Precise Servo-Control System of a Dual-Axis Positioning Tray Conveying Device for Automatic Transplanting Machine

Abstract

To address the issues of poor positioning accuracy, low supply efficiency and inadequate adaptability for different tray specifications of the existing seedling tray conveying device, a dual-axis positioning tray conveying device was developed, which can accommodate seedling trays ranging from 21 to 288 holes. A dual-sensor positioning algorithm and variable displacement positioning method were proposed to increase the efficiency, ensuring precise initial positioning and intermittent movements both along the seedling conveyance (X-axis) and platform movement (Y-axis). The system utilizes a precise positioning servo-control system with three-closed-loop controls and a PID algorithm enhanced through simulation to refine seedling positioning accuracy. Experiments with nine different tray specifications were conducted on a step-controlled platform to test suitability, validating the performance of the initial positioning and intermittent transport in both the X and Y directions. On the X-axis, the initial positioning deviation of the seedling tray was up to 1.34 mm and the maximum deviation in the intermission conveying was 0.85 mm. Comparatively, the deviation on the Y-axis was smaller, with the initial positioning deviation up to 0.99 mm and the intermission moving deviation up to 0.98 mm. These results demonstrate that the designed device meets the requirements for precise transport, providing essential technological foundations for seedling tray transport and retrieval steps in fully automated transplanting machines.

1. Introduction

Seedling tray technology emerged in the mid-1970s as a modern cultivation method designed for efficient factory production, pioneered by European and American countries [1]. Compared with the traditional seedling production method, it boasts several advantages [2]: high seedling emergence rates, orderly growth patterns, increased transplant survival rates, shorter growth cycles, reduced incidence of pests and diseases, seed and energy conservation, and facilitation of variety promotion and standardized production management [3]. This technology plays a crucial role in mechanizing and scaling the production of numerous vegetable and cash crops, ensuring their sustainable and efficient development [4].

As vegetable planting mechanization progresses, the industry has transitioned from manual to semi-automatic and fully automatic transplanting machines [5,6]. There is no seedling tray conveying and picking device for the semi-automatic transplanter, and these are the most critical technologies when compared with the fully automatic transplanter [7]. The cultivated neat seedlings need to be transported to the picking device and planting mechanism for planting [8].

Seedling tray transport technology in developed countries started earlier. The XT616 transplanter for tea seedling trays produced by Transplant Systems in Australia [9] is equipped with various types of manipulator end actuators to adapt to the transplanter of different specifications. The PF2R fully automatic vegetable transplanter made by Yanma in Japan [10] can control the horizontal feeding plate through the double screw mechanism, and realizes the longitudinal feeding of seedlings through the linkage of the ratchet mechanism and chain transmission mechanism. To ensure the continuous and accurate transmission of the seedlings, a special winding seedling tray is used to realize the non-gap placement of adjacent seedling trays, and the side push rod of the chain and designed placement are used in the device. A nursery tray conveying mechanism was developed by Saramin in Sri Lanka [11] to feed the seedlings to the planting mechanism, along with a proximity sensor, which can stop at the designed position. The above mechanisms in these countries use special seedling trays that are flexible or made of foam [12,13], which means the conveying devices are not universal.

In response to these challenges, Chinese research institutes and universities have carried out relevant research. Chuanhua et al. [14] devised an electric seedling tray conveying device equipped with positioning profiling blocks. Sensors are installed at the lowest point of each set of profiling blocks to detect the position of the seedling tray. This method can accurately position the seedling tray, but it needs to add profiling blocks to each placed seedling tray, which is relatively low in practicability. Qizhi et al. [15] designed an automatic transplanter tray shifting control method. The stepper motor is used to drive the chain transmission mechanism, and then to drive the seedling tray to carry out longitudinal feeding. The photoelectric sensor installed on the side of the seedling tray conveying device is used to obtain the position information of the seedling tray, and then the transmission and positioning of the seedling plate are realized by controlling the pulse signal output of the motor. While the reliability of this device is relatively low, once the seedling tray is damaged or there is a gap on the side of the tray, it will affect the accuracy of positioning [16]. The above conveying devices are all transported in one direction [17], which may reduce the efficiency of conveying the seedlings and further lower the speed of picking and planting.

A device was designed by Gaohong et al. [18] for moving the seedling tray and fixing the picking device; the ratchet pawl is driven by the motor to realize the longitudinal intermittent movement of the seedling plate, and the double helix shaft is driven by the motor to realize the transverse reciprocating movement. This method has a complex mechanical structure and processing errors will lead to inaccurate positioning. Changjie [19] designed a seedling tray feed mechanism for the hanging basket transplanter, which also uses a stepper motor to control the shift cylinder for reciprocating linear motion and a rocker rod–ratchet mechanism to control the seedling plate for longitudinal intermittent feeding. The devices generally control the special mechanical structure for movement and the structure is also complex. Furthermore, these devices are inclined to place the seedling tray, whose own gravity will affect the longitudinal positioning accuracy. Xin et al. [20] designed a seedling tray conveying mechanism, with transverse and longitudinal seedling feeding functions, and photoelectric sensors were used for positioning. This device is easier to use and more effective than other mechanisms that move in two directions.

In summary, three types of positioning methods are utilized for the fully automatic transplanter’s seedling tray [21]. Firstly, mechanical mechanisms like the crank lever, gap rotating plate rack, or incomplete gear systems achieve longitudinal movement for pot seedling plates. Although accurate, these methods are singular in their positioning approach and may involve complex design structures. Adjusting the movement distance is challenging, limiting adaptability to specific pot and seedling tray sizes. Secondly, the DC motor or stepping motor is used to drive the seedling tray conveying mechanism, the photoelectric switch positioning mode is accurate and the greatest advantage is that the spacing change is flexible. Thirdly, the conveying device with visual system positioning can enable two-dimensional positioning of the seedling tray [22], which has a specific function. However, it is more sensitive to the vibration of the transplanting device and it is too expensive to be applied.

To enhance positioning accuracy, improve low efficiency of conveying and accommodate various specifications, this study introduces a dual-axis positioning tray conveying device integrated with a dual-sensor system and precise servo-control system. It employs a dual-sensor positioning algorithm and variable displacement method to optimize parameter combinations within the control system and its transfer function. The step-controlled bench was used for experimental validation with different tray specifications to validate the efficacy of this approach. This research lays crucial technological groundwork for seedling tray transportation and retrieval in fully automated transplanting machinery.

2. Materials and Methods

2.1. Size of Different Specifications for Seedling Trays

According to the People’s Republic of China Agricultural Industry standard [23], the specifications of plastic plug tray for seedling production can be divided into 21-hole, 32-hole, 50-hole, 72-hole, 98-hole, 105-hole, 128-hole, 200-hole and 288-hole trays. The parameters are shown in

Table 1. Parameters of different specifications for seedling trays.

Image	Row × Column	Upper × Lower Caliber/mm	Thickness/mm	Weight/g	Image	Row × Column	Upper × Lower Caliber/mm	Thickness/mm	Weight/g
	21 = 3 × 7	62 × 30	0.23	153.73		105 = 7 × 15	31 × 13	0.08	149.25
	32 = 4 × 8	55 × 27	0.22	150.93		128 = 8 × 16	30 × 14	0.12	154.83
	50 = 5 × 10	48 × 23	0.22	151.08		200 = 10 × 20	23 × 10	0.08	152.64
	72 = 6 × 12	40 × 20	0.16	152.72		288 = 12 × 24	19 × 8	0.08	152.64
	98 = 7 × 14	32 × 12	0.14	152.82

. All types of seedling trays were bought from the same manufacturer, and the upper and lower caliber, thickness and weight were measured. The row represents the long side and the column represents the short side. The nine types of seedling tray have the same dimensions, 540 mm × 280 mm × 42 mm, which are shown in Figure 1. The material is PS/PVC. The difference is the hole size, that is the distance between each two holes.

2.2. Dual-Axis Conveying Device for Seedling Tray

The conveying device is composed of platform, conveying chain, push rod, smooth roller, two servo motors (MF3S-60CS30B1-504, Xinjie Co., Wuxi, China), three photoelectric sensors (M6, Xianli Co., Guangzhou, China) and bench, and is shown in Figure 2. One motor (M_X) is used for longitudinal conveying of trays and another (M_Y) is for transverse moving of whole platform. Two sensors (S_X1 and S_X2) are used for positioning and conveying of seedling tray on the X-axis and another sensor (S_YP) is used for positioning of platform on the Y-axis.

On the X-axis, two parallel conveying chains are located on two sides of the platform, and the push rods are fixed on the chain at equal intervals. The groove of hole at the bottom of the seedling tray can be put on the push rod, and the middle of the conveying platform is a fixed plate, which can support the seedling tray. The driving wheel is connected with the servo motor, and the driven wheel is connected with the sprocket. The driven wheel is driven by the driving wheel to rotate the chain. The last row of the seedling tray has to be placed on the push rod, and the chain can push the seedling tray forward in the X direction. The S_X1 is used for sensing whether there is a tray and the S_X2 is used for sensing the push rod for precise orientation. Because of the instability of the seedling tray, which makes it unable to position accurately, another sensor was added. The position of the two sensors is at least greater than the distance between the two push rods. On the Y-axis, two smooth rollers are fixed to four pedestals which are on the bench; the conveying platform with the servo motor can move along the rollers. The device can drive the nut screw mechanism and realize the left and right movement of the seedling tray with the positive reversal of the servo motor in the Y direction. The S_YP was located at the side of the bench, which provides the origin position for platform.

Considering the transfer of the seedling tray, a pressure plate needs to be installed above the device. This device uses the 08B chain, the chain pitch of which is 12.7 mm; the width of the tray is 280 mm, so the interval between the two push rods is set to 22 chain pitch, the distance of which is 279.4 mm. One tray can be placed in the middle of two push rods, and there needs to be some distance between two trays. In order to ensure that the conveying platform can be placed on a seedling tray being picked up and a tray being waiting to be picked up at the same time, the length and width of the platform designed are 1400 mm × 400 mm.

2.3. Working Principle of Seedling Tray Positioning and Conveying

2.3.1. Precise Positioning Method for Trays

In both directions of transverse transmission and longitudinal movement, the trays were driven by servo motors and equipped with sensors for positioning. On the X-axis, two sensors (S_X1 and S_X2) were used for conveying positioning longitudinally. The thickness of different seedling trays (in Table 1) can affect the accuracy of identifying the trays with photoelectric sensor, so another one was added to sense the fixed push rod for precise positioning, which was more stable than seedling tray. The S_X1 installed at the front end of one side of the conveying platform was used to sense whether there was a seedling tray, and S_X2 installed at the back end of the same side was used to sense the fixed rod, which was inside the device and there was a plate on the top for blocking the sun. A 128-hole tray was used in the initial positioning method which is shown in Figure 3b; D is the distance of interval between the two push rods.

• The last row of the seedling tray is put on the push rod; the rod will push the seedling tray forward. The servo motor (M_X) drives the seedling tray conveying it forward from the starting point. The push rod before the one which seedling tray is put on is M1.
• With the conveying, S_X1 will recognize the seedling tray and the motor (M_X) will continue to move forward. At the same time, the signal of S_X2 will start being effective after the tray being sensed by S_X1.
• When S_X2 recognizes the nearest push rod M1, the previous displacement of the motor will be cleared to zero; after that, the displacement can be obtained anew which is the transmission distance D_W. The conversion of pulse number and displacement amount has been set in the system.
• From front location to the target position, the transmission distance D_W is obtained by preliminary experiment, which is write-in data by control system. The motor can drive the seedling tray to the position where the center of the first row is right on target.

The working time sequence of seedling tray positioning is shown in Figure 3a; the motor starts to run, the push rod pushes the seedling tray forward and, when the first sensor is triggered, the second sensor is activated. The fixed displacement corresponding to different seedling trays is taken as the written data D_W, and the seedling trays are finally transported to the designated position.

On the Y-axis, one sensor (S_YP) was used as the zero position; the moving distance in Y direction depends on the hole spacing for seedling trays.

2.3.2. Precise Conveying Distance of Different Seedling Trays

The dual-axis conveying device designed in this paper can be applied to nine kinds of national standard seedling trays. For the initial positioning on X-axis, as mentioned in Figure 3a, S_X1 can identify the outer size of the tray, and the outer size of different seedling trays is the same, so the difference in sensing whether there is a seedling tray will not be very large. While the transmission distance D_W is different for several specifications of seedling trays which depends on the hole spacing of trays, the target position corresponds to the center of the first row; the distance D_W measured with preliminary experiment is in

Table 2. Specific parameter for precise conveying in two directions.

Size	Hole Spacing (HX)/mm	Hole Spacing (HX)/mm	DW/mm	Size	Hole Spacing (HX)/mm	Hole Spacing (HX)/mm	DW/mm
21	89.84	73.58	40.81	105	34.60	34.55	21.24
32	64.96	64.51	34.58	128	32.41	31.81	20.35
50	50.68	50.64	29.32	200	25.32	25.30	17.87
72	42.22	42.54	25.24	288	22.11	22.01	13.31
98	36.71	36.44	22.66

. According to the characteristics of the seedling tray, the hole spacing is the width of both upper caliber of one hole and the edge of two holes, which is shown in Figure 4.

For the interval conveying, the system will convey the seedling trays with hole spacing H_X longitudinally on X-axis, and move the whole platform with the hole spacing H_Y transversely on Y-axis. As is shown in Figure 4a, 4b, the hole spacing of 72-hole tray is greater than that of 128-hole tray. The hole spacing of each specification is different, and the parameters measured are shown in Table 2. The hole spacing of trays in two direction is similar except the 21-hole tray, because the width of edge of which in X direction is higher than that in Y direction. There are some millimeters of difference while it is mentioned in People’s Republic of China Agricultural Industry standard [23] that an error of 1 mm can be allowed.

2.4. Electronic Control of Precise Positioning Module

2.4.1. Hardware of the Control System

The precise positioning control system for seedling trays comprises five key components as depicted in Figure 5: the signal module, control module, driving module, executive module and power module. In addition to photoelectric sensors, the traditional switch button has been replaced by inputs from a touch screen (TG465 Touchwin, Xinjie Co., Wuxi, China). Acting as the central controller is a PLC (XD5-48T6-C, Xinjie Co., Wuxi, China). The power supply for servo motor and its driver is 220 V, so the three-phase plug is used to connected the switching power supply directly. This setup also includes a 24 V conversion for powering the touch screen, sensors and PLC. The servo motor is equipped with a 17-bit magnetic encoder for precise single-turn feedback.

The servo motor driver features ports for signal input and output, communication with the encoder for feedback, and both power input and output. Figure 6 illustrates the interconnections among the servo motor driver, servo motor and PLC. The servo power wiring (R01, S01, T01) is linked to the UVW terminals for 220 V power supply. The PLC, operating on an NPN configuration, connects the motor driver’s pulse signal (P-) to PLC’s Y1 input and the direction signal (D-) to Y2. SI1 serves as the grounding point for the enable signal. Ensuring a closed loop between the servo motor and PLC involves establishing input and output connections that facilitate seamless control and feedback.

2.4.2. Software of the Seedling Positioning

Electronic control of precise positioning module plays an important role in the system. Only on the premise of ensuring the accurate transmission of the seedling tray in both the X and Y directions can the next operation be carried out, and corresponding cooperation is also needed to ensure that the entire process can complete the cycle operation.

The flow chart of the seedling positioning is shown in Figure 7. After the system is powered on and reset, the transmission platform in the Y direction is located at the origin position, and it is also the position of picking seedlings, S_YP will be on to sense the platform. After placing the seedling tray on the seedling conveying platform manually, the feed button can be pressed, and the seedling tray can be transported forward. After the first sensor S_X1 senses the seedling tray and the second sensor S_X2 senses the push rod, the seedling tray in the X direction can be transported to the specified position after the compensation displacement of the write-in data. After the positioning is completed in the X and Y directions, the seedling can be taken.

2.4.3. Three-Closed-Loop Control of Servo Motor

In the control system of precise positioning for seedling trays, the accuracy is important for the control of motor, and the strategy plays a crucial role in the work of motor, adjusting the parameters of speed, position, torque and other characteristics of motor. The servo motor driver and servo motors in both directions are the same; there is no loss of power brake and there are ordinary joints. Bearing specification of shaft is B, and there are keys, oil seals and threaded holes. The size of the base is 60 mm.

Servo motors are generally three-loop control systems; from the inside to the outside, there are the current loop, speed loop and position loop [24]. The current loop has the fastest response speed, and the speed loop must have a higher response speed than the position loop; otherwise, it will cause vibration or poor response of the motor operation, that is, the current loop gain value is higher than the speed loop gain value, and the speed loop gain value is higher than the position loop gain value.

As is shown in Figure 8, the first loop which is the innermost is the current loop. This loop is completely performed inside the servo drive, and it does not need to be changed. The second loop is the speed loop, the middle loop. The input of the speed loop is the output of the position loop PID adjustment and the feedforward value of the position setting. The feedback of the speed loop comes from the feedback value of the encoder, which is calculated by the speed operator. The third loop is the position loop, the outermost loop. The input of the position loop is the external pulse. The function of the position loop is to perform adjustment P on the difference between the input value and the feedback value of the position loop (the retention pulse). The feedback of the position loop comes from the pulse signal of the encoder feedback, which is calculated by the deviation counter. The design of the servo drive can ensure that the current loop has good responsiveness as much as possible, so the gains of the position loop and speed loop need to be adjusted.

Within the range where the mechanical system does not vibrate, the larger the speed loop gain setting value, the more stable the servo system and the better the responsiveness. After debugging, the speed loop is set to 1000 Hz. The gain of speed loop and the speed loop integral time constant roughly satisfy the following relationship: P1-00 × P1-01 = 636,620, so it is set to 636.62 ms. The higher the position loop gain setting, the higher the responsiveness and the shorter the positioning time. After debugging, the position loop is set to 1000 per second. When the machine vibrates due to the servo drive, it is possible to eliminate the vibration if the following torque command filter time parameters are adjusted. The smaller the value, the better the responsiveness of the control, but it is subject to the constraints of the machine conditions, which are set to 100 ms. The parameters are shown in

Table 3. Parameters of three-closed-loop control.

Parameter	Implication	Unit	Factory Setting	Setting Range
P1-00	Gain of velocity loop	0.1 Hz	200	10~20,000
P1-01	Integral time constant of velocity loop	0.01 ms	3300	15~51,200
P1-02	Gain of position loop	0.1/s	200	10~20,000
P2-35	Time constant of torque instruction filter	0.01 ms	100	0~65,535

.

2.4.4. PID Control and Transfer Function Model

PID control can effectively restrain the system error [25] and improve the control precision of servo motor by adjusting the three parameters of proportion, integral and differential [26]; the basic block diagram of PID algorithm is shown in Figure 9. The control system of precise positioning for seedling trays is shown in Figure 10. In the seedling plate conveying device, the programmable controller controls the servo motor driver, and then the servo motor driver controls the servo motor, and then drives the chain transmission mechanism through the coupling to drive the seedling plate conveying. The servo motor has encoder, which can constitute the closed-loop positioning control system of the plant disc, so the programmable controller, driver, servo motor, chain drive mechanism and encoder constitute a closed-loop control system. The displacement of hole spacing is taken as input, the actual measured displacement is taken as output and the difference between them $e\left(t\right)$ is taken as the error value. After the PID module, the output signal is transmitted to the controller to drive the servo motor driver and the servo motor to transport the seedling tray.

In Figure 9, the formula of the control principle is as follows:

$$e\left(t\right)=r\left(t\right)-c\left(t\right)$$

(1)

$$u\left(t\right)=K_P\left[e\left(t\right)+{\displaystyle \frac{1}{Ti}}\int e\left(t\right)dt+TD{\displaystyle \frac{de\left(t\right)}{dt}}\right]$$

(2)

where $e\left(t\right)$ is the deviation, $r\left(t\right)$ is the given value, $c\left(t\right)$ is the actual output and $u\left(t\right)$ is the control quantity. $K_P$ is proportional coefficient, $Ti$ is the integral time coefficient and $TD$ is the differential time coefficient.

The transfer function of the positioning control system is used; the ratio of a system’s output to its input is called the transfer function. As can be seen from the structure block diagram of the positioning control system in Figure 10, the total transfer function is as follows:

$$G\left(s\right)={\displaystyle \frac{G_c\left(s\right)G_d\left(s\right)G_m\left(s\right)G_i\left(s\right)}{1+G_c\left(s\right)G_d\left(s\right)G_m\left(s\right)G_i\left(s\right)G_E\left(s\right)}}$$

(3)

where $G_c\left(s\right), G_d\left(s\right)$, $G_m\left(s\right)$, $G_i\left(s\right)$ and $G_E\left(s\right)$ are, respectively, the transfer functions of programmable controller, servo motor driver, servo motor, chain driven mechanism and encoder. The transfer function of servo motor is as follows:

$$G_m\left(s\right)={\displaystyle \frac{{\theta }_m\left(s\right)}{{\bigcup }_a\left(s\right)}}={\displaystyle \frac{C_m}{s\left(J_{m}s+\left(f_m+C_{\omega }\right)\right)}}$$

(4)

where $C_m$ is calculated with locked-rotor torque ${\mathrm{M}}_{\mathrm{s}\mathrm{e}}$ and nominal voltage E. $J_m$ is the total moment of inertia, $f_m$ is the total viscous friction coefficient and $C_{\omega }$ is the damping coefficient.

The transfer function of servo motor can be obtained by using the relevant parameter in

Table 4. Parameters of servo motor.

Parameter	Value	Parameter	Value
Nominal voltage	0.4 KW	Rated torque	1.27 Nm
Voltage classes	48 V	Maximum torque	5 Nm
Rated speed	3000 RPM	Locked-rotor torque	0.85 kg·m2
Rated current	10 mA	Encoder bit	17
Maximum current	30 mA	Friction coefficient	1
Damping coefficient	0.08

and Formula (4), which is shown in Formula (5).

$$G_m\left(s\right)={\displaystyle \frac{0.147}{s^2+1.27s}}$$

(5)

The servo motor drive can be viewed as a proportional step, $G_d\left(s\right)$ = 10. The encoder is regarded as a proportional step, $G_E\left(s\right)$ = 100. Chain drive converts the angular displacement of the motor into the linear displacement motion of the seedling plate transport, which is regarded as a proportional link, $G_i\left(s\right)$ = (π⋅D₁)/360 = 0.637, where D₁ is the dividing circle diameter of the driving sprocket. The programmable controller converts the difference between the given displacement amount and the displacement amount fed back by the encoder into the actual displacement amount controlling the motor motion, as a proportional link; the transfer function is $G_c\left(s\right)$ = 0.0087. Therefore, the transfer function of the closed-loop positioning control system is as follows:

$$G\left(s\right)={\displaystyle \frac{G_c\left(s\right)G_d\left(s\right)G_m\left(s\right)G_i\left(s\right)}{1+G_c\left(s\right)G_d\left(s\right)G_m\left(s\right)G_i\left(s\right)G_E\left(s\right)}}={\displaystyle \frac{0.0815}{s^2+1.27s+0.8147}}$$

(6)

The transfer functions of each link of the above control system were substituted into the Simulink platform in MATLAB (2019a, MathWorks Co., South Dakota, MA, USA) [27] to build a simulation model of positioning control system, as shown in Figure 11. In general, the pulse given by the programmable controller is a square-wave pulse, so the step function module is taken as the input of the control system here, and the ideal step response curve is obtained by adjusting the values of the proportional coefficient $K_P$, the differential coefficient $Ti$ and the integral coefficient $TD$. PID control instructions are introduced into the control system, and the optimal sampling time and parameter values are obtained by manual method, thus improving the control accuracy.

2.5. The Dual-Axis Conveying Device and Performance Bench Test

The bench test aimed to validate the consistency between actual and theoretical distances. It assessed the accuracy of positioning seedling trays on the X-axis and the conveying platform on the Y-axis. The experimental setup is depicted in Figure 12, featuring step-by-step debugging capability. The Y-axis represents the horizontal direction, while the X-axis is vertical, as illustrated in Figure 1.

To ensure precise tray positioning in both directions, rows of spaced picking claws [28] were installed as positional references on the bench. These claws remain fixed and are solely used for positioning during the test. A pasteable scale is affixed to one side of the bench to aid in measuring X-axis displacement, while sensors are fitted on the opposite side.

The experiment involved 9 different sizes of empty seedling trays, ranging from 21 to 288 holes, respectively. A digital vernier caliper was employed to measure actual distances and deviations from theoretical records. The accuracy of seedling tray positioning was assessed using positioning deviation, which denotes the difference between the actual and theoretically specified stop positions of the seedling tray. The theoretically specified position corresponds to the location of the seedling picking claws as per the operational principle of the fully automatic transplanter. In this study, the positioning deviation is used as the experimental index, which is the same for both X and Y directions. Measurement involved the use of the pasteable scale and vernier caliper. Data stability was verified by calculating the coefficient of variation. The formula is as follows:

$$C_v={\displaystyle \frac{\sigma }{m}}\times 100\%$$

(7)

where $C_v$ is the coefficient, $\sigma$ is the standard deviation and $m$ is the average.

2.5.1. Accurate Positioning and Conveying Test on X-Axis

Due to the fixed position of the picking claws, the zero point of the calibrated scale aligns with the position of the picking claws in the X direction. The seedling tray is then transported forward to a designated position where the picking claws align with the holes in the seedling trays.

This setup allows for single-step control. After the seedling tray is conveyed from its starting position, it will stop at the position of S_X1 and then at S_X2, and finally will stop at the position of the seedling claws. Each step is initiated by pressing a button on the touch screen. The vernier caliper is used to measure the displacement difference between the hole center and the picking claws, which is the deviation in initial positioning on X-axis, as is shown in Figure 13a. Intermittent conveying is initiated by pressing another button on the touch screen, causing the seedling tray to move forward one line. Specifications for various data are detailed in Table 2. The displacement of the forward transmission needs to be modified. The deviation of hole and the picking claws after conveying is recorded, which is the intermission conveying on X-axis, as is shown in Figure 13b. For each seedling tray specification, initial positioning and intermittent conveying are performed five times each. Average values, standard deviations and coefficients of variation for the deviations are calculated.

2.5.2. Accurate Positioning and Conveying Test in Y Direction

The position of the conveying platform at the zero point is the same as the position of the picking claws on the Y-axis. After the seedling tray is conveyed to the specified position on the X-axis, the displacement difference between the hole center and the picking claws, which is the deviation in initial positioning on Y-axis, is recorded, as is shown in Figure 13c. The input signal of intermission moving is pressing the button on the touch screen, and the seedling tray will be conveyed one column forward; the data on different specifications are in Table 2. The deviation of hole and the picking claws after moving is recorded, which is the intermission moving on X-axis, as is shown in Figure 13d. As well as the X-axis, five settings of initial positioning and five settings of intermission conveying for the conveying platform with different specifications of seedling tray were carried out, and the average value, standard value and coefficient of variation of deviation were calculated.

3. Results and Discussion

3.1. Simulation Results of Positioning Control System Based on Simulink

The simulation results of the positioning control system based on Simulink are shown in Figure 14. The influence on the transmission is researched by changing the three parameter values of $K_P,K_i$ and $K_d$. And the best combination of values are chosen to be set.

In the debugging process, the value of $K_P$ is initially adjusted. It is observed that there exists a positive correlation between $K_P$ and its effect, with a stronger effect associated with larger values of kp and a weaker effect associated with smaller values. Additionally, it is noted that excessively small values lead to a slow response while excessive values cause overshoot. After careful debugging, it has been determined that an overshoot will not occur when $K_P$ = 30. The proportional control algorithm alone cannot eliminate static errors; these errors can only be addressed through the integration link. Therefore, adjustments are made to the value of $K_i$. The integral component accumulates errors from time 0 to t, effectively eliminating cumulative errors as long as they exist. A shorter integration time results in a stronger integration effect, while increasing the gain value strengthens this effect further. However, excessive gain may lead to resonance and system instability. Therefore, parameters should be fine-tuned based on response curves. When error changes rapidly, output also changes quickly [29]. Finally, $K_i$ is controlled within the range from 5 to 15. However, despite these adjustments, the system’s dynamic performance remains poor and further tuning of $K_d$ should be set. Increasing $K_d$ enhances its differentiating effect but excessively large differences can induce oscillations that hinder control efforts. In summary, the fundamental principle is to initially apply proportional control and subsequently incorporate integral differential control. The aim is to minimize overshoot through precise proportioning, followed by the addition of integral control for stability and rapid response without oscillation. The Z-N method is used to adjust the PID parameters. After debugging and modification, when the three PID controller parameter values are $K_P$ = 30, $K_i$ = 10 and $K_d$ = 10, then the step response output curve is ideal when the integral time $Ti$ = $K_P/K_{i }$ = 3 and the differential time $TD$ = $K_d/{ K}_P$ = 0.33.

3.2. Results of Conveying and Positioning on X-Axis

The results of seedling tray conveying and positioning on the X-axis are shown in

Table 5. The deviation in seedling tray conveying and positioning.

Size	Initial Positioning				Intermission Conveying
	Max/mm	Min/mm	Average/mm	Variable Coefficient/%	Max/mm	Min/mm	Average/mm	Variable Coefficient/%
21	1.02	0.62	0.75	26.11	0.72	0.49	0.63	13.11
32	0.94	0.55	0.75	24.45	0.78	0.53	0.62	14.23
50	1.01	0.53	0.69	24.13	0.82	0.61	0.68	12.48
72	0.79	0.63	0.71	7.08	0.63	0.51	0.59	7.91
98	1.12	0.66	0.87	22.24	0.71	0.53	0.63	9.67
105	0.99	0.53	0.75	26.28	0.85	0.46	0.64	19.81
128	1.34	0.86	1.03	16.35	0.72	0.61	0.62	10.54
200	1.05	0.61	0.82	19.14	0.63	0.54	0.59	7.66
288	0.79	0.52	0.64	16.31	0.69	0.50	0.60	11.49

. The average deviation in the initial positioning across different specifications ranged from 0.69 mm to 1.03 mm. The maximum deviation was observed with the 128-hole seedling tray at 1.34 mm, while the minimum deviation of 0.53 mm was recorded for both the 50-hole and 105-hole trays. Among the coefficient of variation values for deviation across nine trays, the highest was 26.28% for the 105-hole tray and the lowest was 7.08% for the 72-hole tray. For intermission positioning, the average deviation across different specifications ranged from 0.59 mm to 0.68 mm. The maximum deviation was 0.85 mm for the 105-hole seedling tray and the minimum deviation, also for the 105-hole tray, was 0.46 mm. Among the nine coefficients of variation for intermission positioning, the largest value was 19.81% for the 105-hole tray and the smallest was 7.91% for the 72-hole tray. In general, the intermittent positioning deviation was smaller than that of the initial positioning, which may be caused by long distance conveying for the first positioning. The coefficient of variation of the intermission positioning for the deviation was smaller than that of the initial positioning. The coefficient of variation was generally large, which may be related to the number of tests for each specification; there were only five groups.

For various sizes of seedling trays, each has its own positioning deviation, which shows no correlation. Notably, the 105-hole tray tends to exhibit larger positioning deviations. This can be observed in Table 1, where the weight of the 105-hole tray is lighter compared to other trays. A lighter weight indicates a thinner tray. This phenomenon arises because the signal detected by the photoelectric sensor from the tray is influenced by the material’s light transmittance, leading to recognition errors. Compared with other studies [14,20], it was further proved that using two sensors and a servo-control system can increase the accuracy to within a millimeter level.

Although each transmission for the initial positioning and intermission conveying will produce a certain deviation, it is mentioned in the national standard and other papers that the error of the positioning deviation can be allowed within 2 mm [30], so the first positioning and intermittent positioning deviation of all seedling trays on the X-axis can still meet the requirements.

3.3. Results of Moving and Positioning on Y-Axis

The results of the conveying platform moving and positioning on the Y-axis are shown in

Table 6. The deviation in conveying platform moving and positioning.

Size	Initial Positioning				Intermission Moving
	Max/mm	Min/mm	Average/mm	Variable Coefficient/%	Max/mm	Min/mm	Average/mm	Variable Coefficient/%
21	0.89	0.63	0.75	11.53	0.89	0.55	0.65	19.27
32	0.66	0.45	0.55	12.61	0.91	0.63	0.76	16.82
50	0.98	0.71	0.87	11.79	0.91	0.59	0.73	16.07
72	0.96	0.57	0.72	19.19	0.92	0.63	0.78	13.17
98	0.86	0.63	0.72	12.84	0.98	0.69	0.76	6.58
105	0.97	0.59	0.82	18.45	0.96	0.71	0.87	10.56
128	0.86	0.72	0.76	7.35	0.97	0.53	0.78	19.33
200	0.99	0.68	0.81	16.80	0.92	0.55	0.70	18.53
288	0.97	0.71	0.86	11.58	0.96	0.63	0.76	14.72

. It shows that the average deviation in initial positioning for different specifications ranged from 0.55 mm to 0.87 mm. The maximum deviation observed was 0.99 mm for the 200-hole seedling tray, while the minimum deviation recorded was 0.45 mm for the 32-hole seedling tray. Among the coefficient of variation values for deviation across nine trays, the largest was 19.19% for the 72-hole tray and the smallest was 7.35% for the 128-hole tray. The average deviation in intermission positioning across different specifications ranged from 0.65 mm to 0.87 mm. The maximum deviation was 0.98 mm for the 98-hole seedling tray, whereas the minimum deviation was 0.53 mm for the 128-hole seedling tray. Among the nine coefficients of variation for intermission positioning, the largest value was 19.33% for the 128-hole seedling tray and the smallest was 6.58% for the 98-hole tray.

For different sizes of seedling trays on the Y-axis, each positioning deviation had no correlation. While the deviation for the moving and positioning of the platform was smaller than the deviation for the conveying and positioning of the seedling tray, that is because the seedling tray was put on the conveying platform and the positioning can rely on the recognized sensor on the Y-axis for the stable device; the whole platform was fixed and had less activity space. So, the deviation for the initial positioning and intermission conveying on the X-axis was smaller than that for the initial positioning and intermission moving on the Y-axis, as with the coefficient of variation. The positioning deviation in the intermission moving on Y-axis was larger than that of the initial positioning, but it was also smaller than that of the intermittent movement in the X direction.

3.4. Discussion

The deviation in the seedling positioning in two directions indicates that the dual-axis positioning tray conveying device with precise servo-control system is effective; there are some errors within the allowable range. Some researchers simply place pallets on delivery plates, which can affect positioning during delivery [20]. Our paper solves this problem by using inverted V clearance to fix the pallet on the push rod, and the tray can be fixed because the width coincides with that of the conveying platform, ensuring that, even if the pallet has transverse inertia displacement [16], it can be controlled within a reasonable mechanical error range.

The method studied in this paper is crucial for the positioning of seedling trays, especially the ordinary plastic trays used in China, because the quality of the seedling trays available on the market is uneven, and the results of a heavier seedling tray will be more stable. At the same time, the device can be applied to different specifications of the same external size of the seedling tray; with only the need to change the operation parameters in the control system, it can be applied to large, small and medium seedling pots for conveying and extraction in various fields such as vegetables, flowers, tobacco and fruits. It is more versatile than the previous device for a single seedling tray or even a special seedling tray [10,14,20].

This study also provided a useful reference for the subsequent seedling selection. This dual-axis conveying device can be applied to pick seedlings at intervals in rows [28], and can extract 8 or 16 seedlings at the same time [31]. Therefore, the efficiency of picking seedlings was improved and it can greatly improve the efficiency of the transplanter with a high-speed planting device.

4. Conclusions

To enhance the versatility of the seedling tray conveying device used in fully automatic transplanting machines across various specifications, and improve the positioning accuracy of commonly used PVC/PC seedling trays in China, a dual-axis positioning tray conveying device was developed. This device supports seedling trays ranging from 21 to 288 holes, enabling X-axis tray conveyance and Y-axis platform movement. It employs a dual-sensor positioning algorithm and a variable displacement positioning method to achieve precise initial positioning and intermittent movement in both the X and Y directions.

The device utilizes a servo motor control system with a three-closed-loop control and a PID algorithm to achieve precise positioning. The schematic of the precise positioning control system and its transfer function were validated using Simulink software to optimize the parameter combinations. The results showed that $K_P$ = 30, $K_i$ = 10 and $K_d$ = 10 performed optimally, producing an ideal step response output curve with an integral time $Ti$ = 3 and differential time $TD$ = 0.33.

The initial positioning and intermission conveying on the X-axis and Y-axis were tested on a bench with single-step debugging; nine different sizes of seedling trays were used to measure the deviations. The data showed that the initial positioning deviation of the seedling tray on the X-axis was up to 1.34 mm, the maximum deviation in intermission conveying was 0.85 mm and the maximum coefficient of variation was 26.28%. The positioning deviation on the Y-axis was smaller than that on the X-axis, the initial positioning deviation was up to 0.99 mm, the deviation in intermission moving was up to 0.98 mm and the coefficient of variation was up to 19.33%. The experimental results show that the deviation in seedling tray positioning and conveying can meet the requirements of accurate conveying, and is accurate for a fully automatic transplanting machine.