Control method, control system and equipment for underwater robot

By analyzing the movement tendency and abnormality of the underwater robot in different directions, and dynamically adjusting the proportional gain of the PID controller, the problems of low control accuracy and high operation difficulty of underwater robots in the prior art are solved, and higher control accuracy and adaptability are achieved.

CN119322526BActive Publication Date: 2025-04-01SHIHANG INTELLIGENT TECHNOLOGY (SUZHOU) CO LTD
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Patent Information

Application Number
CN202411834519.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-13
Publication Date
2025-04-01
Estimated Expiration
2044-12-13

AI Technical Summary

Technical Problem

In the existing underwater robot control methods, the proportional gain of the PID controller is usually preset artificially and cannot be dynamically adjusted according to the external underwater environmental conditions, resulting in a decrease in control accuracy and an increase in operation difficulty.

Method used

By obtaining the moving elements of the movement direction in different directions at several moments, analyzing the movement tendency of the underwater robot between different directions, constructing the main direction of the machine movement, the degree of abnormality of the computer, and dividing the categories to be adjusted by the core machine based on this information, finally obtaining the correction and adjustment component elements to be controlled by the underwater robot.

Benefits of technology

The proportional gain of the PID controller is dynamically adjusted according to the underwater environmental conditions, which improves the control accuracy and operation difficulty of the underwater robot during underwater operation, adapts to the influence of water flow buoyancy, and improves the adaptive ability of the control system.

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Abstract

The present invention relates to the field of underwater robot posture control, and specifically to a control method, control system and equipment for underwater robots, including: based on the moving direction travel element, comparing the movement tendency of the underwater robot between different directions to obtain the degree of movement state; then constructing the machine movement main direction travel sequence of the underwater robot; in the machine movement main direction travel sequence, analyzing the travel degree of the machine movement main direction within a preset local time range, comparing the abnormal changes of the moving direction travel elements between different machine movement main directions, and obtaining the core machine to be adjusted category; analyzing the to-be-adjusted situation of the moving direction travel elements in the same core machine to be adjusted category, and performing posture control. The present invention makes the proportional gain of the PID controller more in line with the requirements of the underwater environment, and makes the control of the underwater robot more accurate during underwater operation.
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Description

Technical Field

[0001] The present invention relates to the field of underwater robot posture control, and in particular to a control method, a control system and equipment for underwater robots. Background Art

[0002] Underwater robots, also known as ROVs, can be widely used in ocean exploration, environmental monitoring, resource exploration, marine engineering and other fields. With the complexity and diversity of the underwater environment, the demand for the use of underwater robots continues to increase. At present, traditional control technologies for underwater robots face many challenges, such as underwater signal attenuation, the influence of fluid dynamics and changeable environmental conditions, all of which require greater control accuracy for underwater robots.

[0003] At present, the control behavior of underwater robots is usually controlled by PID controllers. When using PID controllers to control underwater robots, the proportional gain in the PID controller is usually preset manually and cannot be adjusted according to the external underwater environmental conditions, which increases the difficulty of operating the underwater robot and reduces the control accuracy of the underwater robot. Summary of the invention

[0004] The present invention provides a control method, a control system and a device for an underwater robot to solve the existing problem that, in general, the proportional gain of a PID controller in an underwater robot is usually preset manually for control, and the braking cannot be adjusted according to the external underwater environmental conditions.

[0005] The control method for an underwater robot of the present invention adopts the following technical solution:

[0006] The following steps are involved:

[0007] Get the moving direction elements in different directions at several moments;

[0008] Based on the moving direction elements, the movement tendency of the underwater robot in different directions is compared to obtain the movement state degree of the moving direction elements in different directions; according to the movement state degree, the main movement direction of the machine at different times is screened out from all directions, and the main movement direction sequence of the underwater robot is constructed;

[0009] In the main direction travel sequence of the machine movement, the travel degree of the main direction of the machine movement within the preset local time range is analyzed to obtain the machine abnormality degree at different times; according to the machine abnormality degree, the abnormal changes of the movement direction travel elements between different machine movement main directions are compared, and the movement direction travel elements are divided into the core machine to be adjusted categories;

[0010] The adjustment conditions of the moving direction elements in the same core machine to be adjusted category are analyzed to obtain the corrected adjustment component elements; the posture of the underwater robot is controlled according to the corrected adjustment component elements.

[0011] Preferably, the method for acquiring the degree of motion state is:

[0012] Take any direction as the target direction and any moment as the target moment, compare the difference in the moving direction elements between the target direction and all the overall directions at the same moment, and obtain the degree of the moving state of the target direction at the target moment.

[0013] Preferably, after calculating the degree of motion state, the method further includes:

[0014] Normalize the degree of motion state.

[0015] Preferably, the method for acquiring the main direction travel sequence of the machine movement is:

[0016] Take any moment as the marking moment; at the marking moment, take the direction of the motion direction element with the largest motion state as the main direction of the machine motion at the marking moment; and take the sequence of the main directions of the machine motion at all moments arranged in ascending order as the main direction sequence of the machine motion.

[0017] Preferably, the method for obtaining the abnormality degree of the machine is:

[0018] Take any moment as a reference moment; obtain a preset local time range of the reference moment; analyze the degree of travel in the main direction of the machine movement within the preset local time range to obtain the range machine attitude stability at the reference moment; based on the range machine attitude stability, combined with the analysis of the extreme conditions of the movement tendency at the reference moment in the travel sequence of the main direction of the machine movement, obtain the degree of machine abnormality at the reference moment under the reference moment.

[0019] Preferably, the method for obtaining the range machine posture stability is:

[0020] The stability of the motion state of the overall machine in the main direction of motion within the preset local time range is analyzed to obtain the range machine attitude stability at the reference time.

[0021] Preferably, the method for obtaining the category of the core machine to be adjusted is:

[0022] By comparing the differences in the degree of motion state between the main directions of machine motion at different times, and combining the degree of machine abnormality, the degree of similarity between different times is obtained; based on the degree of similarity, the elements in the motion direction are divided into the core machine category to be adjusted.

[0023] Preferably, the method for obtaining the correction adjustment component elements is:

[0024] By comparing the changes in the degree of machine anomalies between different core machine categories to be adjusted, the machine anomaly control time range is obtained; the coverage length within the machine anomaly control time range is analyzed to obtain the correction adjustment component elements.

[0025] A control system for an underwater robot comprises a memory, a processor and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the above method.

[0026] A control device for an underwater robot, the device comprising:

[0027] A motion direction travel element acquisition module, a machine control command analysis module and an underwater robot control module; wherein the motion direction travel element acquisition module is used to obtain the motion direction travel elements in different directions at several moments, the machine control command analysis module implements the steps of the control method for the underwater robot by calling a computer program to obtain the correction adjustment component elements, and the underwater robot control module performs posture control on the underwater robot according to the correction adjustment component elements.

[0028] The beneficial effects of the technical solution of the present invention are as follows: based on the moving direction travel element, the moving tendency of the underwater robot between different directions is compared to obtain the moving state degree of the moving direction travel elements; wherein the moving state degree is used to reflect the directional tendency of the machine operation in each direction when the underwater robot is working underwater, so that the machine control behavior of the underwater robot in different directions is more obvious; then according to the moving state degree, the moving degree of the main direction of the machine movement within the preset local time range is analyzed to obtain the machine abnormality degree at different times; wherein the machine abnormality degree is used to reflect the difficulty of the underwater robot to maintain the original predetermined direction for machine operation, so that the buoyancy of the external water body on the underwater robot at different times is more easily observed; finally, according to the machine abnormality degree, the adjustment status of the moving direction travel element is analyzed and the posture control of the underwater robot is performed; the present invention analyzes the influence of the water flow buoyancy on the robot device in different directions at different times when the underwater robot is working underwater, adaptively obtains the correction adjustment component element, and then adjusts the proportional gain, and performs posture control on the subsequent operation of the underwater robot through the PID controller, so that the proportional gain of the PID controller is more in line with the requirements of the underwater environment, and the control of the underwater robot during underwater operation is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0030] Figure 1 The present invention is a flowchart of the steps of the control method, control system and equipment for underwater robots. DETAILED DESCRIPTION

[0031] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the control method, control system and equipment for underwater robots proposed by the present invention, their specific implementation methods, structures, features and effects are described in detail below in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0032] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0033] The specific scheme of the control method, control system and equipment for an underwater robot provided by the present invention is described in detail below with reference to the accompanying drawings.

[0034] See also Figure 1 , which shows a flow chart of a control method, a control system and a device for an underwater robot provided by an embodiment of the present invention, the method comprising the following steps:

[0035] Step S001: Obtain movement direction elements in different directions at several moments.

[0036] It should be noted that at present, the control behavior of underwater robots is usually controlled by PID controllers. When using PID controllers to control underwater robots, the proportional gain in the PID controller is usually preset manually and cannot be adjusted according to the external underwater environmental conditions, which increases the difficulty of operating the underwater robot and reduces the control accuracy of the underwater robot.

[0037] In a specific implementation of an embodiment of the present invention, a method for acquiring a moving direction element is as follows: using a three-axis sensor to acquire acceleration elements in each direction of an underwater robot working underwater for nearly a day; and using each acceleration element as a moving direction element.

[0038] It should be noted that the collection interval of acceleration elements is 1 second / time.

[0039] It should be noted that the three-axis sensor can obtain acceleration elements in three directions, and each acceleration element includes a value and a direction.

[0040] So far, the moving direction elements of different directions at several moments are obtained through the above method.

[0041] Step S002: Based on the motion direction travel elements, compare the motion tendencies of the underwater robot between different directions to obtain the motion state degrees of the motion direction travel elements; according to the motion state degrees, select the main directions of the machine motion at different times from all directions, and construct the main direction travel sequence of the machine motion of the underwater robot.

[0042] It should be noted that when an underwater robot is operating underwater, the water flow around it will flow to varying degrees with the robot's behavior and actions, causing the buoyancy of the water in all directions of the underwater robot to change with the flow of water, thereby generating a certain resistance to the underwater robot's predetermined operating behavior, interfering with the underwater robot's movement tendency and thus interfering with the motion state; therefore, based on the moving element of the moving direction, the movement tendency of the underwater robot in different directions can be compared to obtain the degree of the motion state of the moving elements in different moving directions; where the greater the degree of the motion state, the more obvious the movement tendency of the underwater robot in the corresponding direction at the corresponding moment, reflecting that the underwater robot is performing a larger range of operating behavior in the corresponding direction.

[0043] Preferably, in some implementations of the embodiments of the present invention, the method for obtaining the degree of motion state is: taking any direction as the target direction, taking any moment as the target moment, comparing the difference in the moving direction element between the target direction and all the overall directions at the same moment, and obtaining the degree of motion state of the target direction at the target moment. The specific process is as follows:

[0044] The modulus of the moving element of the motion direction of each direction at the target moment is taken as the reference motion tendency component of each direction at the target moment; the mean of the reference motion tendency components of all directions at the target moment is taken as the total reference motion tendency component at the target moment; the normalized value of the ratio between the reference motion tendency component of the target direction at the target moment and the total reference motion tendency component is taken as the degree of motion state of the target direction at the target moment.

[0045] It is particularly noted that in this embodiment The normalization process is performed by taking the function as an example, wherein the normalization function can be determined according to the specific implementation situation.

[0046] It should be noted that, if the degree of the motion state is greater, it means that at the corresponding moment, the movement tendency of the underwater robot in the corresponding direction is more obvious, reflecting that the underwater robot performs a larger range of operation behavior in the corresponding direction.

[0047] It should be noted that the degree of motion state to a certain extent characterizes the motion possibility of the underwater robot at a single moment and in a single direction. For a single moment, the operating state of the underwater robot is mainly characterized by the motion tendencies in various directions. If there is a greater possibility of motion in a certain direction, the motion state of the underwater robot after the overall direction characterization at the corresponding moment will also be close to the corresponding direction. Therefore, according to the degree of motion state, the main direction of the machine motion at different moments can be screened out from all directions, and the main direction movement sequence of the machine motion of the underwater robot can be constructed. In this way, the main motion direction that best characterizes the underwater robot at the corresponding moment can be determined at different moments.

[0048] Preferably, in some implementations of the embodiments of the present invention, the method for acquiring the main direction travel sequence of the machine motion is: taking any moment as the marking moment; at the marking moment, taking the direction of the motion direction travel element with the largest motion state degree as the main direction of the machine motion at the marking moment; and arranging the main directions of the machine motion at all moments in ascending order of time as the main direction travel sequence of the machine motion.

[0049] So far, the main direction movement sequence of the machine is obtained through the above method.

[0050] Step S003: In the main direction movement sequence of the machine, analyze the movement degree of the main direction of the machine within the preset local time range to obtain the machine abnormality degree at different times; according to the machine abnormality degree, compare the abnormal changes of the movement direction movement elements between different machine main directions, and divide the movement direction movement elements into the core machine category to be adjusted.

[0051] It should be noted that in the actual underwater environment, due to the presence of other small organisms and microorganisms underwater, the movement of these organisms may also affect the water flow to a certain extent, making the underwater water flow change relatively rich, resulting in the underwater robot having a sudden change in motion state at a single moment, and these sudden moments are usually less matched with the motion state in the surrounding range; therefore, in the main direction of the machine movement sequence, the degree of movement of the machine in the preset local time range can be analyzed to obtain the machine abnormality degree at the reference moment at different moments. Among them, if the machine abnormality degree is greater, it means that the underwater robot at the corresponding moment is more obviously affected by the buoyancy of the external water body, and the underwater robot is more difficult to maintain the original predetermined direction for machine operation, reflecting that the underwater robot at the corresponding moment is more likely to have control abnormality.

[0052] Preferably, in some implementations of the present invention, the method for obtaining the degree of machine abnormality is: taking any moment as a reference moment; obtaining a preset local moment range of the reference moment; analyzing the degree of travel in the main direction of the machine movement within the preset local moment range to obtain the range machine attitude stability at the reference moment; according to the range machine attitude stability, combined with analyzing the extreme situation of the movement tendency in the main direction of the machine movement sequence at the reference moment, obtain the degree of machine abnormality at the reference moment under the reference moment. The specific process is as follows:

[0053] Preset a time quantity , the reference time before and after The time period constructed by each moment is used as the preset local time range of the reference moment. This example is described as an example, and this embodiment is not specifically limited. It may depend on the specific implementation situation.

[0054] In particular, if the number of actual moments before and after the reference moment does not satisfy , then the preset local time range is obtained based on the actual number of times before and after the reference time.

[0055] Preferably, in some implementations of the present invention, the method for obtaining the range machine posture stability is: analyzing the stability of the motion state of the overall machine in the main direction of motion within a preset local time range to obtain the range machine posture stability at the reference time. The specific process is as follows:

[0056] The average value of the motion state degree of all machines in the main direction of motion within the preset local time range is used as the machine posture stability within the reference time range.

[0057] Furthermore, the main direction of machine movement with the smallest degree of motion state in the main direction movement sequence of the machine movement except for the reference moment is taken as the extreme main direction of machine movement; the absolute value of the difference in degree of motion state between the main direction of machine movement at the reference moment and the extreme main direction of machine movement is taken as the degree of machine abnormality at the reference moment.

[0058] It should be noted that, if the degree of machine abnormality is greater, it means that the underwater robot at the corresponding moment is more obviously affected by the buoyancy of the external water body, and the underwater robot is more difficult to maintain the original predetermined direction to perform machine operations, which reflects that the underwater robot at the corresponding moment is more likely to have control abnormalities.

[0059] Preferably, in some implementations of the present invention, the method for obtaining the category of the core machine to be adjusted is: comparing the difference in the degree of motion state between the main directions of the machine motion at different times, and combining the degree of machine abnormality to obtain the same category at different times; according to the same category, the moving direction elements are divided into the category of the core machine to be adjusted. The specific process is as follows:

[0060] Taking the main direction of machine movement at any two moments as an example, the absolute value of the difference in the degree of motion state of the moving elements in the motion direction between the two main directions of machine movement is taken as the directional motion difference component at the two moments; the normalized value of the product of the directional motion difference component at the two moments and the machine abnormality degree is taken as the degree of belonging to the same category between the two moments.

[0061] Preset two similarity attribute thresholds , the same category belonging degree is greater than and less than The moment is regarded as the abnormal moment of robot control; the category composed of the moving direction elements at the abnormal moment of robot control is regarded as a core machine category to be adjusted; the category with the same degree of belonging greater than The moment is regarded as the abnormal moment of robot control; the category composed of the moving direction elements of all robot control abnormal moments is regarded as a core machine to be adjusted category. This example is described as an example, and this embodiment is not specifically limited. It may depend on the specific implementation situation.

[0062] Optionally, in another embodiment, the specific process of obtaining the category of the core machine to be adjusted is as follows:

[0063] The degree of belonging to the same category between different moments is used as a distance metric, and the machine motion main direction travel sequence is hierarchically clustered according to the distance metric to obtain a number of cluster clusters; the category composed of the motion direction travel elements of all the machine motion main directions in each cluster cluster is used as the core machine category to be adjusted. The process of hierarchical clustering based on the distance metric is a well-known content of the hierarchical clustering algorithm, and will not be repeated in this embodiment. The machine motion main direction travel sequence contains multiple machine motion main directions, and each machine motion main direction corresponds to a moment.

[0064] At this point, the categories of core machines to be adjusted are obtained through the above method.

[0065] Step S004: Analyze the adjustment status of the moving direction elements in the same core machine to be adjusted category to obtain the correction adjustment component elements; and perform posture control on the underwater robot according to the correction adjustment component elements.

[0066] Preferably, in some implementations of the present invention, the method for obtaining the correction adjustment component element is: comparing the change difference of the machine abnormality degree between different core machine adjustment categories to obtain the machine abnormality control time range; analyzing the coverage length within the machine abnormality control time range to obtain the correction adjustment component element. The specific process is as follows:

[0067] The mean of the motion state degree of all the moving elements in each category of core machines to be adjusted is taken as the abnormal motion component of each category of core machines to be adjusted; the variance of the motion state degree of all the moving elements in each category of core machines to be adjusted is taken as the stability of the abnormal motion component of each category of core machines to be adjusted. Each category of core machines to be adjusted contains multiple moving elements in different motion directions, and each moving element in different motion directions corresponds to a moment.

[0068] Furthermore, any core machine to-be-adjusted category is taken as the target adjustment category, and the absolute value of the difference between the abnormal motion components of the target adjustment category and each other core machine adjustment category is taken as a category abnormality difference component of the target adjustment category; the mean of all category abnormality difference components of the target adjustment category is taken as the category abnormality overall difference component of the target adjustment category; the product of the category abnormality overall difference component, the abnormal motion component and the stability of the abnormal motion component of the target adjustment category is taken as the momentary abnormality control degree of the target adjustment category; the momentary abnormality control degree of each core machine to-be-adjusted category is obtained; within the core machine to-be-adjusted category with the largest momentary abnormality control degree, the maximum time range consisting of the times corresponding to the moving elements in all motion directions is taken as the machine abnormality control time range.

[0069] Furthermore, the product of the extreme difference of the motion state degree of the moving element in the motion direction within the machine abnormal control time range and the total number of moments contained in the machine abnormal control time range is used as a correction adjustment component element. The correction adjustment component element is used as a proportional adjustment coefficient and input into the PID controller, and the posture adjustment control of the underwater robot is performed through the PID controller.

[0070] It should be noted that the process of controlling the robot through a PID controller according to the proportional adjustment coefficient is a well-known technology and will not be described in detail in this embodiment.

[0071] At this point, this embodiment is completed.

[0072] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A control method for an underwater robot, characterized in that: The method comprises the following steps: Get the moving direction elements in different directions at several moments; Based on the moving direction elements, the movement tendency of the underwater robot in different directions is compared to obtain the movement state degree of the moving direction elements in different directions; according to the movement state degree, the main movement direction of the machine at different times is screened out from all directions, and the main movement direction sequence of the underwater robot is constructed; In the main direction travel sequence of the machine movement, the travel degree of the main direction of the machine movement within the preset local time range is analyzed to obtain the machine abnormality degree at different times; according to the machine abnormality degree, the abnormal changes of the movement direction travel elements between different machine movement main directions are compared, and the movement direction travel elements are divided into the core machine to be adjusted categories; Analyze the adjustment status of the moving direction elements in the same core machine to be adjusted category to obtain the correction adjustment component elements; perform posture control on the underwater robot according to the correction adjustment component elements; The method for obtaining the main direction travel sequence of the machine movement is: Take any moment as the marking moment; at the marking moment, take the direction of the moving direction element with the largest moving state as the main direction of the machine movement at the marking moment; and take the sequence of the main directions of the machine movement at all moments in ascending order as the main direction movement sequence of the machine movement; The method for obtaining the category of the core machine to be adjusted is: Compare the differences in the degree of motion state between the main directions of machine motion at different times, and combine the degree of machine abnormality to obtain the same category at different times; according to the same category, divide the elements of the motion direction into the category of core machines to be adjusted; The method for obtaining the correction adjustment component element is: By comparing the changes in the degree of machine anomalies between different core machine categories to be adjusted, the machine anomaly control time range is obtained; the coverage length within the machine anomaly control time range is analyzed to obtain the correction adjustment component elements.

2. The control method for an underwater robot according to claim 1, characterized in that: The method for obtaining the degree of the motion state is: Take any direction as the target direction and any moment as the target moment, compare the difference in the moving direction elements between the target direction and all the overall directions at the same moment, and obtain the degree of the moving state of the target direction at the target moment.

3. The control method for an underwater robot according to claim 1, characterized in that: After calculating the degree of motion, it also includes: Normalize the degree of motion state.

4. The control method for an underwater robot according to claim 1, characterized in that: The method for obtaining the abnormality degree of the machine is: Take any moment as a reference moment; obtain a preset local time range of the reference moment; analyze the degree of travel in the main direction of the machine movement within the preset local time range to obtain the range machine attitude stability at the reference moment; based on the range machine attitude stability, combined with the analysis of the extreme conditions of the movement tendency at the reference moment in the travel sequence of the main direction of the machine movement, obtain the degree of machine abnormality at the reference moment under the reference moment.

5. The control method for an underwater robot according to claim 4, characterized in that: The method for obtaining the machine attitude stability in the range is: The stability of the motion state of the overall machine in the main direction of motion within the preset local time range is analyzed to obtain the range machine attitude stability at the reference time.

6. A control system for an underwater robot, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the steps of the control method for an underwater robot as described in any one of claims 1 to 5 are implemented.

7. A control device for an underwater robot, the device comprising: Movement direction travel element acquisition module, machine control command analysis module and underwater robot control module; The motion direction travel element acquisition module is used to obtain the motion direction travel elements in different directions at several moments, and the machine control command analysis module implements the steps of the control method for the underwater robot as described in any one of claims 1 to 5 by calling a computer program to obtain the correction adjustment component elements, and the underwater robot control module performs posture control on the underwater robot according to the correction adjustment component elements.

Citation Information

Patent Citations

  • Underwater robot pose control method

    CN104155991A

  • Underwater unmanned aerial vehicle self-balancing control method and system

    CN108563234A