was,

therefore, the development of a program capable of con-

tinuously adjusting the set-point of ambient greenhouse

air conditions (AGAC) for relative humidity, temper-

ature, CO

and incident radiation, to maximize the crop

yield value less energy cost, being termed net pro"t in this

text.

Several projects have developed programs to optimizeAGAC, but these programs have been limited to one or

two parameters. Daytime temperature is a major factor

a!ecting crop yield and energy consumption. Seginer

et al. (1991) formulated a model to optimize this para-

meter using Pontryagin's control strategy (Pontryagin

et al., 1962). For a crop of lettuce, the model predicted

that the set-point for daytime temperature should be

slowly decreased throughout the growing period as of the

"rst day. Nevertheless, some day-to-day #uctuations

need superimposition, in response to exterior temper-

atures and incoming radiation. While this strategy wasfound to be consistent with the physiological need of the

crop, the daily economic gain was minimal at $0)05 m\.

Further economic gains were anticipated with the hourly

adjustment of the temperature set-point.

Stanghellini and van Meurs (1992) proposed a climate

control algorithm based on the use of a set-point for crop

transpiration rate rather than for temperature and/or

relative humidity. The model was able to predict plant

transpiration rate with a maximum error of 10%. Never-

theless, the desired transpiration rate could only be

achieved as well as the AGAC could be controlled insidethe greenhouse. Relative humidity and incident radiation

were the two main factors in#uencing the transpiration

set-point.

Jolliet (1994) developed the HORTITRANS model, pre-

dicting greenhouse relative humidity, crop transpiration

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Notation

A ground surface area of the greenhouse,m

b coe$cient, K\

CE

CO

injection rate, g [CO

] m\ s\

CGT

CO#ux by ventilation and in"ltration,

g [CO

] m\ s\

CM

exterior CO

concentration, g [CO

]

kg\ [air]

CR

greenhouse interior CO

level at time t,

g [CO

] m\

CN?

air-speci"c thermal heat capacity,

J kg\ [dry air] K\

cR, c

, c

, empirical constants, dimensionless

c

, c

, c

,

c

, c

, c

E?BB

mass of water vapour added or

removed by humidi"cation or de-

humidi"cation, kg [water] m\ s\

EA

water vapour condensation rate on

walls, kg [water] m\ s\

EGT

water vapour removed by in"ltration

and ventilation, kg [water] m\ s\

ER

transpiration rate of the plants, kg

[water] m\ s\eA

interior air water vapour pressure at the

wall, Pa

eG

interior air water vapour pressure, Pa

eM

exterior air water vapour pressure, Pa

eQ

air saturation water vapour pressure,

Pa

eR

external parameters (CO

, temperature,

relative humidity, incoming radiation,

energy cost, product value) at time t,

g [CO

] m\, K, %, Wm\, $ J\,

$kg\

, respectivelyf(x

R, p

R, e

R) the estimated harvest value calculated

from the AGAC inside at time t,

$m\ s\

G(CR

,R) net rate of photosynthesis, g [CO

]

m\ s\

g(xR, p

R,

uR, e

R)

the cost of maintaining the AGAC at

time t, $m\ s\

GEJ

global rate of photosynthesis, g [CO

]

m\ s\

gQ

leaf conductance to CO

, kg [air]

m\

s\

h average height of the greenhouse, m

H?

Hamiltonian function, $m\ s\

HA

heat #ux through the glazing,

W m\

HD

heating system heat #ux, Wm\

HQ heat transferred between the soil andthe air, Wm\

HGT

the greenhouse heat lost by ventilation

and air in"ltration, W m\

HT

the energy cost per unit #oor area to

ventilate the greenhouse, W m\

hA

heat transfer coe$cient between the air

and the walls, W m\ K\

hGT

sensible heat transfer coe$cient due to

the air renewal, W m\K\

hP

greenhouse relative humidity, %

hR

heat transfer coe$cient between the

plants and the air, W m\ K\I*

foliar surface index, m [leaves]m\

[#oor area]

J objective function, $m\

K!

cost of CO

injection, $ g\ [CO

]

KD

heating energy cost, $ J\

KE

estimated harvest value, $kg\ [har-

vested]

KT

ventilation energy cost, $ J\

p!

cost of CO

injection, $ g\ [CO

] m\

p2

heating energy cost, $m\K\

pR variations in plant state at time t, kg[fruit mass] m\

pU

dehumidi"cation energy cost, $kg [dry

air]kg\ [water] m\

Q ventilation and in"ltration rates, m s\

R photosynthetically active radiation,

W m\

RB

respiration rate, g [CO

] m\ s\

RL

net incident radiation, W m\

RP

reference respiration rate per unit crop

mass, g [CO

] g\ [crop CO

] s\

t time interval, st

beginning of the harvesting period, s

tD

end of the harvesting period, s

M

exterior air temperature, K

P

reference temperature, K

Q

soil temperature, K

R

greenhouse air temperature, K

;A

global heat transfer coe$cient between

the inside air and the glazing,

W m\ K\

;Q

global heat transfer coe$cient between

the inside air and the soil, W m\

K\

uBR

latent heat #ux, W m\

uR

greenhouse climate control parameters

(heating, dehumidi"cation, lighting and

CO

injection) at time t, W m\, g

[CO

] m\

M. TRIGUI E A .408

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