# Energy-Efficient Wireless Communication Strategy for Precision Agriculture Irrigation Control
## 2 Precision Irrigation Control System
### Process Identification and Model Validation  
Soil moisture dynamics have complex non-linear behavior; however, a linear model can be approximated by identifying the main soil moisture regions delimited by the soil field capacity (FC) and crop permanent wilting point (PWP) thresholds. The FC refers to the level where the soil can no longer retain water, and the PWP is the limit where below this, the crop cannot absorb water from the crop. As shown in Figure 3, the FC and PWP define three soil moisture regions with different dynamics: gravitational water, available water, and unavailable water. To properly model the soil moisture dynamics, different values for the matrices \(\Phi\) and \(\Gamma\) must be identified appropriately in model Equation (4) for each region. The maximum  
Figure 1: Experimental pecan crop field with the sensor node locations illustrated with the red circles: (**a**) Area 1 lateral view; yellow arrows indicate the sensor placements. (**b**) Satellite view. Figure 2: Networked control system for precision agriculture irrigation. allowable depletion (MAD) is the reference value for crop irrigation typically located in the middle of the available water region; below this (negative soil moisture values), the crop will become water-stressed, while, above this (positive soil moisture values ), water may be wasted. Sensor node readings have been normalized to provide soil moisture measurements as a relative percentage value to this reference point. Over four weeks, irrigation, soil moisture, and reference evapotranspiration data were gathered at a sampling rate of 10 min, since, as suggested by [4], this represents, in practice, the minimum sampling time to capture the irrigation process dynamics. The obtained data was divided according to the soil moisture regions, and then coefficients values for \(\Phi\) and \(\Gamma\) were identified using the estimation algorithm proposed by [9] to model the process dynamics. Table 1 shows the obtained coefficients for each irrigation area. A new four-week dataset was acquired from the networked control system to validate the identified model. We compared the latest measured data with the estimated soil moisture values obtained from the model by using the correlation coefficient \(R^{2}\) defined as  
\[R^{2}=1-\frac{\sum_{i=1}^{n}(\theta_{i}-\hat{\theta}_{i})^{2}}{\sum_{i=1}^{n}( \theta_{i}-\bar{\theta})^{2}}, \tag{6}\]  
where \(\theta_{i}\) represents the soil moisture readings, \(\widehat{\theta_{i}}\) represents the model-based estimated values, \(\bar{\theta}\) is the mean value from all measurements, and \(n\), with a value of 4032, is the number of measurements for the validation period. Figure 4 shows the correlation between the estimated soil moisture values calculated from the state-space model (\(\bar{\theta}\)) and the measured soil moisture values obtained from the sensor readings (\(\theta\)). There was no automatic irrigation control during the validation process, and we applied irregular watering to cover the different soil moisture regions. Thus, during week 2, intensive irrigation shifted the moisture values to the gravitational \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Matrix** & **Region** & \multicolumn{2}{c}{**Coefficients**} & **Matrix** & **Region** & \multicolumn{2}{c}{**Coefficients**} \\ \hline \(\Phi\) & Gravitational & 0.98501 & 0.00001 & \(\Gamma\) & Gravitational & 0.00245 & \(-\)0.00004 \\  & 0.00001 & 0.98491 & & & 0.00300 & \(-\)0.00021 \\ \(\Phi\) & Available & 0.99998 & 0.00003 & \(\Gamma\) & Available & 0.00136 & \(-\)0.00062 \\  & 0.00001 & 0.98495 & & & 0.00324 & \(-\)0.00049 \\ \(\Phi\) & Unavailable & 0.99999 & 0.00002 & \(\Gamma\) & Unavailable & 0.00123 & \(-\)0.00005 \\  & 0.00001 & 0.98488 & & & 0.00151 & \(-\)0.00035 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Identified coefficient values for state–space model matrices according to the soil moisture region. Figure 3: Soil moisture dynamics for the different regions, figure obtained from [9].