development of a dielectric sensor model for soil moisture ...

OPEN-SOURCE MODELICA-BASED MODELING AND SIMULATION
FOR MEASURING SOIL MOISTURE CONTENT
Alan Kardek Rêgo Segundo 1* , José Helvecio Martins 2 , Paulo Marcos de Barros
Monteiro 3
1 Assistant Professor, Department of Control and Automation, Federal University of Ouro
Preto, 611 Três Lagoas Street, ZIP 35400-000, Ouro Preto, MG, Brazil.
2 Professor, Department of Agricultural Engineering, Federal University of Viçosa, P.H. Rolfs
Avenue, University Campus, ZIP 36570-000, Viçosa, MG Brazil.
3 Associate Professor, Department of Control and Automation, Federal University of Ouro
Preto, 122 Paraná Street, ZIP 35400-000, Ouro Preto, MG, Brazil.
*Corresponding author. E-mail: alankardek@em.ufop.br
Abstract
The dielectric soil property can be used as a parameter to measure the soil moisture content,
because the dielectric constant of water is much larger than the dielectric constant of the
other soil components. Soil moisture sensor can be used to automate the traditional irrigation
systems based on real-time moisture content measurement. This paper reports on the
development of a dielectric sensing model based on the capacitive method. This model will
support a future hardware development and will be used for results comparison.
Key words: Capacitive sensor; Automation; Soil moisture; Irrigation; OpenModelica.
1. Introduction
Dielectric properties of materials are finding increasing applications in agriculture
(Nelson and Trabelsi, 2008). These applications have included the sensing of moisture
content in grain, legume, fruit and meat; radio-frequency and microwave dielectric heating for
pest control, product conditioning and seed treatment; and the sensing of soil moisture
content.
The irrigation management based on the monitoring of the soil moisture content
allows for the minimization of the amount of water applied, making its use more efficient.
The relative dielectric constant of water is about 80 at 20°C. On the other hand, the
dielectric constant of the others soil components are not larger than 10 (Silva, 2005).
Therefore, the soil moisture content can be predicted from the dielectric constant of the soil.
The capacitive method can be used to measure the dielectric constant of soil, where
the soil is the dielectric material localized between the plates of the sensor.
In an ideal capacitor the dielectric material located between its plates is an insulator.
However, there is no perfect insulator. Although it has high resistance to the flow of charge,
its value is finite.
So, in a real capacitor, there is a very small current that flows through your dielectric
material. Thus, its equivalent circuit can be modeled as an ideal capacitor in parallel with a
resistor (Salmazo et al., 2006).
The aim of this paper is to develop and study a capacitive sensing model which can
be used to measure the dielectric constant of soil to determine its water content. Two
situations were considered and compared: (i) the model includes the electrical conductivity of
soil; (ii) the model doesn’t include the electrical conductivity soil.

2. Materials and methods
To predict the relative dielectric constant and the electrical conductivity, it is needed
to measure the current flow through the sensor, the phase angle between the current and
voltage, and the voltage at the sensor output. Therefore, to measure the current in the circuit,
it was needed to insert a known resistor, R
2
, in series with the sensor (Figure 1).
Figure 1 – Circuit designed to predict the complex permittivity.
The admittance, G, and the susceptance, B, of the sensor can be determined
mathematically, from the voltages (V 1 and V 2 ) and the difference phase between them,
allowing predicting the relative dielectric constant. The vector’s diagram for the circuit
designed to predict the complex permittivity (Figure 1) is presented in Figure 2.
Figure 2 – Vector’s diagram for the circuit designed to predict the complex permittivity.
The capacitive part of the sensor causes a phase difference between the source
voltage and the total current flow (Figure 3). The phase of the voltage at the resistor R
2
is
the same as the current flow.
Figure 3 – Phase difference between the source voltage (in black) and the voltage at the
resistor R
2
(in red).

The impedance of the resistive part of the sensor is much smaller than the impedance
of the capacitive part for low frequencies. This decreases the sensibility not only of the phase
difference change between voltage and current but also of the changes in voltage at the
sensor’s output. Furthermore, hardware for high frequency is often more expensive and its
project is more complex. Thus, an alternative solution is adding an insulator to the plates of
the sensor.
It was considered, just for simulation, that the resistance of the insulator is equal to
500 k . But it will depend on the material and its thickness.
OpenModelica was chosen to simulate this circuit because it is a free Object-Oriented
language. Besides, it is a fast-growing area of modeling and simulation that provides a
structured, computer-supported way of doing mathematical and equation-based modeling.
Nowadays, Modelica is the most promising modeling and simulation language in that it
effectively unifies and generalizes previous object oriented modeling languages and provides
a sound basis for the basic concepts (Fritzson, 2006).
In the present work there were assembled four model types: (i) Soil Model; (ii) A
Resistive Model for the resistive part of the sensor; (iii) A Capacitive Model for the capacitive
part of the sensor; and (iv) A Circuit Model.
For the Soil Model, it was used the relationships not only between soil moisture
content and soil conductivity but also between soil moisture content and relative dielectric
constant of the soil found by Santos (2008) for a specific type of soil, as described by
Equations 1 and 2.
26.36 0.101
(1)
( ) 5.01 2
21.32 5.717 (2)
r
where:
-
1
Soil’s conductivity, Sm .
3 3
- Soil’s water content, m m .
- Relative material dielectric constant.
r
It was considered that the sensor is a parallel plates’ capacitor with soil as the
dielectric material between its plates. The distance between its plates was considered equal
2
to 0.002 m , and its area equal to 0.010 m .
Only for simulation purpose, the soil moisture content was supposed to vary with time
3 3
3 3
according to the Equation 3, from 0.06 m m to 0.40 m m .
0.34t 0.06 (3)
For the Resistive Model, it was considered that the resistive part of the sensor varies
according to the conductivity of the soil.
For the Capacitive Model, it was considered that the capacitive part of the sensor
varies according to the relative dielectric constant of the soil.
The Circuit Model is the same as that in the Figure 1. Furthermore, for this model, it
was implemented algorithms to determine the root mean square (RMS) values of the
voltages, and determine the phase angle between them. Thus, the relative dielectric constant
of the soil was predicted from these values.
The RMS value of the sinusoidal signal is defined by Equation 4.
Vp
Vrms
(4)
2
where:
V - Root mean square of the sinusoidal voltage signal, V .
rms
V - Peak value of the sinusoidal signal, V .
p

The peak value was calculated by the first derivative of the signal. When it is around
zero, the signal is around the peak value. Thus, this maximum value was divided by the
square root of two. When the algorithm records the peak value, it is also recorded the value
of time. Thus, the phase of the signal is calculated from the difference of two consecutive
peak times. Other models were used from Modelica’s Library, such as Source, Resistor and
Ground Model.
The frequency and the amplitude of the voltage source used in simulations were
1 kHz and 10 V , respectively.
A comparison was made between the dielectric constant predicted by this model and
the dielectric constant estimated by a model that does not consider the electrical conductivity
of the soil. This means that the resistor in parallel with the capacitor in the sensor model was
not considered in this case.
3. Results and discussion
The results are presented in the following figures and discussed further.
In the Figure 4 it is represented the changes in the root mean square voltage at the
sensor output over time. It can be observed that when the soil water increases the voltage at
the sensor output decreases, because the impedance of the sensor also decreases.
Figure 4 – Changes in root mean square voltage at the sensor output.
In the Figure 5 it is shown the phase angle variation of the voltage at the resistor
(which has the same phase as the total current) and of the voltage at the sensor.
Figure 5 – Phase of the voltage at the resistor R
2
(in red) and the phase of the voltage at the
sensor (in black).
The predicted variation of the relative dielectric constant of the soil is represented in
the Figure 6. It should be observed that the relationship between the predicted dielectric
constant of the soil and time is not linear (Equation 2), although it apparently seems to be.

Figure 6 - Predicted variation of the relative dielectric constant of the soil.
The correlation between the relative dielectric constant of soil model and the
predicted relative dielectric constant of the soil is shown in the Figure 7. It was obtained an
almost perfect correlation between them, with an uncertainty equals 0.356 , considering
95% of probability of occurrence of random error, that is, two standard deviations for more or
for less in relation to the estimated value of the dielectric constant of the soil.
Figure 7 – Correlation between measured and predicted dielectric constants.
The correlation between the relative dielectric constant of soil model and the
predicted relative dielectric constant of the soil, neglecting the electrical conductivity effect of
the soil, is shown in the Figure 8. It was obtained a very good correlation between them, with
an uncertainty equals 0.537 , also considering 95% of probability
Figure 8 – Correlation between measured and predicted dielectric constants neglecting the
electrical conductivity effect of the soil.

The circuit for measuring the dielectric constant of soil is simpler and cheaper than
the circuit which measures the electrical conductivity and dielectric constant of soil. In
addition, the electrical conductivity is an important parameter for the crop, because it has
high correlation with soil salinity.
4. Conclusions
The following conclusions were drawn based on the results of this work:
The models allow a better understanding about capacitive sensors.
The OpenModelica has proven to be a powerful tool to simulate physical models.
The dielectric constant of the soil can be predicted from the proposed circuit.
Neglecting the electrical conductivity of the soil increases the uncertainties in measurements.
References
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Acknowledgements
The authors would like to thank the Foundation for Support to Research of the State
of Minas Gerais - FAPEMIG, Brazil; the National Council of Scientific and Technological
Development – CNPq, Brazil; Coordination of Improvement of Higher Education Personnel –
CAPES, Brazil; the Federal University Federal of Ouro Preto, Brasil; and the Gorceix
Fundation, Brazil, for their financial support, and the Federal University of Viçosa, Brazil, for
the great opportunity.