LQR-ipc anti-toppling control method based on tower modal observation and feedback and related device

The independent pitch LQR control method based on tower modal observation and feedback estimates the tower modal state in real time and generates the optimal torque compensation command, thus solving the risk of tower sweeping and tower collapse caused by wind turbine tower vibration and achieving effective vibration suppression and risk reduction.

CN123044441APending Publication Date: 2026-11-06HUANENG CLEAN ENERGY RES INST
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Patent Information

Application Number
CN202611324349.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-08-28
Publication Date
2026-11-06

AI Technical Summary

Technical Problem

Tower vibration issues in wind turbine generators lead to risks of tower sweeping and tower collapse. Existing control strategies cannot effectively suppress large-scale tower vibrations and lack direct state awareness.

Method used

The independent pitch LQR control method, which utilizes tower top acceleration, blade root bending moment, and rotational speed data, estimates the tower modal state in real time, calculates the optimal torque compensation command, generates pitch control commands, and achieves independent pitch control.

Benefits of technology

It effectively suppresses large-scale tower vibration, reduces the risk of tower sweeping and collapse, improves the wind turbine's resistance to wind disturbance, avoids additional hardware costs, and has good industrial scalability.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention provides an independent pitch LQR control method and related apparatus based on tower modal observation and feedback, comprising: acquiring tower measurement data, including tower top acceleration and blade root bending moment, rotational speed, and azimuth signals; calculating tower modal state estimates based on the measurement data, including tower modal displacement and velocity estimates; calculating optimal torque compensation commands based on the obtained tower modal state estimates; and generating pitch control commands based on the optimal torque compensation commands and controlling blade operation. This invention reconstructs the tower modal state, which cannot be directly measured, in real time using a reduced-order linear extended state observer, and calculates the optimal torque compensation commands using LQR optimal control theory. Then, through inverse Park transform, it generates independent pitch commands for each blade, which can actively and directly suppress large-amplitude tower vibrations, effectively reducing tower top amplitude, ensuring dynamic clearance, and reducing tower alternating stress.
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Description

Technical Field

[0001] This invention belongs to the field of wind turbine generator control technology, specifically relating to the LQR-IPC anti-tower-fall control method and related devices based on tower modal observation and feedback. Background Technology

[0002] As the global wind power industry moves towards larger and more flexible structures, the tower height of wind turbines is continuously increasing while the diameter is relatively decreasing, significantly enhancing structural flexibility. This leads to a continuous decrease in their first-order natural frequency, making them more susceptible to coupling with the excitation frequency of the wind turbine rotor. Against this backdrop, the dynamic vibration problem of the tower, especially the low-order modal vibrations in the longitudinal direction, has evolved from a simple fatigue load issue into a potentially significant structural safety risk, specifically manifested as follows: (1) The risk of tower sweeping is aggravated. The abnormal increase in the amplitude of the tower top directly leads to the dynamic compression of the clearance distance between the blade tip and the tower. The huge swing of the tower top may cause the blade tip to collide with the tower, i.e., tower sweeping accident.

[0003] (2) Risk of tower collapse: The continuous large-scale tower vibration will significantly increase the alternating stress at the tower foundation connection. Long-term action will cause fatigue crack propagation, and blade sweeping accidents will also induce tower collapse accidents.

[0004] (3) Traditional control strategies have safety gaps. Existing wind turbines usually use uniform pitch control, which is basically unable to suppress large-scale tower vibrations. Secondly, wind turbines with independent pitch control technology lack direct state perception and cannot accurately perceive the precise position and trend of tower swaying.

[0005] Therefore, the wind power industry needs a control method that can directly target and actively suppress large-amplitude tower vibrations to reduce the risk of tower sweeping and collapse at the source. Summary of the Invention

[0006] The purpose of this invention is to provide an independent pitch LQR control method and related device based on tower modal observation and feedback, which solves the above-mentioned shortcomings in the prior art. The primary goal of this invention is to actively and directly suppress the large amplitude vibration of the tower, thereby fundamentally reducing the risk of tower sweeping and tower collapse accidents of wind turbine generators.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides an independent pitch LQR control method based on tower modal observation and feedback, comprising the following steps: Acquire measurement data of the tower, including tower top acceleration and blade root bending moment, rotational speed and azimuth angle signals; Based on the measurement data, the estimated values ​​of the tower modal state are calculated, which include the estimated values ​​of displacement and velocity of the tower modes; Based on the obtained tower modal state estimates, the optimal torque compensation command is calculated. Based on the optimal torque compensation command, pitch control command is generated and the blade operation is controlled.

[0008] Preferably, the obtained measurement data is used as the input to the observer equation, and the output is the displacement estimate and velocity estimate of the tower mode, wherein the expression of the observer equation is:

[0009]

[0010] Where z represents the internal state of the observer; L represents the tower's modal state estimate; L is the observer gain matrix. , All are matrices with constant coefficients; For measurement data.

[0011] Preferably, the observer gain matrix is ​​obtained using the pole placement method.

[0012] Preferably, the obtained tower modal state estimate is used as the input to the real-time control law, and the output is the optimal torque compensation command, wherein the expression of the real-time control law is:

[0013] in, The optimal feedback gain matrix; This is an estimate of the tower's modal state. and These are the optimal torque compensation commands for suppressing the forward and backward and left and right vibrations of the tower, respectively.

[0014] Preferably, the pitch control command is generated based on the optimal torque compensation command. Specifically, the method is as follows: Based on the real-time azimuth angle of the wind turbine, the optimal torque compensation command is subjected to inverse Parker transformation to obtain the pitch angle increment of each blade. The obtained pitch angle increments are superimposed with preset reference pitch angles to generate pitch control commands.

[0015] Secondly, the LQR-IPC anti-collapse control system based on tower modal observation and feedback provided by the present invention includes: The measurement data acquisition unit is used to acquire the measurement data of the tower, including the tower top acceleration and the bending moment, rotational speed and azimuth angle signals of the blade root; The estimation calculation unit is used to calculate the tower modal state estimate based on the measurement data. The tower modal state estimate includes the tower mode displacement estimate and velocity estimate. The compensation command calculation unit is used to calculate the optimal torque compensation command based on the obtained tower modal state estimation value; The pitch control command generation unit is used to generate pitch control commands based on the optimal torque compensation command and control the blade operation.

[0016] Thirdly, the present invention provides an electronic device including a processor and a memory, wherein the memory stores computer instructions, and when the computer instructions are executed by the processor, the electronic device performs the method described thereon.

[0017] Fourthly, the present invention provides a computing device cluster, characterized in that it includes at least one computing device, each computing device including a processor and a memory; The processor of the at least one computing device is used to execute instructions stored in the memory of the at least one computing device to cause the cluster of computing devices to perform the method.

[0018] Fifthly, the present invention provides a computer program product, the computer program product including computer-executable instructions, which, when executed, implement the method described.

[0019] In a sixth aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the method described herein.

[0020] Compared with the prior art, the beneficial effects of the present invention are: This invention provides an independent pitch LQR control method based on tower modal observation and feedback. By acquiring measurement data such as tower top acceleration, blade root bending moment, rotational speed, and azimuth angle, and using a reduced-order linear extended state observer, the method performs real-time and accurate reconstruction of tower modal displacement and velocity, which cannot be directly measured. This solves the problem of blind control caused by the lack of real-time tower oscillation status in traditional control strategies, providing accurate state feedback for active suppression. Then, based on LQR optimal control theory, the optimal feedback gain matrix is ​​systematically calculated by balancing vibration suppression effect with the power consumption and physical capabilities of the pitch actuator. This generates the optimal torque compensation command to suppress the forward and backward vibration and left and right vibration of the tower, ensuring that the control action achieves the globally optimal vibration suppression effect under limited execution capability. Finally, based on the real-time azimuth angle of the wind turbine, an inverse Parker transform is performed to accurately convert the torque compensation command into an independent pitch angle increment for each blade and superimpose it with the reference pitch angle. This allows the control torque to be applied accurately as the wind turbine rotates, achieving time-varying and synchronous independent pitch control.

[0021] In summary, this invention differs from traditional unified pitch control, which can only adjust speed and power but cannot suppress tower vibration, and from existing independent pitch technology, which lacks direct state perception. It can actively and directly suppress large-amplitude tower vibration, effectively reducing tower top amplitude to ensure dynamic clearance between blade tip and tower, thereby avoiding tower sweep accidents. At the same time, it significantly reduces the alternating stress on the tower to extend its fatigue life and significantly reduce the probability of tower collapse. Furthermore, it can achieve millisecond-level rapid response under extreme gusts or turbulence conditions to enhance the unit's wind disturbance resistance and survivability. Ultimately, it reduces the risk of tower sweep and tower collapse accidents in wind turbine units from the root. Moreover, this method does not require additional high-cost hardware equipment; it can be implemented simply by upgrading the control algorithm based on existing sensors. It has good industrial scalability and engineering practical value. Attached Figure Description

[0022] Figure 1 This is a diagram illustrating the overall architecture of the control system according to an embodiment of the present invention. Figure 2 This is a physical layout diagram of the system involved in an embodiment of the present invention. Detailed Implementation

[0023] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0024] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0025] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0026] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0027] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0028] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0029] Example 1 This embodiment provides an independent pitch LQR control system based on tower modal observation and feedback, including: Sensor modules are installed in key locations at the top of the tower, wheel hub, and nacelle. The measurement data acquisition unit is used to acquire the measurement data of the tower, including the tower top acceleration and the bending moment, rotational speed and azimuth angle signals of the blade root; The estimation calculation unit is used to calculate the tower modal state estimate based on the measurement data. The tower modal state estimate includes the tower mode displacement estimate and velocity estimate. The compensation command calculation unit is used to calculate the optimal torque compensation command based on the obtained tower modal state estimation value; The pitch control command generation unit is used to generate pitch control commands based on the optimal torque compensation command and control the blade operation.

[0030] In this embodiment, the sensor module includes: Dual-axis accelerometer at the top of the tower: measures the vibration acceleration of the tower in the front-back and left-right directions; Leaf root bending moment sensor: Installed at the root of three blades to measure bending moment in the flapping direction; Low-speed shaft speed encoder: measures wind turbine speed; Azimuth encoder: measures the real-time azimuth angle of the wind turbine; Blade pitch encoder: Feeds back the actual pitch angle of each blade.

[0031] In this embodiment, the measurement data acquisition unit includes: Signal conditioner: filters and amplifies signals; Data Acquisition Card (DAQ): Converts analog signals into digital signals and transmits them to the main controller via Ethernet. In this embodiment, the pitch control command generation unit includes: Coordinate transformation unit: converts torque commands in the rotating coordinate system into pitch angle increments for each blade; Command synthesis unit: superimposes the increment with the unified pitch reference value; Pitch driver: Receives the final command and drives the pitch motor to execute it.

[0032] Example 2 This embodiment provides an independent pitch LQR control method based on tower modal observation and feedback, which includes the following steps: Step 1: Model Building S1, Establish a linearized state-space model A linearized state-space model of the main components (blades, tower, and drive train) of the wind turbine is constructed at the rated operating point, resulting in a mathematical model of the following form:

[0033]

[0034] Where: x is the state vector, which includes the generalized displacement and velocity in the front-to-back and left-to-right directions of the tower, the torsional angle and velocity of the transmission chain, and the pitch angle of the three blades; u is the control input, i.e., the independent pitch angle command of the three blades; d is the external disturbance, i.e., the unbalanced aerodynamic load at the hub; y is the measurement output, which includes the tower top acceleration, blade root bending moment, and low-speed shaft speed; matrices A, B, C, and F are constant coefficient matrices that describe the internal dynamic relationships of the system. This is the predicted state vector.

[0035] S2, Design a reduced-order linear extended state observer The goal of this step is to estimate the tower's modal states in real time, which cannot be directly measured. The state vector is divided into parts to be estimated. (Tower modal displacement and velocity) and the rest .

[0036] The observer equation is:

[0037]

[0038] Where: z represents the internal state of the observer; L represents the tower's modal state estimate; L is the observer gain matrix. , and All are matrices with constant coefficients; The observer gain matrix is ​​designed using the pole placement method: the characteristic frequency of the observer pole is set to 3 to 5 times the tower mode frequency, and the damping ratio is set to 0.7 to ensure that the estimated value converges quickly and effectively filters out measurement noise.

[0039] S3, LQR Optimal Feedback Controller Design First, define the cost function:

[0040] Where: Q is the state weight matrix, with the larger value taken for the elements on the diagonal corresponding to the tower modal velocities; R is the control weight matrix, set according to the physical capabilities of the pitch actuator.

[0041] Then, the optimal feedback gain matrix K is obtained by solving:

[0042]

[0043] The real-time control law is:

[0044] in, and These are torque compensation commands for suppressing the forward and backward, and left and right vibrations of the tower, respectively.

[0045] Step 2: Collect measurement data, including tower top acceleration, blade root bending moment, rotational speed, and azimuth angle signals; Step 3: Based on the measurement data, calculate the tower modal state estimate, which includes the tower mode displacement estimate and velocity estimate; Based on the obtained tower modal state estimates, the optimal torque compensation command is calculated.

[0046] Step 4: Perform coordinate transformation and command synthesis on the optimal torque compensation command to generate pitch control command and control the blade operation.

[0047] First, based on the real-time azimuth angle ψ of the wind turbine, perform the inverse Parker transformation:

[0048] The transformation matrix is:

[0049] Then compare the independent pitch increments with the reference pitch angle given by the unified pitch controller. Overlay:

[0050] The final command is sent to the pitch drive for execution via the industrial bus.

[0051] Steps 2 to 4 are executed cyclically at intervals of 10-50 milliseconds to achieve active suppression of tower vibration.

[0052] Example 3 This embodiment also provides a computing device. The computing device includes a bus, a processor, a memory, and a communication interface. The processor, memory, and communication interface communicate with each other via the bus. The computing device can be a server or a terminal device. It should be understood that this application does not limit the number of processors and memory in the computing device.

[0053] A bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, a bus can include a path for transmitting information between various components of a computing device (e.g., memory, processor, communication interfaces).

[0054] The processor may include any one or more of the following: central processing unit (CPU), graphics processing unit (GPU), tensor processing unit (TPU), application specific integrated circuit (ASIC), field-programmable gate array (FPGA), microprocessor (MP), or digital signal processor (DSP).

[0055] Memory can include volatile memory, such as random access memory (RAM). Processors can also include non-volatile memory. volatile memory, such as read-only memory (ROM). ROM (memory only), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0056] The memory stores executable program code, which the processor executes to implement the functions of the aforementioned units, thereby achieving, for example, the method described in Embodiment 1. That is, the memory may store instructions for the methods and functions relating to the computing device in any of the above embodiments.

[0057] The communication interface uses transceiver modules such as, but not limited to, network interface cards and transceivers to enable communication between computing devices and other devices or communication networks.

[0058] Example 4 This embodiment also provides a computing device cluster. The computing device cluster includes at least one computing device. The computing device can be a server, such as a central server, an edge server, or a local server in a local data center. In some embodiments, the computing device can also be a terminal device such as a desktop computer, a laptop computer, or a smartphone.

[0059] The computing device cluster includes at least one computing device. The memory of one or more computing devices in the computing device cluster may store the same instructions for performing the methods and functions related to the computing devices in any of the above embodiments.

[0060] In some possible implementations, the memory of one or more computing devices in the computing device cluster may also store partial instructions for performing the methods and functions of the computing devices involved in any of the above embodiments. In other words, a combination of one or more computing devices can jointly execute the instructions for performing the methods and functions of the computing devices.

[0061] It should be noted that the memory in different computing devices within a computing device cluster can store different instructions, which are used to execute parts of the device's functions.

[0062] In some possible implementations, one or more computing devices in a computing device cluster can be connected via a network. This network can be a wide area network (WAN) or a local area network (LAN), etc. Two computing devices are connected via the network. Specifically, they connect to the network through communication interfaces on each computing device.

[0063] Embodiments of this disclosure also provide a computer program product containing instructions that, when run on a computer, cause the computer to perform the methods and functions related to a computing device in any of the above embodiments.

[0064] Example 5 This embodiment also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, cause the processor to perform the methods and functions of the computing device involved in any of the above embodiments.

[0065] Generally, the various embodiments of this disclosure can be implemented in hardware or dedicated circuitry, software, logic, or any combination thereof. Some aspects can be implemented in hardware, while others can be implemented in firmware or software, which can be executed by a controller, microprocessor, or other computing device. Although various aspects of the embodiments of this disclosure are shown and described as block diagrams, flowcharts, or represented using some other illustration, it should be understood that the blocks, apparatuses, systems, techniques, or methods described herein can be implemented as, as non-limiting examples, in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0066] Example 6 This embodiment provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods as described above with reference to the accompanying drawings. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0067] Computer program code used to implement the methods of this disclosure may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus, such that when executed by the computer or other programmable data processing apparatus, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be performed. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0068] In the context of this disclosure, computer program code or related data may be carried on any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and so on. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0069] Computer-readable media can be any tangible medium that contains or stores programs for or relating to an instruction execution system, apparatus, or device, or a data storage device such as a data center containing one or more available media. Computer-readable media can be computer-readable signal media or computer-readable storage media. Computer-readable media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. More detailed examples of computer-readable storage media include electrical connections with one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0070] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A tower collapse prevention control method based on tower modal observation and feedback using LQR-IPC, characterized in that, Includes the following steps: Acquire measurement data of the tower, including tower top acceleration and blade root bending moment, rotational speed and azimuth angle signals; Based on the measurement data, the estimated values ​​of the tower modal state are calculated, which include the estimated values ​​of displacement and velocity of the tower modes; Based on the obtained tower modal state estimates, the optimal torque compensation command is calculated. Based on the optimal torque compensation command, pitch control command is generated and the blade operation is controlled.

2. The LQR-IPC anti-tower-fall control method based on tower modal observation and feedback as described in claim 1, characterized in that, The obtained measurement data is used as input to the observer equation, and the output is the displacement estimate and velocity estimate of the tower mode. The expression of the observer equation is as follows: Where z represents the internal state of the observer; L represents the tower's modal state estimate; L is the observer gain matrix. , All are matrices with constant coefficients; For measurement data.

3. The LQR-IPC anti-tower-fall control method based on tower modal observation and feedback as described in claim 2, characterized in that, The observer gain matrix is ​​obtained using the pole placement method.

4. The LQR-IPC anti-tower-fall control method based on tower modal observation and feedback as described in claim 1, characterized in that, The obtained tower modal state estimate is used as the input to the real-time control law, and the output is the optimal torque compensation command. The expression of the real-time control law is as follows: in, The optimal feedback gain matrix; This is an estimate of the tower's modal state. and These are the optimal torque compensation commands for suppressing the forward and backward and left and right vibrations of the tower, respectively.

5. The LQR-IPC anti-tower-fall control method based on tower modal observation and feedback as described in claim 1, characterized in that, Based on the optimal torque compensation command, pitch control commands are generated. The specific method is as follows: Based on the real-time azimuth angle of the wind turbine, the optimal torque compensation command is subjected to inverse Parker transformation to obtain the pitch angle increment of each blade. The obtained pitch angle increments are superimposed with preset reference pitch angles to generate pitch control commands.

6. An LQR-IPC anti-collapse control system based on tower modal observation and feedback, characterized in that, include: The measurement data acquisition unit is used to acquire the measurement data of the tower, including the tower top acceleration and the bending moment, rotational speed and azimuth angle signals of the blade root; The estimation calculation unit is used to calculate the tower modal state estimate based on the measurement data. The tower modal state estimate includes the tower mode displacement estimate and velocity estimate. The compensation command calculation unit is used to calculate the optimal torque compensation command based on the obtained tower modal state estimation value; The pitch control command generation unit is used to generate pitch control commands based on the optimal torque compensation command and control the blade operation.

7. An electronic device, characterized in that, It includes a processor and a memory, the memory storing computer instructions that, when executed by the processor, cause the electronic device to perform the method of any one of claims 1 to 5.

8. A computing device cluster, characterized in that, It includes at least one computing device, each computing device including a processor and memory; The processor of the at least one computing device is configured to execute instructions stored in the memory of the at least one computing device to cause the cluster of computing devices to perform the method according to any one of claims 1 to 5.

9. A computer program product, characterized in that, The computer program product includes computer-executable instructions that, when executed, implement the method of any one of claims 1 to 5.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions that, when executed by a processor, implement the method of any one of claims 1 to 5.