Precise measurements and control of the position of the rolling shutter and rolling film in a solar greenhouse

Journal of Cleaner Production 228 (2019) 645e657

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Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro

Precise measurements and control of the position of the rolling shutter and rolling film in a solar greenhouse Guoxiang Zhang a, Xingxing Liu a, Zetian Fu a, b, Stevan Stankovski c, Yuhong Dong a, Xinxing Li a, b, * a b c

China Agricultural University, Beijing, 100083, PR China Beijing Laboratory of Food Quality and Safety, Beijing, 100083, PR China University of Novi Sad, Novi Sad, 21000, Serbia

a r t i c l e i n f o

a b s t r a c t :

Article history: Received 2 July 2018 Received in revised form 10 April 2019 Accepted 11 April 2019 Available online 25 April 2019

Against the background of the depletion of fossil fuel energy sources and environmental degradation, solar greenhouses represent an efficient and sustainable agricultural production method in China. The precise measurement and control of the position of the rolling shutter and rolling film is not only one of the core issues in the modification of the greenhouse environment in actual production but also the basis for improving the cleaner production efficiency of solar greenhouses. In this study, a mathematical algorithm for the control of a rolling shutter and rolling film was developed and is based on the simplification of the circular arc of the greenhouse surface. The “Liaoshen-IV” solar greenhouse was used as an example to illustrate the calculation steps of the algorithm. Any position on the light surface can be determined by calculating the angle at the bottom of the back wall of the greenhouse so that the position of the rolling shutter and the rolling film can be measured accurately by the angle sensor. Experiments using a scale model with one or two surface segments were conducted to demonstrate the advantages of the control algorithm with regard to the accuracy and stability compared with the existing control method of a time-delay relay. The relative errors of the control algorithm were stable and less than 1%. The use of the algorithm improved the control accuracy of the rolling shutter and rolling film and the average relative error was reduced by 6.37% in the first stage and by 3.40% in the second stage compared with the time-delay relay. The precise measurement and control of the position of the rolling shutter and rolling film in a solar greenhouse demonstrated in this study has great significance for practical applications. The proposed method may result in a reduction in energy consumption and greenhouse gas (GHG) emissions in greenhouse environments, thereby contributing to the improvement of resource efficiency and a cleaner production. The study also provides application examples and theoretical references for the automation of rolling shutters and rolling film in greenhouses worldwide. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Solar greenhouse Simplification Mathematical algorithm Scale model Accuracy and stability

1. Introduction Increasing resource efficiency is a key element of cleaner production and one measure is to reduce the fuel input while maintaining the same product output (Spinelli et al., 2018). Against the background of the depletion of fossil fuel energy sources and environmental degradation, solar greenhouses represent an

* Corresponding author. China Agricultural University, Beijing, 100083, PR China. Tel.: þ861062737653. E-mail addresses: [email protected] (G. Zhang), liuxingxing56285@ 163.com (X. Liu), [email protected] (Z. Fu), [email protected] (S. Stankovski), [email protected] (Y. Dong), [email protected] (X. Li). https://doi.org/10.1016/j.jclepro.2019.04.129 0959-6526/© 2019 Elsevier Ltd. All rights reserved.

efficient and sustainable agricultural production method in China (Wei et al., 2012; Zhang et al., 2017a). In 2012, the area covered by greenhouses in China (including multi-greenhouses, solar greenhouses, plastic houses) was 3.79 Mha and solar greenhouses covered an area of 0.928 Mha, comprising 24.5% of the total greenhouse area (Yuan et al., 2013). A large number of solar greenhouses influences the environment in the region; solar greenhouse construction has been supported by the Chinese government because of the goals of carbon mitigation and the reduction in greenhouse gas (GHG) emissions worldwide (Ma et al., 2018). The precise measurements and control of the position of the rolling shutter and rolling film is a core issue in the modification of the greenhouse environment, as well as the basis for improving the

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cleaner production efficiency of solar greenhouses. Rolling shutters and rolling films are materials used for covering solar greenhouses and represent an important component of solar greenhouses. In a solar greenhouse, the solar energy is absorbed by the back wall in the daytime and heat is released at night (Guan et al., 2012). By changing the position of the rolling shutter, the amount of light entering the greenhouse and the temperature are controlled to maintain an appropriate indoor temperature for growing crops (Liu et al., 2015; Zhang et al., 2017b). For example, Tong et al. (2010) demonstrated that the position of the rolling shutter of a solar greenhouse during the daytime affected the solar energy transmitted into the greenhouse and the heat dissipation through the light surface, thereby affecting the indoor temperature. In a solar greenhouse, the rapid exchange of energy and materials (such as heat, water vapor, and CO2) with the external environment are achieved through the natural ventilation of the upper and lower vents (Zhang et al., 2012; Bartzanas et al., 2013). The efficiency of natural ventilation is controlled by the position of the rolling film because it controls the opening of the upper and lower vents (Khaoua et al., 2006; Romero et al., 2006). For example, Fu and You (2013) demonstrated that the air temperature and humidity could be controlled by changing the position of the rolling film using an experiment in a solar greenhouse used for strawberry production. In the review by Bournet and Boulard (2010), it was stated that the ventilation processes strongly affect the air exchange and internal climatic conditions, thereby influencing the growth and homogeneity of the crop. Adjustments of the position of the rolling shutter and rolling film significantly impacted the production efficiency of solar greenhouses. Optimal adjustments can reduce energy consumption and GHG emissions in greenhouse operations (Ma et al., 2019). The complex shapes of different light surfaces represent a problem for improving the accuracy of the measurements and the control of the position of the rolling shutter and rolling film. The rolling shutter and rolling film cover the light surface of a solar greenhouse and the machines controlling the rolling shutter and rolling film in solar greenhouses are similar in working principle, structure, and type (Ding, 2011). When solar greenhouses were first developed, the shape of the light surface was a smooth plane. By the 1970s, the shape of the surface had changed to a circular arc, which improves the lighting conditions for the crops in the solar greenhouse (Wei et al., 2012). The circular arc is the most common shape of the light surface of solar greenhouses. (Zhang et al., 2014). There are optimal designs for the surface shape with regard to illumination and support and the shape has been simplified into different types of geometric curves (Tong et al., 2013). For example, Wang et al. (2010) compared the bearing loads and total sunlight permeation of four roof shapes (triple spline, circular, ellipsoid, and parabolic). Solar greenhouses exhibit large differences in the architectural design in different areas, i.e., different geographical locations require different surface shapes. Zhang and Zou (2017) investigated the relationship between the angle of incline of the lighting surface and the transmitted light intensity. The surfaces of solar greenhouses in China are quite complex, which makes the precise measurement and control of rolling shutters and rolling film difficult for the operators (Ma et al., 2013). Generally, the control of the rolling shutter and rolling film is relatively simplistic and lacks direction; the operator either opens or closes the film and shutters completely (Zhang et al., 2016). As a result, the use of rolling shutters and rolling film does not always have positive impacts on the environment inside the solar greenhouse (Kong and Su, 2015; Villagran et al., 2012). Many studies have been conducted on the measurement and control of the position of rolling shutters and rolling film. The conventional method for controlling the position of rolling shutters

and rolling film is a mechanical limit switch. Mechanical limit switches were used in the rear fixed-type rolling shutter device designed by Zhang et al. (2016) to limit the position of the shutter. The stop or start of the rolling shutter and rolling film can only be achieved in specific positions and complex control cannot be achieved. The position of the rolling shutter and rolling film can be controlled by the running time, which is a widely used approach because of its good applicability and simple operation for various shapes of the light surface (Zhang et al., 2012). In the automatic intelligent rolling shutter system designed by Wang and Li (2014), the position of the rolling shutter is controlled by using a timedelay relay. In theory, it is an open-loop control method (without feedback) so that it is difficult to respond to and eliminate the errors in time. This is a disadvantage and requires manual correction. Many other measurement and control technologies have been used to control the position of the rolling shutter and rolling film. For example, Fan et al. (2015) used a near-infrared sensor for this purpose and achieved good control accuracy. Angle sensors can also be used to control the position of the rolling shutter and rolling film. Wang (2016) proposed the use of angle sensors to position the rolling shutter in a solar greenhouse but the study did not provide sufficient theoretical background and discussion on the influence of different shapes of the light surface. In this study, a mathematical algorithm for the control of a rolling shutter and rolling film was developed and is based on the simplification of the circular arc of the greenhouse surface. The accuracy and stability of the proposed algorithm were evaluated using comparative experiments with a system with a time-delay relay. Any position on the light surface can be determined by calculating the angle at the bottom of the back wall of the greenhouse so that the position of the rolling shutter and the rolling film can be measured accurately by the angle sensor. This method provides effective feedback to achieve high-precision control of the rolling shutter and rolling film and has great value and significance for practical operations. The high-precision adjustment provides optimal control of the greenhouse environment, improves resource efficiency, and allows for cleaner production. The remainder of the paper is organized as follows. The basic principles of the algorithm are described in Section 2. The materials and methods for the comparison experiment of the time relay and control algorithm are discussed in Section 3. The performance evaluation results of the control algorithm are described in Section 4. The conclusions and future work are presented in Section 5. 2. Theory In this study, a mathematical algorithm is developed for the precise measurement and control of the rolling shutter and rolling film in a solar greenhouse. This section presents the theoretical background on the simplification of the light surface of a solar greenhouse. The “Liaoshen-IV” solar greenhouse was used as an example and the light surface was simplified to one and two circular arc. In section 2.1, the calculation steps of the mathematical algorithm for the simplification of one circular arc are explained; in section 2.2, the calculation for the simplification of two circular arcs is described; in section 2.3, the algorithm of the simplification into three segments is used as an example for the generalization of the algorithm (Fig. 1). 2.1. Mathematical algorithm for simplifying the light surface to one circular arc 2.1.1. Division and simplification of the light surface The “Liaoshen-IV” solar greenhouse is a common type of

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Fig. 1. Diagram of the calculation steps of the mathematical algorithm.

greenhouse used in China's northern areas (Wei et al., 2012). The rolling shutter and rolling film on the light surface are shown in Fig. 2. The surface of the solar greenhouse was simplified to a circular arc and the structure of the solar greenhouse was reduced to a simple geometric model, as shown in Fig. 2. It is evident from Fig. 2 that the width of the solar greenhouse is greater than the height and the shape of the surface is not a complete 1/4 round. The center and the radius of the circular arc cannot be measured directly and are determined by considering the geometry of the structure and performing mathematical calculations to ascertain the position of the rolling shutter and rolling film on the surface of the solar greenhouse. 2.1.2. Determination of the center of the circular arc corresponding to the surface As shown in Fig. 3, bc represents the height of the rear wall of the solar greenhouse, ce represent the width at the ground. a is the highest point of the greenhouse and represent the upper limit for

the movement of the rolling shutter or rolling film. ad is perpendicular to ce. q (the unit is radian,p/4q
Fig. 2. Photos of the Chinese solar greenhouse and a graphic simplification of the Liaoshen IV solar greenhouse.

(1)

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between ad and dg, which can be obtained by using angle sensors installed on the auxiliary support. b is the central angle of the circular arc ag, which is variable in this study. The units of a and b are radian and meet conditions 0
l2 ¼ ðp  2q  bÞ  R

(6)

The equation for determining the opening size of the rolling shutter and rolling film is:

K¼

l2 ðp  2q  bÞ  R p  2q  b ¼ ¼ 2  ð p2  qÞ  R l p  2q

(7)

where K is the opening size of the rolling shutter and rolling film. Fig. 3. Geometric diagram of the solar greenhouse.

R¼

1S 2

1S S2 ¼ 2H ¼ cosq 2H S

2.1.4. Determination of the position of the rolling shutter and rolling film Based on the sine theorem:

(2)

From the above formula, R can be obtained. Based on the Pythagorean theorem, S can be obtained by calculating:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S ¼ H 2 þ L2

(3)

The arc length of the circular arc corresponding to the entire surface is obtained by:

l¼2ð

p 2

 qÞ  R ¼ ðp  2qÞ  R

(4)

The angle q can be measured directly or obtained by calculation.

q ¼ arctan

L H

(5)

2.1.3. Equation to determine the opening size of the rolling shutter and rolling film In Fig. 4, dg is the auxiliary support, g is the position of the rolling shutter or rolling film on the surface. a is the acute angle

R RH ¼ sinðp  aÞ sinða  bÞ

(8)

The relationship between b and a is:



b ¼ a  arcsin

1

  H sina R

(9)

where H can be directly measured and are considered known quantities. R can be obtained by calculation of Eq. (2). a will be obtained by using angle sensors. The opening size of the rolling shutter and rolling film is obtained by:



p  2q  a þ arcsin 1 

l2 p  2q  b ¼ ¼ l p  2q p  2q  R  H sina p  2q  a þ arcsin R ¼ p  2q p  2q  a þ arcsinðcosðp  2qÞsinaÞ ¼ p  2q K¼

  H sina R

(10) The specific position of the rolling shutter and rolling film can be determined from Eq. (10). 2.2. Mathematical algorithm for simplifying the light surface to two circular arcs

Fig. 4. Structure diagram for rolling shutter or rolling film on the circular arc ae.

The light surface of the solar greenhouse can also be simplified to a shape consisting of two circular arcs. The proposed mathematical algorithms can be applied and the different positions on the surface can be calculated, as shown in Fig. 5. In Fig. 5, the surface is simplified to two circular arcs. The point m is the common node (split point) of the two circular arcs. l3 is the arc length of the circular arc am and l4 is the arc length of the circular arc em. The two circular arcs have different centers and radius. b1 and R1 are the central angle and radius corresponding to the circular arc am. b’1 is the central angle corresponding to the circular arc aq. b2 and R2 are the central angle and radius corresponding to the circular arc em. b’2 is the central angle corresponding to the circular arc ep. a1 and a2 can be obtained by using angle sensors installed on the auxiliary support.

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q1 ¼ arctan

649

L1 h1

(14)

Based on the sine theorem:

R1 R1  H  ¼ sinðp  a1 Þ sinða1  b1 0

(15)

The relationship between b1’ and a1 is obtained by:



b1 0 ¼ a1  arcsin ¼ a1  arcsin

Fig. 5. Structure diagram for simplifying the light surface to two circular arcs.

2.2.1. The position of the rolling shutter and rolling film on the circular arc am In Fig. 6, same as above, the location of the rolling shutter on the circular arc am is determined. A straight line is drawn perpendicular to line segment am through the midpoint of am, and crossing the ad extension line at O1. The point O1 is regard as the center of circular arc am and R1 (the radius of the circular arc am) can be obtained. 1S h 1 cosq1 ¼ 2 ¼ 1 R1 S1

R1 ¼

1S S2 2 1 ¼ 1 cosq1 2h1

(11)

(12)

R1 is obtained from Eq. (12). Based on the Pythagorean theorem, S1 (the length of line segment am) can be obtained by:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S1 ¼ h21 þ L21

2h1 sinðp  a1 Þ S21



S21 H 2h1

!! (16)

where a1,H, S1, and h1 can be directly measured and are considered known quantities. a1 and b1’ meet conditions 0




b2  R2 þ （b1  a1 þ arcsin sinR1a1 ðR1  HÞ ）  R1 K¼ b2  R2 þ b1  R1

(17)

2.2.2. The position of the rolling shutter and rolling film on the circular arc em In Fig. 7, same as above, the location of the rolling shutter on the circular arc em is determined. A straight line is drawn perpendicular to line segment em through the midpoint of em, and crossing the de extension line at O2. The point O2 is regard as the center of circular arc em and R2 (the radius of the circular arc em) can be obtained. L2 is the horizontal distance between points e and m. S2 is the length of line segment em. Based on the above calculations: 1S L 2 cosq2 ¼ 2 ¼ 2 R2 S2

(13)

The angle q1 can be measured directly or obtained by calculation.

sinðp  a1 Þ ðR1  HÞ R1

R2 ¼

1S 2 2

cosq2

¼

S22 2L2

(18)

(19)

In Eq. (19), S2 and L2 can be directly measured and are considered known quantities. Based on the sine theorem:

L  R2 R2 ¼ sinðb2 0  a2 Þ sina2

(20)

The relationship formula between b2’ and a2 is obtained by:

Fig. 6. Structure diagram of the rolling shutter or rolling film on the circular arc am.

Fig. 7. Structure diagram of the rolling shutter or rolling film on the circular arc em.

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b2 0 ¼ arcsin



 sina2 ðL  R2 Þ þ a2 R2

(21)

The position of the rolling shutter and rolling film on the circular arc em is obtained by:

K¼

（arcsin



sina2 R2



ðL  R2 Þ þ a2 ）  R2 b2  R2 þ b1  R1

(22)

2.3. Generalization of the mathematical algorithm Another simplified scheme is considered, the light surface of the solar greenhouse can also be simplified to a shape consisting of more than two circular arcs. The proposed mathematical algorithms can be applied to other similar simplified schemes and the different positions on the surface can be calculated, as shown in Fig. 8. The crux of the mathematical algorithm is determining the center of the circular arcs based on the graphic simplification. As shown in Fig. 8, the surface was simplified into three segments of circular arcs. The points j and t are the common nodes (split points) of the three segments. O1, O2, and O3 are the centers corresponding to the three segments. The positions meet the following conditions: O1 is located on the extension of the line segment ad; O3 is located on the line segment de; O2 is located on the extension of the line segment O3t. Subsequently, the radius and the corresponding formulas can be obtained (the calculations are similar to those in section 2.1 and section 2.2). If the surface was simplified to n segments, the position needs to meet the following conditions: On (the center of the nth circular arc, n is an integer and is greater than 3) is located on the horizontal line at the bottom of the solar greenhouse. On-1 (the center of the (n-1)th circular arc) is located on an extension line with On and the common node (between the nth circular arc and (n-1)th circular arc). In this manner, the equation for the desired position can be obtained and the position on the surface can be determined. In theory, it is possible to create similar simplified graphs for various types of light surfaces. The equations can be derived based on the aforementioned calculation steps so that the position of the rolling shutter

and rolling film of the solar greenhouse can be determined for other greenhouse surface shapes. 3. Materials and methods Scale models of the “Liaoshen-IV” solar greenhouse were developed and a time relay control method was used to determine the accuracy and stability of the algorithm. Scale models with the simplified light surface were created and the core algorithm programs were established. The experiments included two stages and the time delay programs represented the control group. In the experimental group, the core algorithm programs were input into the SCM of the control circuit system; the key parameters (q, b1, and b2) were slightly adjusted to improve the accuracy and stability of the control method, as shown in Fig. 9. 3.1. Scale models of solar greenhouse In the experiment, the advantages of the application of the mathematical algorithm are demonstrated. The surface was simplified to one or two circular arcs. The scale model was designed using AutoCAD (drawing software) and PVC boards were produced by a cutting machine. The greenhouse surface was supported by two boards on the sides of the scale model, as shown in Figs. 2e6. The verification of the algorithm is based on the correct structure of the model. In principle, the scale of the model has a negligible effect on the experimental results. Considering the convenience of measurement and installation, a 1:20 scale was used for the model. The maximum height of the scale model was 250 mm and the width was 600 mm. For the installation of the angle sensor and auxiliary support, additional height (50 mm) was added to the three vertical boards. The main body of the scale model consists of PVC boards (the thickness is 12 mm). The surface was simplified to one and two circular arcs (Fig. 10). The scale model has an aluminum frame and is covered with plastic film (the thickness is 0.8 mm). The auxiliary support consists of aluminum tubes installed on the right side of the scale model. A deceleration motor is installed on top of the auxiliary support. The deceleration motor is the power source of the scale model and connects the rolling pole and auxiliary support. The model of the deceleration motor is 634JSX101-31ZY (DC12 V, 5000/50 rpm). An angle sensor (RV24YN20S, 10 KU, resistance tolerance: ±5%; mechanical angle: 300 ±5 ; electrical angle: 300 ±10 ) is installed at the bottom of the auxiliary support and is positioned vertically at the maximum angle. The angle sensor was adjusted to a suitable linear range before the test to ensure that the linear changes could occur during the rotation of the auxiliary support (Fig. 11). 3.2. Control circuit for the position of the rolling film in a solar greenhouse

Fig. 8. Structure diagram of the surface simplified to three segments.

A single chip computer (SCM) was used as the main control component in the control circuit for the experiment. The model of the SCM is STC12C5A60S2. The SCM was fixed on a circuit board, which had an LCD display and an A/D conversion module. The I/O port of the SCM links the input keyboard, angle sensor, and motor drive board (the model of the board is L298N). There are two independent power sources for the control circuit and the motor drive board. The control system diagram for the experiment is shown in Fig. 12. The control circuit board uses a 5 V direct-current power supply and the motor driver board uses a 12 V direct-current power supply. In the experiment, the deceleration motor turns the auxiliary support to rotate the angle sensor. Through the A/D conversion module and program, the changes in the resistance of the angle

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Fig. 9. Flowchart of the experiment.

Fig. 10. Scale models of the solar greenhouse.

Fig. 11. Scale model of the greenhouse and rolling film used in the experiments.

sensor were converted to the real changes in the deflection angle of the auxiliary support and the opening sizes of the rolling film. The operator can input an opening size value using the input keyboard. The SCM compared the current opening size with the target value and controlled the rolling shutter and rolling film to arrive at the preset positions, which was shown on the LCD display. A control circuit board and a motor circuit board were used in the experiment. 3.3. Details of the experiment The purpose of this experiment was to prove that the application of the mathematical algorithm would ensure the control accuracy of the rolling shutter and rolling film. The movement of the

rolling film was achieved in the scale model. The motion of the rolling shutter and rolling film has the same path and form in the solar greenhouse. Only the thickness of the shutter and the film are different but this has no influence on the experiment (Zhang et al., 2016). The deceleration motor was installed on the side of the scale model, which resulted in uneven power applications. This caused irregular movements and skewness during the roll-up process, which made it difficult to achieve results in the experiment. During the downward rolling process, the effect of gravity evened out the power on the rolling pole and minimized the irregular movements and skewness of the rolling shutter and rolling film (Ding, 2011). It did not matter whether a roll-up or downward rolling process was chosen in the final experiment; the latter process was used in the experiment. The experiment was divided into two stages: (1) the surface was simplified to one circular arc; (2) the surface was simplified to two circular arcs. Each stage was composed of a test group and a control group. The track of the rolling film was medially divided into 9 parts and the required 10 nodes were obtained, which were the target values for the experiment. Control group tests were conducted using a time-delay relay. The control mode of the time-delay relay was simulated by a simple delay program of the SCM in the experiment. The program time for the track was obtained. Because the target nodes were evenly distributed, the total program time was medially divided into 9 parts. The appropriate 10 time nodes were obtained and each position node corresponding to a time node was measured 5 times in the experiment. There were two methods for the use of the delay program. In the first method, the rolling film moved based on the run distance (e.g., achieving a 20% opening of the rolling film by running the 10% time

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Fig. 12. Control circuit system diagram for the experiment.

programs twice). In the second method, the rolling film moved based on time (e.g., achieving a 10% opening required 2.5 s and a 20% opening required 5 s). The experimental results were better for the second method, which was chosen for the experiment. When the delay program ran once, it obtained a positioning node (running distance of rolling film). Each delay program ran 5 times. The tests of the delay programs were similar for the two stages and were completed using the above-mentioned method.

3.3.1. First stage: the surface was simplified to one circular arc The angle sensor was adjusted to a suitable linear range before the test and was fixed at the mounting base. Using a multi-segment function, the electric signal of the angle sensor was converted to specific angle values (represented by a). The angle values corresponding to the target nodes were measured using an AutoCAD program during debugging. The size of the opening of the first stage was obtained by:

K¼

p  2q  a þ arcsinðcosðp  2qÞsinaÞ p  2q

(23)

where q is 63.5 , which is a fixed angle in the scale model and a is the angle measured by the angle sensor. Equation (23) is converted into code. The electric signal of the angle sensor could be converted to the size of the opening in the SCM. The q was the key parameter in the core algorithm programs and was slightly adjusted to improve the accuracy and stability. In the test, 10 opening sizes (90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, 10%, 0%) were input into the SCM by the input keyboard. 100% means that the surface is completely open and 0% means that the surface is completely closed. The algorithmic program was run once and 10 position nodes were obtained; the test was conducted 5 times.

3.3.2. Second stage: the surface was simplified to two circular arcs The experimental procedures of the second stage were similar to those of the first stage. Using a multi-segment function, the electric signal of the angle sensor was converted to specific angle values (represented by a1 and a2) but the surface was simplified to two circular arcs and the calculation process for the size of the opening was divided into two parts. The join node of the two segments in the scale model was fixed. The angle value corresponding to the join node was measured before the experiment. The size of the opening at 100% was obtained by:





b2  R2 þ （b1  a1 þ arcsin sinR1a1 ðR1  HÞ ）  R1 K¼ b2  R2 þ b1  R1

(24)

where H is 250 mm, b1 is 39.6 , R1 is 750 mm, b2 is 31.2 , and R2 is 150 mm. Those values were fixed in the scale model. a1 is the angle measured by the angle sensor. Equation (24) is converted into code. b1 and b2 were the key parameters in the core algorithm programs and were slightly adjusted to improve the accuracy and stability. The size of the opening for 0% was obtained by:

K¼

（arcsin



sina2 R2

 ðL  R2 Þ þ a2 ）  R2

b2  R2 þ b1  R1

(25)

where L is 500 mm, which was fixed in the scale model. a2 is the angle measured by the angle sensor. Equation (25) was converted to algorithmic programs. In the second stage, 10 opening sizes were input into the SCM using the input keyboard. The tests to determine the results based on Eq. (24) and Eq. (25) were run 5 times. 4. Results and discussion 4.1. Experimental results 4.1.1. Experimental results for the surface simplified to one circular arc In the first stage, the delay program was modified 10 times and the modified programs were run 5 times. The experimental results of the delay programs are shown in Table 1. In the experiment, the angle sensor was installed and debugged. The experimental results of the algorithmic programs are shown in Table 2. 4.1.2. Experimental results for the surface simplified to two circular arcs The experimental process of the delay programs and of algorithmic programs in the second stage was similar to that of the first stage. The experimental results are shown in Table 3 and Table 4. 4.2. Data analysis and discussion In this section, the accuracy and stability of the two stages are compared. The error analysis of time delay program groups and the algorithm groups are discussed.

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Table 1 Experimental result of delay programs. Opening size of rolling film K0

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

Program running time/s

0 2.4 4.8 7.2 9.6 12.0 14.4 16.8 19.2 21.6 24.0

Target running distance/mm

0 58 116 174 232 290 348 406 464 522 580

Running distance of rolling film/mm First

Second

Third

Fourth

Fifth

0 67.9 126.7 188.2 242.8 304.5 368.5 432.4 485.6 533.0 568.5

0 67.9 127.8 186.3 243.7 306.6 365.5 425.1 491.8 536.9 585.0

0 68.8 127.8 186.3 242.8 304.0 368.4 431.2 475.7 528.8 578.8

0 68.8 129.0 188.3 246.3 309.1 373.8 436.9 488.7 523.5 580.5

0 68.8 129.0 186.2 246.5 314.2 361.0 421.8 482.9 534.8 580.0

Table 2 Experimental result of algorithmic programs. Opening size of rolling film K0

Target running distance/mm

Running distance of rolling film/mm First

Second

Third

Fourth

Fifth

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

0 58 116 174 232 290 348 406 464 522 580

0 58.3 116.8 175.2 233.3 290.9 349.8 406.0 464.5 523.8 582.0

0 58.0 116.0 174.3 231.8 289.0 348.5 404.5 462.2 523.5 581.8

0 57.5 116.0 173.7 231.2 290.5 348.1 405.0 464.0 524.5 582.8

0 58.0 115.7 174.1 232.2 290.2 348.3 405.5 463.9 523.5 582.1

0 58.5 116.3 174.2 231.5 289.7 347.2 404.5 462.0 524.3 581.5

Table 3 Experimental result of delay programs. Opening size of rolling film K0

Program running time/s

Target running distance/mm

Running distance of rolling film/mm First

Second

Third

Fourth

Fifth

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

0 60.3 120.6 180.9 241.2 301.5 361.8 422.1 482.4 542.7 603.0

0 72.3 129.3 187.1 243.9 300.0 355.9 413.5 471.4 547.8 605.1

0 70.2 128.5 189.3 243.2. 302.4 354.9 409.7 467.5 546.2 606.8

0 68.9 129.3 188.7 243.9 300.0 354.1 410.8 468.7 550.3 605.1

0 68.9 128.5 185.5 241.8 306.2 357.8 411.7 468.7 551.3 603.5

0 70.2 130.8 185.5 243.9 303.3 354.9 409.7 466.1 547.8 603.5

Table 4 Experimental result of algorithmic programs. Opening size of rolling film K0

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

Target running distance/mm

0 60.3 120.6 180.9 241.2 301.5 361.8 422.1 482.4 542.7 603.0

Running distance of rolling film/mm First

Second

Third

Fourth

Fifth

0 60.4 119.8 181.8 241.2 299.8 362.5 423.9 485.3 541.6 604.5

0 60.3 120.1 180.9 241.5 300.5 361.8 422.8 484.5 541.2 603.5

0 60.3 120.1 180.9 242.2 301.0 361.8 422.1 484.9 542.0 602.3

0 61.1 119.4 180.9 242.7 301.5 361.8 425.4 485.2 541.5 602.2

0 61.2 120.6 180.9 242.7 301.0 361.8 422.6 484.8 542.7 603.0

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4.2.1. Accuracy analysis of the control An accuracy analysis is an important aspect to determine the precise control of the rolling shutter and rolling film. In each stage, the running distance of the rolling film had 10 common target values. The average running distances of each opening size were obtained from Tables 1 and 2. The effect of the start nodes (100%) was ignored. The results of the error analysis for the delay programs and algorithmic programs for the first stage are shown in Fig. 13(a), (b) and the results for the second stage are shown in Fig. 13(c), (d).where d is the absolute error, m is the target running distance of the rolling film, and x is the average measurement corresponding to the opening size. Fig. 13(a), (b) shows that in the first stage, the maximum relative error of the delay programs is 18% and the average value is 6.53%. In contrast, the maximum relative error of the algorithmic programs is 0.37% and the average value is 0.16%.

Fig. 13(c), (d) shows that in the second stage, the maximum relative error of the delay programs is 16.25% and the average value is 3.68% whereas the maximum relative error of the algorithmic programs is 0.60% and the average value is 0.28%. It was observed (Fig. 13(a) and (c)) that the offset from the 1:1 line was smaller for the algorithmic programs than the delay programs. The relative errors of the algorithmic programs were steady and less than 1% (Fig. 13(b) and (d)). The relative errors of delay programs fluctuated and were mostly larger than 1%. The application of the algorithm improved the control accuracy of the rolling shutter and rolling film and the average relative error was reduced by 6.37% in the first stage and by 3.40% in the second stage.

Fig. 13. Comparison of the errors in the two stages.

Relative error ð%Þ:

d jx  mj ¼ m m

The relative errors in Fig. 13 were calculated as follows.

(26)

G. Zhang et al. / Journal of Cleaner Production 228 (2019) 645e657

4.2.2. Stability analysis The stability of the rolling process of the shutter and film is another important index to measure the effectiveness of the proposed control method. The stability was determined based on the standard deviation and the results are shown in Fig. 14. The standard deviation shown in Fig. 14 (a) and (b) were calculated as follows:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u 1 X Standard Deviation ðmmÞ: s ¼ t ðx  mÞ2 N  1 i¼1 i

(27)

where s is the standard deviation, N is the sample sizes (N represents the measuring times in the experiment, N ¼ 5), and xi is the measured value of the running distance of the rolling film. The standard deviation of the first stage is shown in Fig. 14(a). Without the influence of the start nodes (100%), the maximum standard deviation of the delay programs is 6.09 mm and the average value is 3.68 mm. In contrast, the maximum standard deviation of the algorithmic program is 1.14 mm and the average value is 0.66 mm. The standard deviation of the second stage is shown in Fig. 14(b). The maximum standard deviation of the delay programs is 2.59 mm and the average value is 1.61 mm. In contrast, the maximum standard deviation of the algorithmic program is 1.32 mm and the average value is 0.61 mm. The results in Fig. 14 indicate that the stability was better for the algorithmic programs than the delay programs. The application of the algorithm improved the stability of the rolling shutter and rolling film compared with the delay programs. 4.2.3. Discussion and error analysis 4.2.3.1. Error analysis of the time delay program group. The accuracy

Fig. 14. Standard deviation of two stages.

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of the experiment was defined as the difference between the running distance of the film determined in the experiment and the theoretical value. The error of the time delay program groups was attributed to (a) the calculation error of the parameters in the delay program and (b) the change in the speed of the deceleration motor. In this experiment, the error of the parameters in the delay program was small due to the replication of the calculations, whereas the change in the speed was the main error source. In theory, the running distance of the film is controlled by the running time and the speed was a constant value. In practice, the stress applied to the film and the driving device always changes with the increase in the opening size, which results in a change in the speed of the film in the experiment. The stress applied to the film and the driving device in the two stages are shown in Fig. 15. In Fig. 15, G is the gravity of the film and deceleration motor and it consists of the component G1 in the tangential direction and G2 perpendicular to the tangent. In the experiment, the weight of the film gradually decreased as the film was extended but the decrease was relatively small and can be ignored unlike G. Fa is the driving force of the motor, and Fb is the supporting force. Fc is the tension of the film and f is the friction between the film and the light surface. Fc depends on the tightness of the rolling film; the tighter the rolling film, the greater the traction and vice versa. As shown in Fig. 15, the force of the film and deceleration motor in the experiment changed with the position, which resulted in changes in the workload of the deceleration motor. During the experiment, fluctuations were observed in the speed of the deceleration motor due to a change in the workload, which resulted in differences in the running distance. The force that affects the speed of the film and deceleration motor consists of F1 (the force opposite to the direction of movement, including Fc and f) and F2 (the force in the direction of movement, including Fa and G1). As shown in Fig. 13(a) and (c), in the first stage, the actual distance always exceeded the theoretical distance, which indicated that the influence of F2 was larger than that of F1. In the second stage, the actual distance at 20%e40% of opening size was less than the theoretical distance, which means that the influence of F1 was stronger than that of F2. As shown in Fig. 13(b) and (d), the decrease in the relative error indicated that the influence of F2 was gradually weakening. The delay program is an open-loop control method with no feedback and there is no flexibility to adjust the running distance of the rolling film; this resulted in errors in the stability results, as shown in Fig. 14(a) and (b). It has been shown that in actual applications, the errors of the time delay relay programs accumulated during operation, which resulted in poor accuracy and poor stability (Liu et al., 2005). This type of control method needs to be corrected frequently by the operator to ensure good accuracy in practical applications but this is time-consuming and laborious. 4.2.3.2. Error analysis of the algorithm group. The angle sensor control achieved the closed-loop control of the deceleration motor and the proposed control method improved the stability of the rolling shutter and rolling film. Some errors could not be completely eliminated in the control of the algorithmic program; these included errors associated with the angle sensor and errors in the algorithmic program (Zou, 2010; Li et al., 2017). The algorithm program of the second stage was more complex than that of the first stage and improvements were required for certain parameters (actual angles of the scale model), which caused greater fluctuations of the absolute error and relative error in the second stage than the first stage, as shown in Fig. 13. Due to the limited accuracy of the angle sensor, the running distance of the algorithmic program could only be controlled within the threshold

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Fig. 15. Force analysis of the rolling film in the two stages.

range centered on the target value. Vibrations of the film and deceleration motor were observed, which resulted in errors in the stability, as shown in Fig. 14. In summary, the comparison of the accuracy and stability results demonstrates that the experimental results were better for the algorithmic programs than the delay programs in the first stage and second stage. It was verified that the proposed control method provides better accuracy and stability than the existing control method of the time-delay relay. The results were verified by experiments using the scale model, which were tests of the mechanical structure. The movement of the rolling film in the experiment was similar to the movement in practical applications and the reliability of the obtained results was high. The errors observed in the experiment are most likely to occur also in practical applications (Zhang et al., 2016).

5. Conclusion A mathematical algorithm for the automated control of the position of rolling shutter and rolling film in a greenhouse based on the simplification of the greenhouse surface was developed. The “Liaoshen-IV” solar greenhouse was used as an example and the light surface was simplified to one and two circular arcs using the algorithm. The equation for the desired position was obtained and the position on the surface was determined. The novelty of this study is that the proposed method of simplifying the light surfaces of greenhouses can be applied to various roof shapes to achieve the precise control of the rolling shutter and rolling film of solar greenhouses. Any position on the light surface can be determined by calculating the angle at the bottom of the back wall of the greenhouse so that the position of the rolling shutter and the rolling film can be measured accurately by the angle sensor. It was demonstrated that the proposed control method provides better accuracy and stability than the existing control method of time-delay relay. The application of the algorithm improved the control accuracy of the rolling shutter and rolling film and the relative errors of the algorithm programs were stable and less than 1% in the experimental tests. The average relative error was reduced by 6.37% for the one circular arc and by 3.40% for the two circular arcs compared with the delay programs. Fluctuations in the speed of the deceleration motor resulted in errors in the time-delay relay method. The errors in the proposed control method were attributed to the angle sensor and the adjustments of the key parameters in the algorithm. The precise measurement and control of the position of the rolling shutter and rolling film in a solar greenhouse was achieved and the practical value and significance of the research were demonstrated. The proposed control resulted in higher precision of

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