A stepper motor control processing method and system for flow meter

By calculating the control increment and driving the stepper motor to adjust the flow, the control inaccuracy problem caused by direct flow control in the prior art is solved, and the accuracy of flow control is improved.

CN114531069BActive Publication Date: 2025-04-15SUZHOU QINGKESIYUAN TECH DEV CO LTD
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Patent Information

Application Number
CN202210134886.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-02-14
Publication Date
2025-04-15
Estimated Expiration
2042-02-14

AI Technical Summary

Technical Problem

In the prior art, control is directly based on the flow rate, resulting in the problem of inaccurate control.

Method used

By obtaining the current flow value of the flowmeter and the preset target flow value, the first error and at least one second error are determined, the control increment is calculated, and the flow is adjusted according to the control increment is driven to drive the stepper motor to drive the valve movement.

Benefits of technology

Improve the accuracy of flow control and solve the problem of inaccurate control.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present application discloses a stepper motor control processing method and system for a flowmeter, the method comprising: obtaining the current flow value and a preset target flow value of the flowmeter; determining a first error according to the current flow value and the target flow value; obtaining at least one second error obtained before determining the first error; determining a control increment according to the first error and the at least one second error, wherein the increment is used to indicate the amount to be adjusted in the existing control parameters of the stepper motor of the flowmeter, and the control increment is a positive value or a negative value; and driving the stepper motor to drive the valve movement of the flowmeter to adjust the flow of the flowmeter according to the control increment. The present application solves the problem of inaccurate control caused by directly controlling according to the flow rate in the prior art, thereby improving the control accuracy.
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Description

Technical Field

[0001] The present application relates to the field of flow meters, and in particular, to a stepper motor control processing method and system for a flow meter. Background Art

[0002] Flow meter controllers are mainly used in chip manufacturing, pharmaceutical and food processing industries to meet design requirements such as high-precision small flow control (control accuracy of 1mL / min), small size for easy integration, and long service life.

[0003] Due to industry demand, the flow meter valve is in contact with the controlled liquid and cannot contaminate it. The main components of the liquid valve are made of non-polluting materials such as PFA or PTFE. The general design structure is that the screw pushes the diaphragm to adjust the valve gap to achieve flow control of the controlled liquid. When controlling, it is generally controlled directly according to the required flow rate. This control method has a series of problems such as inaccuracy. Summary of the invention

[0004] The embodiments of the present application provide a stepper motor control processing method and system for a flow meter, so as to at least solve the problem of inaccurate control caused by directly controlling according to flow in the prior art.

[0005] According to one aspect of the present application, a stepper motor control processing method for a flowmeter is provided, including: obtaining a current flow value and a preset target flow value of the flowmeter; determining a first error based on the current flow value and the target flow value; obtaining at least one second error obtained before determining the first error; determining a control increment based on the first error and the at least one second error, wherein the increment is used to indicate the amount of adjustment made in the existing control parameters of the stepper motor of the flowmeter, and the control increment is a positive value or a negative value; and driving the stepper motor to drive the valve movement of the flowmeter to adjust the flow of the flowmeter based on the control increment.

[0006] Further, the at least one second error includes: a previous error obtained by a previous measurement before determining the first error and a previous previous error obtained by a measurement before determining the previous error.

[0007] Furthermore, the stepper motor is driven at a constant current according to a preconfigured first current value to drive the valve to move.

[0008] Furthermore, the stepper motor is driven by a constant current according to a preconfigured first current value to drive the valve movement, including: step S1, selecting a predetermined current value, wherein the stepper motor drives the screw of the valve and the connecting part of the valve film to get stuck under the control of the predetermined current value; step S2, rotating the stepper motor to one end, controlling the stepper motor to lose steps for a predetermined time; step S3, judging whether the stepper motor can be rotated in the reverse direction, and if so, recording the current value and using the current value as the first current value; if not, lowering the current value and executing steps S2 and S3 again, until the stepper motor can be rotated in the reverse direction, and using the lowered current value as the first current value.

[0009] Further, driving the stepper motor according to the control increment includes: determining whether the control increment is within a predetermined range, wherein the predetermined range is used to indicate that when the control increment is within the predetermined range, the stepper motor is not controlled according to the control increment; and when the control increment is not within the predetermined range, driving the stepper motor according to the control increment.

[0010] According to another aspect of the present application, a stepper motor control processing system for a flowmeter is also provided, including: a first acquisition module, used to acquire a current flow value and a preset target flow value of the flowmeter; a first determination module, used to determine a first error based on the current flow value and the target flow value; a second acquisition module, used to acquire at least one second error obtained before determining the first error; a second determination module, used to determine a control increment based on the first error and the at least one second error, wherein the increment is used to indicate the amount of adjustment made in the existing control parameters of the stepper motor of the flowmeter, and the control increment is a positive value or a negative value; a control module, used to drive the stepper motor to drive the valve movement of the flowmeter to adjust the flow of the flowmeter according to the control increment.

[0011] Further, the at least one second error includes: a previous error obtained by a previous measurement before determining the first error and a previous previous error obtained by a measurement before determining the previous error.

[0012] Furthermore, the control module is used to drive the stepper motor with a constant current according to a pre-configured first current value to drive the valve to move.

[0013] Furthermore, the control module is used to perform the following steps: step S1, selecting a predetermined current value, wherein the stepper motor drives the screw of the valve and the connecting part of the valve film to get stuck under the control of the predetermined current value; step S2, rotating the stepper motor to one end, and controlling the stepper motor to lose steps for a predetermined time; step S3, judging whether the stepper motor can be rotated in the reverse direction, and if so, recording the current value and using the current value as the first current value; if not, lowering the current value and performing steps S2 and S3 again, until the stepper motor can be rotated in the reverse direction, and using the lowered current value as the first current value.

[0014] Furthermore, the control module is used to: determine whether the control increment is within a predetermined range, wherein the predetermined range is used to indicate that when the control increment is within the predetermined range, the stepper motor is not controlled according to the control increment; when the control increment is not within the predetermined range, the stepper motor is driven according to the control increment.

[0015] In the embodiment of the present application, the current flow value of the flow meter and the preset target flow value are obtained; a first error is determined according to the current flow value and the target flow value; at least one second error obtained before the first error is determined is obtained; a control increment is determined according to the first error and the at least one second error, wherein the increment is used to indicate the amount to be adjusted in the existing control parameters of the stepper motor of the flow meter, and the control increment is a positive value or a negative value; the stepper motor is driven according to the control increment to drive the valve movement of the flow meter to adjust the flow of the flow meter. The present application solves the problem of inaccurate control caused by direct control based on flow in the prior art, thereby improving control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0017] Figure 1 It is a schematic diagram of the structure of an integral flow meter according to an embodiment of the present application.

[0018] Figure 2 It is a stepper motor control flow chart according to an embodiment of the present application.

[0019] Figure 3 is a flow chart of a current determination method according to an embodiment of the present application.

[0020] Figure 4 is a flowchart of a dead zone algorithm according to an embodiment of the present application. DETAILED DESCRIPTION

[0021] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0022] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0023] In this embodiment, a stepper motor control processing method for a flow meter is provided, and the steps included in the method are described below.

[0024] Step S102, obtaining the current flow value of the flow meter and the preset target flow value;

[0025] Step S104, determining a first error according to the current flow value and the target flow value;

[0026] Step S106, obtaining at least one second error obtained before determining the first error;

[0027] In this step, at least one second error may be implemented in multiple ways. For example, the at least one second error includes: determining the last error obtained by the last measurement before the first error and the last-last-last error measured before the last error.

[0028] Step S108, determining a control increment according to the first error and the at least one second error, wherein the increment is used to indicate an amount to be adjusted in an existing control parameter of the stepper motor of the flow meter, and the control increment is a positive value or a negative value;

[0029] Step S110: driving the stepper motor to drive the valve of the flow meter to move according to the control increment to adjust the flow of the flow meter.

[0030] By using the control increment as the control parameter through the above steps, the problem of inaccurate control caused by directly controlling according to the flow rate in the prior art is solved, thereby improving the control accuracy.

[0031] In actual application, the following problems may occur with stepper motors: when the stepper motor drives the valve to rotate to one end, the valve cannot continue to rotate. At this time, since the thread between the valve screw and the film fixing is a fine thread, and the film fixing is made of plastic, it will deform after pressure is applied, and it is easy for the screw and the film fixing to get stuck, that is, they get stuck when rotating forward, and cannot reverse smoothly when reversing again, causing the stepper motor to be stuck and unable to continue to control the flow.

[0032] To solve this problem, in this embodiment, the following steps can be adopted.

[0033] Step S1, selecting a predetermined current value, wherein the stepper motor drives the screw of the valve and the connecting piece of the film of the valve to be stuck under the control of the predetermined current value;

[0034] Step S2, rotating the stepper motor to one end, and controlling the stepper motor to lose steps for a predetermined time;

[0035] Step S3, determine whether the stepper motor can be rotated in the reverse direction. If so, record the current value and use the current value as the first current value; if not, adjust the current value lower and execute steps S2 and S3 again until the stepper motor can be rotated in the reverse direction, and use the lowered current value as the first current value.

[0036] At the same time, as another optional implementation, in order to prevent frequent adjustment of the stepper motor, it can also be determined whether the control increment is within a predetermined range, wherein the predetermined range is used to indicate that when the control increment is within the predetermined range, the stepper motor is not controlled according to the control increment; when the control increment is not within the predetermined range, the stepper motor is driven according to the control increment.

[0037] An optional embodiment of the present application is described below with reference to the accompanying drawings.

[0038] In this embodiment, the valve is in contact with the controlled liquid and cannot pollute it. The main components of the liquid valve are made of non-polluting materials such as PFA or PTFE. The general design structure is that the screw pushes the film to adjust the valve gap to achieve flow control of the controlled liquid. This part of the principle can be referred to the company's patent content on valve design in detail, and will not be repeated here. The structure of this valve determines the following characteristics:

[0039] Due to the limited range of film movement, the screw rotation angle range is limited to about 1 to 2 turns (360 to 720 degrees);

[0040] In order to improve the accuracy, the screw adopts fine teeth, which may cause jamming when it rotates to one end;

[0041] In the working process, fine pitch threads also face wear caused by repeated transmission, which affects their lifespan. The screw is made of metal, and the threaded fixing at the end of the film is made of plastic. The friction between different materials is easy to cause wear and eventually lead to failure: the wear of metal screws mainly takes the form of shallowing of threads and accumulation of wear debris; the wear of plastic fixings mainly takes the form of thread misalignment and failure.

[0042] After demonstration and practical verification, the solution described in this embodiment uses a stepper motor to connect with the screw, and the internal logic control circuit adopts an incremental PID algorithm to control the flow rate. At the same time, several special designs are carried out to ensure that the above problems can be well solved.

[0043] In response to the above design goals, the main design tasks of this embodiment are:

[0044] 1. Incremental PID algorithm controls the stepper motor;

[0045] 2. Stepper motor drives specific current driving mode to prevent jamming;

[0046] 3. Dead zone control algorithm improves transmission life.

[0047] The structure of the integral flow meter in this embodiment is as follows Figure 1 As shown, the flow meter is an ultrasonic flow meter, and it can also be other types of flow meters. The valve and the ultrasonic flow meter are connected in series on a liquid pipeline. The real-time flow information detected by the flow meter is input to the logic controller. The logic controller runs an incremental PID controller and other supplementary algorithms inside, and finally calculates the required stepper motor movement angle and transmits it to the stepper motor driver. The stepper motor driver controls the stepper motor to complete the movement, driving the valve to control the flow, forming a closed-loop control.

[0048] 1. Incremental PID algorithm to control stepper motor

[0049] There are two main types of motors that can be selected to drive the screw to rotate. One is a servo device with a code disk, and the other is a stepper motor. For this application, the volume and complexity are reduced, which is conducive to system integration.

[0050] The first type of servo device with a code disk mainly includes a rotary encoding device (photoelectric code disk or magnetic grid, etc.), a brushless DC motor, a servo driver and other components. It is large in size, complex in installation, expensive in installation, and has relatively high subsequent maintenance costs.

[0051] The second type of stepper motor is small in size, has its own position lock, and operates in single step (for example, a two-phase four-wire stepper motor with a step angle of 1.8°). It can quantify the rotation angle without losing steps, and at the same time, complex rotary encoding devices such as code disks can be omitted, which is more beneficial to the present invention.

[0052] Therefore, the present invention adopts a small-volume 28-inch stepper motor to greatly reduce the volume of the entire machine. For example, it has obvious advantages in applications where dozens of flow controllers are installed in a single device.

[0053] However, due to the limited range of valve rotation, which is only 360 to 720 degrees, rather than continuous unlimited rotation, it is impossible to give the valve a fixed opening when the power is turned on. Due to the following factors:

[0054] Valve thread manufacturing errors and the existence of thread gaps;

[0055] The thermal expansion state of the valve material is uncertain;

[0056] The wear of valve thread transmission continues to increase;

[0057] The subsequent resistance of the liquid pipeline is uncertain.

[0058] Therefore, it is not possible to open-loop control pipeline flow by setting the valve opening. A closed-loop control strategy must be adopted. The closed-loop control strategy is executed in the logic controller.

[0059] The program flow of the logic control circuit in this embodiment using the incremental PID control strategy is Figure 2 Shown, in Figure 2 Middle: Get the pre-installed PID parameters, read the current flow value and the target flow value, and then perform incremental PID calculations to finally control the stepper motor rotation and cache related variables.

[0060] When the controller power is turned off, the existing rotation angle is uncertain, and the motor cannot be directly controlled to rotate to a specific angle when it is turned on next time. An incremental PID control strategy is required. Compared with the position PID algorithm, the incremental calculation result is the increment of the current opening, rather than a specific opening value, which is more suitable for the technical solution of stepper motor driving the valve. The incremental calculation formula is as follows:

[0061] Δu(k)=u(k)-u(k-1)

[0062] =K P [e(k)-e(k-1)]+K I e(k)+K D [e(k)-2e(k-1)+e(k-2)]

[0063] in:

[0064] Proportion P: e(k)-e(k-1) this error-last error;

[0065] Integral I:e(i) error;

[0066] Differential D: e(k)-2e(k-1)+e(k-2) this error-2*last error+the previous error.

[0067] K was determined based on multiple experiments P , K I , K D After the parameters are set, these three parameters are three constants. Using the deviation of the three measured values ​​before and after, the current control increment can be calculated by the formula. If the increment is a positive value, the corresponding stepper motor rotates the angle represented by the increment in the direction of increasing the valve opening; if the increment is a negative value, the corresponding stepper motor rotates the angle represented by the increment in the direction of reducing the valve opening. The above control does not need to know the current specific angle position of the stepper motor, that is, it does not need to care about the current specific opening of the valve, but only needs to increase or decrease the opening according to the increment.

[0068] 2. Stepper motor drives specific current driving mode to prevent jamming.

[0069] When the stepper motor drives the valve to rotate to one end, the valve cannot continue to rotate. At this time, since the thread between the valve screw and the film fixing is a fine thread, and the film fixing is made of plastic, it will deform after pressure is applied, and it is easy for the screw and the film fixing to get stuck, that is, they get stuck when rotating forward, and cannot reverse smoothly when reversing again, causing the stepper motor to be stuck and unable to continue to control the flow.

[0070] In the face of this technical problem, the method adopted in this embodiment is to adjust the stepper motor driver to select a suitable current value for constant current driving. The stepper motor needs a dedicated driver to operate normally. This driver can generally set the size of the driving current. According to the setting, the voltage is applied to the coil of the motor for driving. The current directly affects the torque of the stepper motor. Too small a torque will cause the motor to lose steps when rotating rapidly. Too large a torque will cause the stepper motor to run with increased noise and vibration. Most importantly, it will cause the screw and the film fixing to get stuck. Finding a current value that meets a certain speed of operation without causing the screw to get stuck can solve this problem.

[0071] exist Figure 3 Select a current value that is sufficient to get stuck, then rotate the stepper motor to one end, the electrode loss step lasts for 30S, and the motor is rotated in the reverse direction. If it can be reversed, record the current value. If it cannot be reversed, repeat the test to find the current value.

[0072] Following this process can ensure that a maximum current is found without jamming, guarantee the motor torque, and obtain the highest transmission efficiency of the system.

[0073] After setting the appropriate drive current, when the stepper motor drives the valve to rotate to one end, the stepper motor applies a driving force to the screw with a low torque, and the stepper motor loses steps, but does not cause jamming. In serious cases, it will directly damage the screw and the film fixing parts. When reversal is required, since there is no jamming, the stepper motor can rotate in the opposite direction to drive the valve to continue working.

[0074] 3. Dead zone control algorithm improves transmission life

[0075] When the flow controller is working normally, due to the presence of disturbances, the output of the incremental PID algorithm will frequently switch between positive and negative values, and the values ​​are small. Corresponding to the level of mechanical transmission components, the screw repeatedly and rapidly rotates forward and reverse, which aggravates the wear of the screw and the film fixings. The flow controller described in this patent needs to have the advantage of long life in order to operate continuously and normally in industrial scenarios, reduce the frequency of shutdown inspections as much as possible, and be competitive.

[0076] For this reason, this embodiment introduces a dead zone control algorithm as an auxiliary control strategy for incremental PID. Figure 4 As shown, the control strategy includes the following steps: reading the incremental PID output, determining whether the output is greater than the dead zone threshold, if not, canceling the drive of the stepper motor, and if yes, completing the drive.

[0077] Among them, the dead zone is a smaller, positive and negative symmetrical output value range. When the output value falls within this range, the controller chooses not to output. This avoids frequent forward and reverse rotation of the motor and reduces losses. However, this method will introduce additional control errors as long as the error is within the allowable range.

[0078] In this embodiment, an electronic device is provided, including a memory and a processor. The memory stores a computer program, and the processor is configured to run the computer program to execute the method in the above embodiment.

[0079] The above program can be run in the processor, or it can be stored in the memory (or computer-readable medium), which includes permanent and non-permanent, removable and non-removable media. Information storage can be achieved by any method or technology. Information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined in this article, computer-readable media does not include temporary computer-readable media (transitory media), such as modulated data signals and carrier waves.

[0080] These computer programs can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps of the functions specified in one or more blocks can be implemented by different modules corresponding to different steps.

[0081] Such a device or system is provided in this embodiment. The system is called a stepper motor control processing system for a flowmeter, and includes: a first acquisition module, used to acquire the current flow value and a preset target flow value of the flowmeter; a first determination module, used to determine a first error based on the current flow value and the target flow value; a second acquisition module, used to acquire at least one second error obtained before determining the first error; a second determination module, used to determine a control increment based on the first error and the at least one second error, wherein the increment is used to indicate the amount of adjustment in the existing control parameters of the stepper motor of the flowmeter, and the control increment is a positive value or a negative value; a control module, used to drive the stepper motor to drive the valve movement of the flowmeter to adjust the flow of the flowmeter according to the control increment.

[0082] The system or device is used to implement the functions of the method in the above-mentioned embodiment. Each module in the system or device corresponds to each step in the method, which has been explained in the method and will not be repeated here.

[0083] For example, the control module is used to drive the stepper motor with a constant current according to a pre-configured first current value to drive the valve to move. Optionally, the control module is used to perform the following steps: Step S1, select a predetermined current value, wherein the stepper motor drives the screw of the valve and the connecting piece of the valve film to get stuck under the control of the predetermined current value; Step S2, rotate the stepper motor to one end, and control the stepper motor to lose steps for a predetermined time; Step S3, determine whether the stepper motor can be rotated in the reverse direction, if so, record the current value, and use the current value as the first current value; if not, adjust the current value down and perform steps S2 and S3 again, until the stepper motor can be rotated in the reverse direction, and use the adjusted current value down as the first current value.

[0084] For another example, the control module is used to: determine whether the control increment is within a predetermined range, wherein the predetermined range is used to indicate that when the control increment is within the predetermined range, the stepper motor is not controlled according to the control increment; when the control increment is not within the predetermined range, the stepper motor is driven according to the control increment.

[0085] The above-mentioned embodiments solve the problem of inaccurate control caused by directly controlling according to flow rate in the prior art, thereby improving control accuracy.

[0086] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

Claims

1. A stepper motor control processing method for a flow meter, characterized in that: include: Obtain the current flow value of the flow meter and the preset target flow value; Determine a first error according to the current flow value and the target flow value; Acquire at least one second error obtained before determining the first error; Determining a control increment based on the first error and the at least one second error, wherein the increment is used to indicate an amount of adjustment to be made in an existing control parameter of a stepper motor of the flow meter, and the control increment is a positive value or a negative value; According to the control increment, the stepper motor is driven to drive the valve movement of the flow meter to adjust the flow of the flow meter; wherein, according ... The motor is driven by constant current to drive the valve to move, including: step S1, selecting a predetermined current value, wherein the stepper motor drives the screw of the valve and the connecting part of the valve film to get stuck under the control of the predetermined current value; step S2, rotating the stepper motor to one end, controlling the stepper motor to lose steps for a predetermined time; step S3, judging whether the stepper motor can be rotated in the reverse direction, and if so, recording the current value and using the current value as the first current value; if not, lowering the current value and executing steps S2 and S3 again until the stepper motor can be rotated in the reverse direction, and using the lowered current value as the first current value.

2. The method according to claim 1, characterized in that The at least one second error includes: a previous error obtained by a previous measurement before determining the first error and a previous previous error obtained by a previous measurement before determining the first error.

3. A stepper motor control processing system for a flow meter, characterized in that: include: A first acquisition module, used to acquire a current flow value of the flow meter and a preset target flow value; A first determination module, configured to determine a first error according to the current flow value and the target flow value; A second acquisition module, used to acquire at least one second error obtained before determining the first error; a second determination module, configured to determine a control increment according to the first error and the at least one second error, wherein the increment is used to indicate an amount to be adjusted in an existing control parameter of a stepper motor of the flow meter, and the control increment is a positive value or a negative value; A control module, used for driving the stepper motor to drive the valve movement of the flow meter to adjust the flow of the flow meter according to the control increment; wherein, driving the stepper motor according to the control increment includes: judging whether the control increment is within a predetermined range, wherein the predetermined range is used to indicate that when the control increment is within the predetermined range, the stepper motor is not controlled according to the control increment; when the control increment is not within the predetermined range, the stepper motor is driven according to the control increment; wherein, the stepper motor is driven with a constant current according to a pre-configured first current value to drive the valve movement, and the stepper motor is driven according to the pre-configured first current value. The stepper motor is driven by constant current to drive the valve to move, including: step S1, selecting a predetermined current value, wherein the stepper motor drives the screw of the valve and the connecting part of the valve film to get stuck under the control of the predetermined current value; step S2, rotating the stepper motor to one end, controlling the stepper motor to lose steps for a predetermined time; step S3, judging whether the stepper motor can be rotated in the reverse direction, and if so, recording the current value and using the current value as the first current value; if not, lowering the current value and executing steps S2 and S3 again until the stepper motor can be rotated in the reverse direction, and using the lowered current value as the first current value.

4. The system according to claim 3, characterized in that The at least one second error includes: a previous error obtained by a previous measurement before determining the first error and a previous previous error obtained by a previous measurement before determining the first error.

Citation Information

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