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 (Ω),

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.

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Copyright © 2012 SciRes. SGRE