s="fsb ws2 v4">2u).
Equation (1) becomes:
 
 
,12
1c
niio paio
g
A
RK KuTTCVTT
A

 



(2)
where K1 and K2 are constants and u is the outside air
speed in m·s–1. Taking into account that Rs,i = τRs,o,
where Rs,o is the outside solar radiation (in W·m–2) and τ
is the greenhouse transmissivity to solar radiation. Thus,
using Equation (2), the greenhouse air temperature Ti can
be calculated by the following relation:



,
12
1
so
io
cg pa
R
TT
A
AKKu CV

  (3)
Dividing both numerator and denominator of second
part of Equation (3) by the term “

1cg
A
AK” we take:



,1
21 1
1
1
so c g
io
p
ac
RAAK
TT
g
K
KuCV KAA




 (4)
If we replace the term


1
1cg
K
AA
by 1
,
the term
21
K
K by 2
and the term
1pcg
CKAA
by 3
, then we obtain:
1,
23
1
so
io
a
R
TT uV



 (5)
Equation (5) is a simplified version of the greenhouse
energy balance must be applied for the determination of
the unknown parameters 1
, 2
and 3
. Accordingly,
measurements of Ti, To, Rs,o,
, u and Va are needed, in
order to calibrate Equation (5) and statistically determine
the values of 1
, 2
and 3
.
3.2. Pad-Fan Subsystem Mathematical Modeling
3.2.1. Fan Mathematical Modeli ng
Pad-fan systems are commonly used for cooling the en-
vironment inside greenhouses to be suitable for growing
plants (e.g., nurseries, residential and commercial vege-
tables or flower production, etc). Fans push outside air
toward a wet pad, bringing cooled and humidified air
into the greenhouse. Typically, the wet pads and fans are
located on opposite walls so that the evaporative cooled
air is pulled from one end of the structure to the other.
A linear model of a simple fan consists of a mechanic-
cal equation and electrical equation as determined in the
following [5,6].
d
d
a
aaaa
I
VEIRL
t
  (6)
d
d
m
eLmm
TTBJt
  (7)
22
fan
PNDv (8)
where N is fan speed, D is fan diameter, v is specific
weight of air (11.82 N/m2), Ra is armature resistance (),
La is armature inductance (H), Va is terminal voltage (V),
J is moment of inertia (kg·m2), B is damping factor of
mechanical system (N·m·s). Ia is armature current (A),
TL is load torque (N·m), Te is developed torque, and ω
is speed of rotation (rpm).
3.2.2. Pad Mathematical Modeli ng
The cooling efficiency ηc of the evaporative pad cooling
system is defined by [7,8]:
,
,,
db o
c
db owb o
TT
TT
(9)
Copyright © 2012 SciRes. SGRE
Modeling and Simulation of Evaporative Cooling System in Controlled Environment Greenhouse
Copyright © 2012 SciRes. SGRE
69
where Tdb,o and Twb,o are the dry and wet bulb tempera-
tures of the air outside the greenhouse in ˚C, and T is the
dry bulb temperature of the cooled air passing over the
wet pad in ˚C. Equation (9) works well for evaporative
pad cooling systems because the cooling process (an
adiabatic process) occurs nearly at a constant wet bulb
temperature of the outside air. Equation (9) can be rear-
ranged as [7]:
control signal of the greenhouse fan and pad system vc.
The greenhouse inside temperature and humidity (Tin &
Hin) are the feedback signals to PI the controller.

,,,,
1
dboc dbowboc dbocwbo
TTT TTT

 ,
(10)
The actual greenhouse inside temperature (Tin) is com-
pared with the reference temperature value (Tref = 20˚C)
through a comparator to give an error signal, which is
introduced to the system controller. In this case, the con-
troller uses the input error signal e to improve the system
response by producing the suitable control signal of the
greenhouse fan and pad system vc. Also, second com-
parator is used to compare the actual relative humidity to
the reference relative humidity (RH = 0.7) to obtain the
error signal for the PI controller. The humidity controller
operates between dehumidify and humidify modes for
removing unwanted atmospheric moisture accumulating
within the greenhouse or to add the needed moisture to
the air by means of humidification. In the dehumidifying
mode, high humidity conditions will activate moisture
fan until level drops approximately to 70% in relative
humidity. In the humidifying mode this control operates
pad-fan humidifying system by activating switches and
motors until the relative humidity increased to 70%.
,,db ocdbowb o
TT TTT
 ,
,
(11)
where T is the temperature drop of the air through
evaporative pad cooling systems in ˚C. Equations (10)
and (11) indicate that both T and T depend only on the
dry and wet bulb temperatures of the outside air at a con-
stant cooling efficiency. By assuming a value of 80% for
the efficiency of evaporative pad cooling systems Equa-
tions (10) and (11) can be written as:
,
0.2 0.8
db owb o
TT T (12)
,,
0.8 db owb o
TTT (13)
During this operation of the greenhouse cooling sys-
tem, different situations may appear.
4. Control Strategy and Simulation of the
Greenhouse 4.1. First Situation: Humidity (RH < 0.7)
The evaporative pad-fan cooling system must have ade-
quate controller for the operator to be able to adjust the
greenhouse environment to provide the best growing
conditions for the selected herb and a comfortable envi-
ronment for worker. Two conventional controllers (PI
controllers) [9-11] are employed to maintain, optimal
temperature and relative humidity (Tref = 20˚C & Href =
0.7) inside the greenhouse at any time and to overcome
the load effect of the outdoor undesirable climatic condi-
tions. The block diagram that describes the control strat-
egy is illustrated in Figure 2. Also, the MATLAB SI-
MULINK block diagram of the greenhouse cooling sys-
tem is shown in Figure 3.
The pad-fan system switches on to increase the required
relative humidity.
4.2. Second Situation: Dehumidify (RH > 0.7)
The pad-fan system switches off while roof and side
greenhouse vents are opened for ventilation. In addition,
a roof fan is used to replace the air inside the greenhouse
(loaded with humidity) with the dry air outside the green-
house.
5. Results and Discussions
The cooling system has two controllers which control the
greenhouse inside temperature and relative humidity. PI
The input signal to the suggested controllers is the
system error e, while, the output action is the required
Figure 2. Block diagram of the greenhouse controlled system using PI controller.
Modeling and Simulation of Evaporative Cooling System in Controlled Environment Greenhouse
70
Tin
NPfan volume flow rate
pad syst em
In1 Out1
Tref 2
1000
Tref 1
20
To Work space2
t
To
Relay
Rela t ive Hum i di t y
In1 Out1
RHref
0.70
RH cont rol l er
PID
Product
Mositure Fan
Tl
Va
W
Ia
Logical
Operator
NOT
Gain 2
-K-
Gain 1
-K-
Fcn5
f(u )
Fcn3
f(u )
Fcn2
f(u)
Fcn1
f(u)
.05*u^ 2
Fan Dc Motor
Tl
Va
W
Ia
0
10
0
Clock2
Clock1
Clock
power cur ve1
power curve
PID
Figure 3. MATLAB SIMULINK bloc k diagram of the greenhouse cooling system.
control technique is proposed to fix the greenhouse in-
door temperature and relative humidity at the optimal
value for growing the marjoram herb. The proposed con-
troller is fine tuned and used to achieve a good regulatory
response. The fine-tuned parameters of the temperature
and relative humidity controllers are Kp = 10, KI = 0.0001,
and Kp = 0.1, KI = 0.2 respectively.
The greenhouse outside air temperature during 24
hours is shown in Figure 4. While, Figure 5 indicates
the response of greenhouse inside temperature. It is no-
Figure 4. Ambient temperature.
Figure 5. Greenhouse indoor temperature with control tech-
nique.
ticed that, the greenhouse inside temperature tracks the
reference temperature very well. On the other hand, air
flow rate of the fan is indicated in Figure 6. It also ob-
served from this figure that the maximum air flow rate of
the fan occurs around noon at the corresponding maxi-
mum ambient temperature, while the minimum flow rate
occurs at the mid night at the corresponding minimum
ambient temperature. Also, the controlled relative hu-
midity is shown in Figure 7, which indicates a very good
performance, since there is a small overshoot, fast
Copyright © 2012 SciRes. SGRE
Modeling and Simulation of Evaporative Cooling System in Controlled Environment Greenhouse 71
Figure 6. Air flow rate of the fan.
Figure 7. Greenhouse relative humidity with PI controller.
settling time and good tracking performance.
6. Conclusions
An evaporative cooling system is presented, in this work,
to reduce the air temperature inside the greenhouse that
affects the greenhouse environment and consequently the
growing of cultivated plants. A control technique (PI
controller) is proposed to fix the greenhouse inside tem-
perature and relative humidity at the optimal values (i.e. ,
20˚C and 70% respectively) that are suitable for growing
of marjoram herb. The fine-tuned parameters of PI con-
troller are, Kp =10, KI = 0.0001, and Kp = 0.1, KI = 0.2
respectively.
The proposed cooling system temperature controller is
designed to adjust the air volume flow rate of the fan by
adjusting the speed of the fan motor in pad-fan system; to
fix the greenhouse inside temperature at 20˚C. On the
other hand, the humidity controller operates between
dehumidify and humidify modes for removing unwanted
atmospheric moisture accumulating within the green-
house or to add the needed moisture to the air by means
of humidification, to fix the greenhouse inside relative
humidity at 70%. Also, a mathematical modeling and
MATLAB SIMULINK model for the different compo-
nents of the evaporative cooling system is presented in
this paper.
REFERENCES
[1] K. S. Kumar, K. N. Tiwari and M. K. Jha, “Design and
Technology for Greenhouse Cooling in tropical and Sub-
tropical Regions: A Review,” Energy and Buildings, Vol.
41, 2009, pp. 1269-1275.
doi:10.1016/j.enbuild.2009.08.003
[2] C. Kittas, M. Karamanis and N. Katsoulas, “Air Tem-
perature Regime in a Forced Ventilated Greenhouse with
Rose Crop,” Energy and Buildings, Vol. 37, 2005, pp.
807-812. doi:10.1016/j.enbuild.2004.10.009
[3] R. A. Bucklin, J. D. Leary, D. B. McConnell and E. G.
Wilkerson, “Fan and Pad Greenhouse Evaporative Cool-
ing Systems,” University of Florida, Florida, 2010.
[4] Abdel-Ghany and A. M. Kozai, “Dynamic Modeling of
the Environment in a Naturally Ventilated, Fog-Cooled
Greenhouse,” Renewable Energy, Vol. 31, No. 10, 2006,
pp. 1521-1539. doi:10.1016/j.renene.2005.07.013
[5] A. Hughes, “Electric Motors and Drives Fundamentals,”
Types and Applications, Newnes, 2006.
[6] I. M. Al-Helal, “A Computational Fluid Dynamics Study
of Natural Ventilation in Arid Region Greenhouses,”
Ph.D. Thesis, The Ohio State University, Columbus, 1998.
[7] E. M. Ahmed, O. Abaas, M. Ahmed and M. R. Ismail,
“Performance Evaluation of Three Different Types of
Local Evaporative Cooling Pads in Greenhouses in Su-
dan,” Saudi Journal of Biological Sciences, Vol. 18, No.
1, 2011, pp. 45-51.
[8] A. Ganguly and S. Ghosh, “Modeling and Analysis of a
Fan-Pad Ventilated Floricultural Greenhouse,” Energy
and Buildings, Vol. 39, No.10, 2007, pp. 1092-1097.
doi:10.1016/j.enbuild.2006.12.003
[9] W. Bolton, “Control Engineering,” Longman Group, Har-
low, 1992.
[10] K. Ogata, “Modern Control Engineering,” Prentice-Hall
Inc., Englewood Cliffs, 1990.
[11] J. L. Guzmán, F. Rodríguez, M. Berenguel and S. Dor-
mido, “Virtual Lab for Teaching Greenhouse Climate
Control,” Proceedings of the 16th IFAC World Congress,
IFAC, Prague, 2005, pp. 2158-2163.
Copyright © 2012 SciRes. SGRE