Development and Evaluation of a Calibrating System for the Application Rate Control of a Seed-Fertilizer Drill Machine with Fluted Rollers

: Seed-fertilizer drill machines with ﬂuted rollers generally utilize a calibrated relationship between the ﬂuted-roller rotation speed and mass ﬂow rate to control the application rate. However, this relationship model gradually deteriorates with operating time and is easily a ﬀ ected by working conditions. To maintain the initial operating accuracy, a self-calibrating system for adjusting the control model parameters was designed. It utilizes the application-rate information and ﬂuted-rollers rotation speed data during the operation process to dynamically establish the calibrated relationship. During the ﬁeld tests performed 18 times, the self-calibrating system could dynamically re-calibrate the relationship model. After the model parameters were updated, the application rate control system maintained a high accuracy level, though the relative deviation of control parameters was relatively higher. The average relative deviations between actual and theoretical cumulative application rates were 0.97% and 1.22% for seeding and fertilizing, respectively, and the standard deviations were 0.69% and 0.62%. Correspondingly, the average relative deviations of control parameters were 7.29% and 7.86%, and the standard deviations were 1.16% and 3.06%. These results indicate that the proposed method with closed-looped control can maintain high-quality control performance and improve the productivity of the drill machine, which will beneﬁt the agricultural production.


Introduction
Precision fertilizing and seeding operations are two key parts of the wheat cultivation process. Precision control of the application rate and the wheat seed-fertilizer drill machine has been of interest to researchers [1,2]. Precision control of the wheat application rate depends not only on the measurement and control technology, but also on the performance of the seed-fertilizer drill machine [3].
Zhang et al. proposed a variable rate fertilizing technology. This control system was based on a single-chip microcomputer. The input was the forward speed of the machine and the target application rate of the prescription chart. The output was the rotation speed of the fertilizing and seeding driving shaft, which determined the actual application rate [4]. The motor is generally divided into three types: the stepper motor [5], DC(Direct-current) motor [6], and hydraulic motor [7]. According to their respective control principles, the speed control can be realized. These typical methods of controlling the application rate are, essentially, open-looped control methods. Their common characteristic is to in actual production. The accuracy of the control system for controlling the application rate depends on the correctness of the control model. The control model commonly used at present is based on the calibration relationship model of the mass flow rate and the rotation speed of the fluted-roller driving shaft. The parameters of the calibration relationship model will change with the increase of working time and the change of working conditions, which affect the control performance of the control system. The aim of this paper is to establish a method which can self-calibrate the parameters of the relationship model according to the measured data while working to dynamically adjust the parameters of the control model and maintain the control accuracy of the control system that is running in a closed-loop. In this paper, the application rate measurement device [27], which was based on the weighing principle (and previously designed by the author's team), was used to measure the relationship model between the dynamic cumulative application rate and the dynamic cumulative rotation cycles in a certain period of time. Furthermore, the ratio coefficient between the mass flow rate and rotation speed can be obtained using the established relationship model.

Materials and Methods
This section mainly introduces the method of constructing a closed-looped control system which is based on the self-developed application rate measuring system and control parameter self-calibrating strategy. The commonly used form and existing problems of the control system are described in detail. We focus on the structure, control strategy, and implementation algorithms of the closed-looped control system to provide a reference for researchers with similar research interests.

Application Rate Control Model
The real-time fertilizing and seeding application rate of seed-fertilizer drill machine can be expressed with the following equation: where M(t) is the fertilizing or seeding application rate (kg/ha), F(t) is the material mass flow rate (kg/min), B is the operation width (m), V(t) is the vehicle speed (km/h), and c refers to the unit conversion coefficient between different variables. The relationship model between the rotation speed R(t) of the fluted-roller driving shaft and the mass flow rate F(t) of the seed-fertilizer drill machine can be established as a linear equation by calibration, and can be expressed as: where k is the ratio coefficient of the relationship model between the mass flow rate and rotation speed and represents the amount of material flowing from each single rotation of the fluted rollers (kg/r) and b is the constant term of the fitting equation (kg/min). Using Equations (1) and (2), the rotation speed of the fluted-roller driving shaft can be expressed as Equation (3).
Equation (3) is the basic control model for controlling the application rate of the seed-fertilizer drill machine with fluted rollers. In practice, the main controller calculates the driving shaft rotation speed in real-time, according to the relationship model shown in Equation (3), combining the target application rate with the vehicle speed to ensure that the actual application rate matches the target application rate.

Closed-Looped Control Strategy
In general, the application rate control was realized using the strategy described in Figure 1. It was essentially an open-looped method because there was no feedback data for updating parameters k and b. k and b were the parameters of the control model expressed as Equation (3). The value of the parameters (k and b) varied with the increase of usage time or changes in working conditions. If there was no effective device to sense the change of the model parameters, the fluted-roller rotation speed calculated from Equation (3) deviated the actual control target and caused a control error. Therefore, in order to maintain excellent control performance, effective methods were needed to sense the change of k and b and dynamically adjust the control model parameters.

Closed-Looped Control Strategy
In general, the application rate control was realized using the strategy described in Figure 1. It was essentially an open-looped method because there was no feedback data for updating parameters k and b. k and b were the parameters of the control model expressed as Equation (3). The value of the parameters (k and b) varied with the increase of usage time or changes in working conditions. If there was no effective device to sense the change of the model parameters, the fluted-roller rotation speed calculated from Equation (3) deviated the actual control target and caused a control error. Therefore, in order to maintain excellent control performance, effective methods were needed to sense the change of k and b and dynamically adjust the control model parameters. A closed-looped control system for controlling the application rate was constructed, which is shown in Figure 2. The parameters of the self-calibrating system and application rate measuring system were introduced as the feedback channel to establish a closed-looped control system. The new relationship model between the mass flow rate and rotation speed was linearly fitted by recording the dynamic cumulative application rate Q(t) and the dynamic cumulative rotation cycles N(t) in a certain period. The parameters of the new relationship model were compared to the original model parameters, and then the control model parameters were corrected and updated according to the preset conditions. The k and b measured by the calibrating system replaced k0 and b0 in the original calibration model to maintain the control accuracy of the application rate. Figure 2. Block diagram of a closed-looped control strategy for the application rate control based on the parameter self-calibrating system.

Parameter Self-Calibrating Algorithm for the Application Rate Control
The flow chart of the parameter self-calibrating algorithm for application rate control is shown in Figure 3. The cumulative increment signal of the weighing sensor D(t) was obtained by the application rate measuring system, the vehicle speed V(t) was obtained by the speed measuring sensor, and the rotation speed R(t) of the fluted rollers was obtained by a rotary encoder. The control parameter self-calibrating system, combining the sensor signals from multiple sources, obtained the

R(t)
Motor rotation speed control system Parameters self-calibrating system for application rate control

N(t) Q(t)
Calibration model: A closed-looped control system for controlling the application rate was constructed, which is shown in Figure 2. The parameters of the self-calibrating system and application rate measuring system were introduced as the feedback channel to establish a closed-looped control system. The new relationship model between the mass flow rate and rotation speed was linearly fitted by recording the dynamic cumulative application rate Q(t) and the dynamic cumulative rotation cycles N(t) in a certain period. The parameters of the new relationship model were compared to the original model parameters, and then the control model parameters were corrected and updated according to the preset conditions. The k and b measured by the calibrating system replaced k 0 and b 0 in the original calibration model to maintain the control accuracy of the application rate.

Closed-Looped Control Strategy
In general, the application rate control was realized using the strategy described in Figure 1. It was essentially an open-looped method because there was no feedback data for updating parameters k and b. k and b were the parameters of the control model expressed as Equation (3). The value of the parameters (k and b) varied with the increase of usage time or changes in working conditions. If there was no effective device to sense the change of the model parameters, the fluted-roller rotation speed calculated from Equation (3) deviated the actual control target and caused a control error. Therefore, in order to maintain excellent control performance, effective methods were needed to sense the change of k and b and dynamically adjust the control model parameters. A closed-looped control system for controlling the application rate was constructed, which is shown in Figure 2. The parameters of the self-calibrating system and application rate measuring system were introduced as the feedback channel to establish a closed-looped control system. The new relationship model between the mass flow rate and rotation speed was linearly fitted by recording the dynamic cumulative application rate Q(t) and the dynamic cumulative rotation cycles N(t) in a certain period. The parameters of the new relationship model were compared to the original model parameters, and then the control model parameters were corrected and updated according to the preset conditions. The k and b measured by the calibrating system replaced k0 and b0 in the original calibration model to maintain the control accuracy of the application rate.

Parameter Self-Calibrating Algorithm for the Application Rate Control
The flow chart of the parameter self-calibrating algorithm for application rate control is shown in Figure 3. The cumulative increment signal of the weighing sensor D(t) was obtained by the application rate measuring system, the vehicle speed V(t) was obtained by the speed measuring sensor, and the rotation speed R(t) of the fluted rollers was obtained by a rotary encoder. The control parameter self-calibrating system, combining the sensor signals from multiple sources, obtained the

R(t)
Motor rotation speed control system Parameters self-calibrating system for application rate control

N(t) Q(t)
Calibration model: Figure 2. Block diagram of a closed-looped control strategy for the application rate control based on the parameter self-calibrating system.

Parameter Self-Calibrating Algorithm for the Application Rate Control
The flow chart of the parameter self-calibrating algorithm for application rate control is shown in Figure 3. The cumulative increment signal of the weighing sensor D(t) was obtained by the application rate measuring system, the vehicle speed V(t) was obtained by the speed measuring sensor, and the rotation speed R(t) of the fluted rollers was obtained by a rotary encoder. The control parameter self-calibrating system, combining the sensor signals from multiple sources, obtained the latest relationship model between the mass flow rate and rotation speed during the actual operation of the drill machine. The specific algorithm is described as follows.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 15 latest relationship model between the mass flow rate and rotation speed during the actual operation of the drill machine. The specific algorithm is described as follows. (1) Acquisition of dynamic cumulative application rate Q(t) The dynamic cumulative increment of the weighing sensor D(t) was obtained by the application rate measuring system and was used to determine the cumulative application rate. However, the low stability of the D(t) signal, due to the complexity of field operations, required a more complicated processing method. To obtain more accurate dynamic cumulative application rate signals, a least squares method [28,29] was used to perform a zero-crossing linear fitting of the dynamic cumulative increment D(t) and dynamic cumulative operation area S(t). The linear fitting results gave the dynamic cumulative application rate Q(t). S(t) was calculated by accumulating the product of vehicle speed and operation width of the seed-fertilizer drill machine.
(2) Acquisition of the relationship model between mass flow rate and rotation speed Linear fitting of the dynamic cumulative application rate data Q(t) and dynamic cumulative rotation cycles N(t) over a certain observation time T was used to obtain the relationship model between the mass flow rate and the rotation speed during the operation of the seed-fertilizer drill machine. The parameters of the linear fitting equation included the calibration parameters k and b, and T were determined according to the actual operation condition. The dynamic cumulative rotation cycles N(t) were calculated by accumulating the rotation speed of the fluted rollers over the observation time T.

Hardware System for Measuring the Application Rate
In this study, an application rate measuring device [27] based on the weighing principle (previously designed by our research team) was used as the measuring device during the operation of the seed-fertilizer drill machine. A schematic diagram of the measurement device is shown in Figure 4. This device was used to acquire the cumulative application rate information during the operation of the seed-fertilizer drill machine. Along with the rotation speed information of the fluted rollers, the relationship model between the mass flow rate and speed rotation during the operation process of the seed-fertilizer drill machine was determined, which served as the basis for calibrating the control model parameters k and b.
Control parameters self-calibrating system Application rate measuring system Calculating system of cumulative operation area Calibration determiner (1) Acquisition of dynamic cumulative application rate Q(t) The dynamic cumulative increment of the weighing sensor D(t) was obtained by the application rate measuring system and was used to determine the cumulative application rate. However, the low stability of the D(t) signal, due to the complexity of field operations, required a more complicated processing method. To obtain more accurate dynamic cumulative application rate signals, a least squares method [28,29] was used to perform a zero-crossing linear fitting of the dynamic cumulative increment D(t) and dynamic cumulative operation area S(t). The linear fitting results gave the dynamic cumulative application rate Q(t). S(t) was calculated by accumulating the product of vehicle speed and operation width of the seed-fertilizer drill machine.
(2) Acquisition of the relationship model between mass flow rate and rotation speed Linear fitting of the dynamic cumulative application rate data Q(t) and dynamic cumulative rotation cycles N(t) over a certain observation time T was used to obtain the relationship model between the mass flow rate and the rotation speed during the operation of the seed-fertilizer drill machine. The parameters of the linear fitting equation included the calibration parameters k and b, and T were determined according to the actual operation condition. The dynamic cumulative rotation cycles N(t) were calculated by accumulating the rotation speed of the fluted rollers over the observation time T.

Hardware System for Measuring the Application Rate
In this study, an application rate measuring device [27] based on the weighing principle (previously designed by our research team) was used as the measuring device during the operation of the seed-fertilizer drill machine. A schematic diagram of the measurement device is shown in Figure 4. This device was used to acquire the cumulative application rate information during the operation of the seed-fertilizer drill machine. Along with the rotation speed information of the fluted rollers, the relationship model between the mass flow rate and speed rotation during the operation process of the seed-fertilizer drill machine was determined, which served as the basis for calibrating the control model parameters k and b. In this paper, the S-shaped weighing sensor had a range of 100 kg and a minimum detectable mass of 0.1% FS (Full Scale )The stable support force of each spring during work was 50 kg.

Results and Discussion
The entire testing process was performed in a field which lies in the South Jiangsu Province in China. The experimental equipment with the application rate measuring and control system was installed on a rotary tiller. There were 10 seeding units and six fertilizing units installed in the seedfertilizer drill machine. The maximum capacity of the seed tank was 80 kg, and that of the fertilizer tank was 100 kg. The operation width of the seed-fertilizer drill machine was 2.3 m, and the drill machine was attached to an 80 hp tractor. During the operation, wheat seeds and compound fertilizer were fed simultaneously to the rotary fluted rollers. To evaluate the performance, collection bins were placed underneath the seeding and fertilizing outlets. Figure 5 shows the actual experimental setup.  In this paper, the S-shaped weighing sensor had a range of 100 kg and a minimum detectable mass of 0.1% FS (Full Scale) The stable support force of each spring during work was 50 kg.

Results and Discussion
The entire testing process was performed in a field which lies in the South Jiangsu Province in China. The experimental equipment with the application rate measuring and control system was installed on a rotary tiller. There were 10 seeding units and six fertilizing units installed in the seed-fertilizer drill machine. The maximum capacity of the seed tank was 80 kg, and that of the fertilizer tank was 100 kg. The operation width of the seed-fertilizer drill machine was 2.3 m, and the drill machine was attached to an 80 hp tractor. During the operation, wheat seeds and compound fertilizer were fed simultaneously to the rotary fluted rollers. To evaluate the performance, collection bins were placed underneath the seeding and fertilizing outlets. Figure 5 shows the actual experimental setup. In this paper, the S-shaped weighing sensor had a range of 100 kg and a minimum detectable mass of 0.1% FS (Full Scale )The stable support force of each spring during work was 50 kg.

Results and Discussion
The entire testing process was performed in a field which lies in the South Jiangsu Province in China. The experimental equipment with the application rate measuring and control system was installed on a rotary tiller. There were 10 seeding units and six fertilizing units installed in the seedfertilizer drill machine. The maximum capacity of the seed tank was 80 kg, and that of the fertilizer tank was 100 kg. The operation width of the seed-fertilizer drill machine was 2.3 m, and the drill machine was attached to an 80 hp tractor. During the operation, wheat seeds and compound fertilizer were fed simultaneously to the rotary fluted rollers. To evaluate the performance, collection bins were placed underneath the seeding and fertilizing outlets. Figure 5 shows the actual experimental setup.

Test Conditions
The entire testing process was divided into three stages from 13 to 15 December 2018. The weather condition was usually cloudy during tests. Each stage was arranged in one day to complete three groups of experiments. Each group of experiments targeted one application rate combination of wheat and compound fertilizer and was repeated once. The three target application rate combinations were as follows: 225 and 300 kg/ha, 300 and 375 kg/ha, and 375 and 525 kg/ha, respectively, as listed in Table 1. During the tests, the tractor's driving system was fixed in a certain gear, where the operation speed changed within a range of 2 km/h to 4 km/h because of the changing field resistance or different depth on the accelerator pedal during operation. After effectively traveling for 300 m, the test was deemed complete. Because the field in which we performed the test was relatively small, we needed to turn around the tractor several times to reach a 300 m testing distance. The driving speed, the seed, and the fertilizer application rates used during tests are commonly adopted operation parameters in practice in Jiangsu Province in China. The recording interval for all measurement parameters was 0.5 s during the tests.

Test Scheme
Three stages of the tests carried out in the field are described as follows: The first test stage: The seed fertilizer drill machine controlled the application rate according to the calibrated relationship model between the mass flow rate and rotation speed. After each test, the application rate calibration system fitted the relationship model between the mass flow rate and rotation speed based on the latest test data but did not update the system control parameters.
The second test stage: To significantly and quickly change the calibrated model parameters, the gap between the fluted rollers and the top of the brush was artificially shortened by 1 mm by trimming the brush length of the seed-fertilizer drill machine. This would increase the mass flow rate and change the relationship model between the mass flow rate and rotation speed. The seed-fertilizer drill machine applied the original calibrated relationship model between the mass flow rate and rotation speed to complete the same test as in the first stage.
The third test stage: Using the latest test data from the application rate calibration system, the relationship model parameters of the control system were updated to control the application rate more accurately.
After each test stage, the performance of the application rate calibration system was evaluated by comparing the difference between the relationship model parameters and the relative deviation of application rates. To evaluate the control effect of the actual application rate, bins were placed under each outlet to collect the seeds or compound fertilizers. After the completion of each test, the collected materials were weighed.

Calibration of the Relationship between the Mass Flow Rate and Rotation Speed
The original relationship model between the mass flow rate and rotation speed was calibrated as follows: During each calibration test process, the driving shaft rotation speed of the fluted rollers was controlled to rotate at a constant speed at different set speeds for 3 min. By weighing the actual material collected in the output bins, the relationship model between the mass flow rate and rotation speed was established, as shown in Figure 6. The ratio coefficients of seeds and compound fertilizers were 0.1015 kg per rotation and 0.162 kg per rotation, respectively.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15 material collected in the output bins, the relationship model between the mass flow rate and rotation speed was established, as shown in Figure 6. The ratio coefficients of seeds and compound fertilizers were 0.1015 kg per rotation and 0.162 kg per rotation, respectively.

Calculating Process of the Parameter Self-Calibration
To illustrate the data processing results of each step, one of the test results in the first test stage was taken as an instance in which the target application rate of seeding and fertilizing were 375 kg/ha and 525 kg/ha, respectively. First, the cumulative increment signal D(t) of seeds and compound fertilizers were measured by the application rate measuring system, as shown in Figure 7. The large fluctuation in the signal was due to the lifting and lowering of the tractor when the tractor turned around.

Calculating Process of the Parameter Self-Calibration
To illustrate the data processing results of each step, one of the test results in the first test stage was taken as an instance in which the target application rate of seeding and fertilizing were 375 kg/ha and 525 kg/ha, respectively. First, the cumulative increment signal D(t) of seeds and compound fertilizers were measured by the application rate measuring system, as shown in Figure 7. The large fluctuation in the signal was due to the lifting and lowering of the tractor when the tractor turned around.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15 material collected in the output bins, the relationship model between the mass flow rate and rotation speed was established, as shown in Figure 6. The ratio coefficients of seeds and compound fertilizers were 0.1015 kg per rotation and 0.162 kg per rotation, respectively.

Calculating Process of the Parameter Self-Calibration
To illustrate the data processing results of each step, one of the test results in the first test stage was taken as an instance in which the target application rate of seeding and fertilizing were 375 kg/ha and 525 kg/ha, respectively. First, the cumulative increment signal D(t) of seeds and compound fertilizers were measured by the application rate measuring system, as shown in Figure 7. The large fluctuation in the signal was due to the lifting and lowering of the tractor when the tractor turned around.  Secondly, the zero-crossing linear fitting between D(t) and S(t) of the fertilizing and the seeding area was carried out, and the dynamic cumulative application rate information Q(t) was calculated, as shown in Figure 8.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15 Secondly, the zero-crossing linear fitting between D(t) and S(t) of the fertilizing and the seeding area was carried out, and the dynamic cumulative application rate information Q(t) was calculated, as shown in Figure 8. Finally, the dynamic cumulative application rate Q(t) and the dynamic cumulative rotation cycles N(t) of the fluted rollers were linearly fitted, and the relationship between the mass flow rate and rotation speed was obtained, as shown in Figure 9, from which the updated calibration model parameters (k, b) can be obtained. Finally, the dynamic cumulative application rate Q(t) and the dynamic cumulative rotation cycles N(t) of the fluted rollers were linearly fitted, and the relationship between the mass flow rate and rotation speed was obtained, as shown in Figure 9, from which the updated calibration model parameters (k, b) can be obtained.  rates. Figure 11 shows the absolute relative deviation after each test between the model ratio coefficient k measured by the application rate calibration system and the original calibration parameters. The relative deviation E k defined in Equation (4) is used to describe the change of relationship model parameters. The relevant statistical data are listed in Table 2.

Test Results of the Application Rate Measuring System
where k real is the model ratio coefficient measured by the application rate calibration system and k org is the ratio coefficient of the original relationship model.
is the ratio coefficient of the original relationship model. Note: avg is the average relative deviation of Ek, Std is the standard deviation of the relative deviation of Ek, and max is the maximum relative deviation of Ek.
From the test results, it can be observed that the calibration relationship model was relatively stable for a short period. However, the model parameters for the fertilizing varied more obviously than those for seeding, probably due to the fertilizers being more prone to moisture absorption and their working performance being affected easily by environmental changes. The relative deviation of model parameters increased significantly with usage-time increase or environmental changes.

Test Performance of the Control Parameter Self-Calibrating System
The control model was based on the calibration relationship model between the mass flow rate and rotation speed. The calibration relationship model was established before the operation with no model parameters being updated during the process. The closer the calibration relationship model was to the actual relationship model, the higher the control accuracy. However, the actual relationship model was quite different from the original model because of the impact from working Test serial number  Note: avg is the average relative deviation of E k , Std is the standard deviation of the relative deviation of E k , and max is the maximum relative deviation of E k .
From the test results, it can be observed that the calibration relationship model was relatively stable for a short period. However, the model parameters for the fertilizing varied more obviously than those for seeding, probably due to the fertilizers being more prone to moisture absorption and their working performance being affected easily by environmental changes. The relative deviation of model parameters increased significantly with usage-time increase or environmental changes.

Test Performance of the Control Parameter Self-Calibrating System
The control model was based on the calibration relationship model between the mass flow rate and rotation speed. The calibration relationship model was established before the operation with no model parameters being updated during the process. The closer the calibration relationship model was to the actual relationship model, the higher the control accuracy. However, the actual relationship model was quite different from the original model because of the impact from working conditions. Hence, a dynamic calibration of model parameters was required during the process. In the first and second test stages, the parameters of the actual relationship model were detected based on the measured data from a certain period, but no update of the parameters was introduced. In the third test stage, the test procedure called for an update to the control model parameters to improve the control performance. To evaluate the quality of the operation of the seed-fertilizer drill machine, an evaluation indicator E Q was introduced, as shown in Equation (5).
where W real is the weight of materials collected by the collection container and W rotation is the cumulative application rate, calculated using the relationship model of the mass flow rate and rotational speed of the fluted rollers. The evaluation indicator of each test stage is shown in Figure 12, and related statistical results are listed in Table 3.

Discussion
From the test results, it can be observed that in the first test stage, the actual model ratio coefficient k changed slightly from its original level. Further, the relative deviation of the cumulative application rate was less than 3%, which indicated that the overall control accuracy was excellent, and the calibration relationship model was relatively stable for a short period (in one day of work in our tests). This relative stability is the main reason for the ongoing wide usage of the current openlooped model, as users tend to ignore the fact that the control error gradually increases with the operating time.
In the second and third test stages, the change of the ratio coefficient k was much larger than in the first test stage, as the original parameters of relationship model had been deliberately changed and the relative deviation of the ratio coefficient exhibited a gradual upward trend with the operating time. Since the control parameters were not updated in the second test stage, the relative deviation of the cumulative application rate was significantly higher than in the first test stage. This indicated that the preset control model was quite different from the actual control object model. Because of the essential open-loop of the control system, the control system could not correct the control deviation itself. With the increase of working time, the control effect of the control system weakened or even lost effect.
In the third test stage, the relative deviation of the ratio coefficient k further increased. Deformation or damage in the brushes appeared relatively more frequently than in the first two test stages. Further, the increased moisture absorption by the fertilizer resulted in partial caking and bonding in the rollers and brushes. These phenomena can potentially be the reason for the deviation from the original calibration relationship model. However, the relative deviation of the cumulative application rate did not increase with the increase in the ratio coefficient k. Conversely, it decreased

Discussion
From the test results, it can be observed that in the first test stage, the actual model ratio coefficient k changed slightly from its original level. Further, the relative deviation of the cumulative application rate was less than 3%, which indicated that the overall control accuracy was excellent, and the calibration relationship model was relatively stable for a short period (in one day of work in our tests). This relative stability is the main reason for the ongoing wide usage of the current open-looped model, as users tend to ignore the fact that the control error gradually increases with the operating time.
In the second and third test stages, the change of the ratio coefficient k was much larger than in the first test stage, as the original parameters of relationship model had been deliberately changed and the relative deviation of the ratio coefficient exhibited a gradual upward trend with the operating time. Since the control parameters were not updated in the second test stage, the relative deviation of the cumulative application rate was significantly higher than in the first test stage. This indicated that the preset control model was quite different from the actual control object model. Because of the essential open-loop of the control system, the control system could not correct the control deviation itself. With the increase of working time, the control effect of the control system weakened or even lost effect.
In the third test stage, the relative deviation of the ratio coefficient k further increased. Deformation or damage in the brushes appeared relatively more frequently than in the first two test stages. Further, the increased moisture absorption by the fertilizer resulted in partial caking and bonding in the rollers and brushes. These phenomena can potentially be the reason for the deviation from the original calibration relationship model. However, the relative deviation of the cumulative application rate did not increase with the increase in the ratio coefficient k. Conversely, it decreased to a relatively lower level, similar to the initial test stage. This is because the parameters of the self-calibrating system was in action and the closed-looped control effectively counteracted the negative effects of the parameter change on the control object. This indicates that the dynamic calibration on the parameters of the control model had been realized.
The overall test results showed that the calibration relationship model had a relatively higher stability for a short period, but the parameters of the calibration relationship model gradually deteriorated with the operating time. The relationship model needs an appropriate way to calibrate to support the control model in practice to continue with better performance. Our parameters self-calibrating method provides a feasible way to solve this problem.

Conclusions
Seed-fertilizer drill machines with fluted rollers generally use a calibration relationship model between the mass flow rate and driving shaft rotation speed before initiation to control the application rate of seeding and fertilizing. This calibration relationship model is relatively stable for a short period, but the deviation between the calibrated relationship model and the actual model gradually increases with the operating time of the drill machine because there can be significant changes (such as deformation, damage, caking or bonding by wetted fertilizer, etc.) appearing in fluted rollers, brushes, and other working parts. Thus, the accuracy of the seed and fertilizer application rate is negatively affected. This kind of control mode is essentially open-looped. To keep a high-quality operation performance, frequent calibration of the control model is inevitable. This not only affects the work efficiency, but is also not suitable for the use of ordinary farmers, since special skill is required for calibration.
In this paper, based on a self-developed application rate measuring system, we provided a method for the self-calibrating relationship model between the mass flow rate and driving shaft rotation speed. Because of the function of self-calibrating the control parameters, the control mode is closed-looped. Field tests showed that the calibrating system can effectively correct the control parameters based on the detected data from the application rate measuring system from a certain period. It can be used to hold a continuous high-quality control performance and improve actual productivity. This method can be applied to the existing mainstream seed-fertilizer drill machines, which will benefit agricultural production.
In contrast to other closed-looped control methods, we do not use the real-time feedback information of the application rate for controlling, and instead use the integrated information from a certain period to draw the control parameters. Compared to the real-time detection method, our method provides an easier way to obtain effective information in the complicated field operation environment.
It is also noted that actual field operation is complex and there are still many difficulties that need to be solved. It is difficult to determine suitable duration to calibrate new control parameters. Further, the application rate measuring system can be mixed with significant vibration interference. The proposed application rate calibration strategy is not smart enough and requires further detailed study beyond the conducted extent described in this paper.