4. Set-point manipulation for optimum climate control

#### 4.1. Critical reference borders

The comfort ratio curve, denoted by Cf t- curve, refers to the plot of Cf tðM, t, αs) values calculated for all α<sup>s</sup> ¼ 0 : d<sup>α</sup> : 1. It shows how much close a microclimate parameter can be controlled to different preferred reference borders. The horizontal blue-dashed line at Cf tð Þ¼ M, t, α<sup>s</sup> 1 represents 100% satisfied control objective; that is, parameter M is always inside reference borders of αs. The Cf t- curve can be used as a tool to demonstrate the behavior of Cf tðM, t, αs) in different greenhouses or at different cultivation days for decision making in set-point manipulation for the climate controller. For example, it can be used in finding the largest α<sup>s</sup> for which Cf t M, t, ð Þ¼ α<sup>s</sup> 1 (in other words, finding αmax corresponding to the narrowest achievable reference border by the climate controller). An example is provided in Figure 15 by plotting air temperature response for 2 consecutive days of an experiment inside a tropical greenhouse. It can be observed that the narrowest reference borders of air temperature that was completely satisfied by the climate controller in these two days are, respectively, equal to α<sup>s</sup> ¼ 0:55 and α<sup>s</sup> ¼ 0:67. After these points, comfort ratio starts decreasing until it arrives at its lowest value of 0.42 for both days at α<sup>s</sup> ¼ 1.

Another application of the Cf t- curve includes finding critical reference borders, denoted by αCrit at which Δ ¼ Cf tð Þ� M, t, α<sup>s</sup> Cf tð Þ M, t, α<sup>s</sup> þ E is maximum (reference borders that cause significant loss in comfort ratio). To further explain, comfort ratios of air temperature for two distinct cases are plotted in Figure 16. In the first case, increasing α<sup>s</sup> from 0.3 to 0.65 has not caused significant loss in the resulting comfort ratio. The values of Cf t T, t, ð Þ 0:3 and Cf t T, t, ð Þ 0:75 for this case are nearly the same and equal to 0.8 and 0.77. In other words, by increasing α<sup>s</sup> from 0.3 to 0.75 to provide air temperature response that is more favored by tomato plants, performance of the controller in achieving the extra accuracy was not decreased. In a greenhouse with natural ventilation, this means that the extra 0.35 increase in α<sup>s</sup> comes at no cost (no significant loss of response). In the case of an energy-consuming climate controller (i.e., pad-and-fan-evaporative system or swamp cooler), it means that the

Figure 15. Comparison between air temperature responses from a tropical greenhouse in 2 days of experiment showing raw data (left), and comfort ratios (right). The controller did not satisfy 100% optimal references.

Adaptive Management Framework for Evaluating and Adjusting Microclimate Parameters in Tropical Greenhouse… http://dx.doi.org/10.5772/intechopen.69972 185

Figure 16. Comparison between comfort ratios versus α<sup>s</sup> in 2 days of experiment in a greenhouse with evaporative cooling system for demonstration of αCrit. Left: significant increase in α<sup>s</sup> from 0.3 to 0.75 resulting in significant loss in Cft, right: slight increase in α<sup>s</sup> from 0.7 to 0.75 causing significant loss in Cft.

cooler can be set to maintain air temperature inside a narrower reference border (by selecting α<sup>s</sup> ¼ 0:75 rather than 0.3) without imposing additional energy cost. On the right plot of Figure 16, this situation is, however, different. Significant loss in Cf t T, t, ð Þ α<sup>s</sup> can be observed for a slight increase from α<sup>s</sup> ¼ 0:7 to α<sup>s</sup> þ E ¼ 0:75. Here, increasing α<sup>s</sup> for as little as 0.05 has led to a sudden drop in the comfort ratio by 50% (from 1 to 0.5). The α<sup>s</sup> at which the largest loss appear is referred to αCrit and can be calculated by differentiating Cf t -curve with respect to α as αcrit ¼ d=dαð Þ Cf tð Þ M, t, α .

#### 4.2. Performance of climate controller

4. Set-point manipulation for optimum climate control

arrives at its lowest value of 0.42 for both days at α<sup>s</sup> ¼ 1.

The comfort ratio curve, denoted by Cf t- curve, refers to the plot of Cf tðM, t, αs) values calculated for all α<sup>s</sup> ¼ 0 : d<sup>α</sup> : 1. It shows how much close a microclimate parameter can be controlled to different preferred reference borders. The horizontal blue-dashed line at Cf tð Þ¼ M, t, α<sup>s</sup> 1 represents 100% satisfied control objective; that is, parameter M is always inside reference borders of αs. The Cf t- curve can be used as a tool to demonstrate the behavior of Cf tðM, t, αs) in different greenhouses or at different cultivation days for decision making in set-point manipulation for the climate controller. For example, it can be used in finding the largest α<sup>s</sup> for which Cf t M, t, ð Þ¼ α<sup>s</sup> 1 (in other words, finding αmax corresponding to the narrowest achievable reference border by the climate controller). An example is provided in Figure 15 by plotting air temperature response for 2 consecutive days of an experiment inside a tropical greenhouse. It can be observed that the narrowest reference borders of air temperature that was completely satisfied by the climate controller in these two days are, respectively, equal to α<sup>s</sup> ¼ 0:55 and α<sup>s</sup> ¼ 0:67. After these points, comfort ratio starts decreasing until it

Another application of the Cf t- curve includes finding critical reference borders, denoted by αCrit at which Δ ¼ Cf tð Þ� M, t, α<sup>s</sup> Cf tð Þ M, t, α<sup>s</sup> þ E is maximum (reference borders that cause significant loss in comfort ratio). To further explain, comfort ratios of air temperature for two distinct cases are plotted in Figure 16. In the first case, increasing α<sup>s</sup> from 0.3 to 0.65 has not caused significant loss in the resulting comfort ratio. The values of Cf t T, t, ð Þ 0:3 and Cf t T, t, ð Þ 0:75 for this case are nearly the same and equal to 0.8 and 0.77. In other words, by increasing α<sup>s</sup> from 0.3 to 0.75 to provide air temperature response that is more favored by tomato plants, performance of the controller in achieving the extra accuracy was not decreased. In a greenhouse with natural ventilation, this means that the extra 0.35 increase in α<sup>s</sup> comes at no cost (no significant loss of response). In the case of an energy-consuming climate controller (i.e., pad-and-fan-evaporative system or swamp cooler), it means that the

Figure 15. Comparison between air temperature responses from a tropical greenhouse in 2 days of experiment showing

raw data (left), and comfort ratios (right). The controller did not satisfy 100% optimal references.

4.1. Critical reference borders

184 Plant Engineering

Plots of measured optimality degrees of a response parameter, denoted by Optð Þ¼ M αy, corresponding to the preferred α<sup>s</sup> reference borders can provide a useful graphical tool to monitor performance of the climate control system. For the sake of demonstration, Cf t- curves and performance curves of the climate controller for T, RH, and VPD are shown in Figure 17. For a perfectly control task with a preferred αs, the control system must achieve microclimate parameter M that has optimality degree of at least αs. For example, if reference borders of air temperature control are set at α<sup>s</sup> ¼ 0:8, it is expected that the optimality degree of air temperature response inside the greenhouse is at least α<sup>y</sup> ¼ 0:8 at any measured time. As mentioned earlier, in a 100% perfectly controlled greenhouses, the measured optimality degrees are at least equal to the preferred optimality degrees of the reference border (α<sup>y</sup> ¼ αs). This is shown by the perfect control line (line of α<sup>y</sup> ¼ α<sup>x</sup> ) on the response plot of Figure 17. It should be noted that α<sup>y</sup> can also be calculated by integrating Cf tð Þ M, t, α curve over α ¼ 0 to α ¼ α<sup>s</sup> (Eq. (6)), indicating that α<sup>y</sup> is equal to α<sup>s</sup> only when Cf tð Þ¼ M, t, α<sup>s</sup> 1. In other words, performance of a climate control system in achieving preferred reference borders of M is considered 100% perfect only when 100% of M-response falls inside the α<sup>s</sup> preferred optimal reference borders.

In controlled greenhouses, both Cft curve and performance curve provide a graphical assessment tool for comparing different control strategies and scenarios (i.e., microclimate responses due to different greenhouse designs, cooling systems, and covering materials at different

Figure 17. Comfort ratio of microclimate parameters (left) and response of the climate controller (right) at 0 ≤ α<sup>s</sup> ≤ 1.

growth stages). The performance curve in fact reveals how much a greenhouse microclimate parameter deviates from a perfectly controlled response. Deviation of the greenhouse from this ideal line at any α<sup>s</sup> can be used as an index factor of the perfect climate control task. The lesser deviation means the more perfect control task. Adaptability factor of the controller for microclimate parameter M at a preferred αs, denoted by ADPðM, αsÞ, is then defined as the ability of the controller to adapt itself with different preferred references and is calculated using Eq. (7).

#### 4.3. Optimum reference borders

The optimum preferred reference border for parameter M, denoted by αOpt, is defined as the largest possible α<sup>s</sup> value for which the largest Cf tð Þ M, t, α can be achieved. In other words, it is the value of an unknown α<sup>i</sup> for which Cf tð Þ¼ M, t, α<sup>i</sup> β<sup>i</sup> has the minimum distance to Cf tð Þ¼ M, t, 1 1. In that sense, the cost function for this optimization problem is defined as Di ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ <sup>α</sup><sup>i</sup> � <sup>1</sup> <sup>2</sup> <sup>þ</sup> <sup>β</sup><sup>i</sup> � <sup>1</sup> � �<sup>2</sup> <sup>q</sup> , which is the Euclidean distant between the unknown point (α<sup>i</sup> and β<sup>i</sup> ) on the Cft curve and the point of ideal microclimate (α ¼ 1 and β ¼ 1). The objective is

Figure 18. Demonstration of the algorithm for finding optimum preferred reference border for adjusting the climate controller. Data belongs to VPD response from a random data collection day in a tropical greenhouse experiment.

therefore to minimize this cost function by finding 0 ≤ α<sup>i</sup> ≤ 1 value that leads to the shortest Euclidean distant (minimum Disti) to the Cf tð Þ¼ M, t, 1 1. An example is demonstrated in Figure 18 for VPD response in a random day of experiment with αOpt ¼ 0:77. The plot on the right side of Figure 18 shows the values of Di versus 0 ≤ α<sup>i</sup> ≤ 1, and the position of αOpt is shown as the global minimum point.
