Wind turbine generator transmission chain multi-mode torsional vibration sliding mode control method and system

Abstract

The invention discloses a wind turbine generator transmission chain multi-mode torsional vibration sliding mode control method and system. The method comprises the steps of obtaining resonant frequencies and torsion angular velocities under two torsional vibration modes of a wind turbine generator transmission chain blade symmetric mode and a transmission chain intrinsic mode; performing band-pass filtering on the torsion angular velocity through a band-pass filter in combination with resonant frequencies in the two torsional vibration modes so as to extract torsion angular velocity components in the two torsional vibration modes, extracting compensation torques in the two torsional vibration modes through an improved sliding mode controller, and performing weighted summation to obtain a total compensation torque; and adding the total compensation torque to a reference torque based on a maximum power tracking algorithm as a compensated reference torque for torque control of the generator converter. The method aims at restraining the multi-mode torsional vibration problem of the wind turbine generator transmission chain, directional torsional vibration restraining under different modes is achieved, and the system robustness is improved.

Description

Technical Field

[0001] This invention belongs to the field of wind turbine vibration suppression technology, specifically relating to a method and system for multimodal torsional vibration sliding mode control of wind turbine drive train. Background Technology

[0002] In recent years, with the increase in the size of wind turbines, the increased flexibility of components such as the drivetrain and blades has led to a decrease in system damping, bringing more challenges, including achieving better cost-effectiveness. Rapid changes in voltage amplitude, such as voltage drops and transient phenomena like grid switching, can also cause power oscillations, resulting in torsional vibration in the wind turbine drive system. Torsional vibration can also originate from the aerodynamics of the wind turbine, such as wind turbulence and tower shadow effects. Torsional vibration in the wind turbine drive system significantly reduces the service life of the gearbox and increases the maintenance costs of the wind turbine. Traditional drivetrain vibration suppression methods only consider torsional vibration suppression under a single mode. However, wind turbines are clearly strongly coupled, nonlinear systems. Ignoring torsional vibration problems caused by coupling between mechanical parts can exacerbate the vibration of the system drivetrain and even cause electromechanical coupling, increasing the risk of subsynchronous oscillations in the system. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a method and system for multimodal torsional vibration sliding mode control of wind turbine drive train, which aims to suppress multimodal torsional vibration problems in wind turbine drive train, achieve directional torsional vibration suppression under different modes, and improve system robustness.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for multimodal torsional vibration sliding mode control of a wind turbine drive train includes the following steps: S101, Obtain the resonant frequencies of the wind turbine drivetrain blades under two torsional vibration modes: the symmetrical mode and the inherent mode of the drivetrain. and Obtain the torsional angular velocity of the wind turbine. ; S102, the torsional angular velocity of the wind turbine The resonant frequencies of the two torsional vibration modes are combined using bandpass filters. and Bandpass filtering was performed to extract the torsional angular velocity components under the two torsional vibration modes. and ; S103, torsional angular velocity components under two torsional vibration modes and The compensation torque under two torsional vibration modes is extracted by improving the sliding mode controller and then weighted and summed to obtain the total compensation torque. The total compensation torque Reference torque attached to the maximum power point tracking algorithm The above serves as the reference torque after compensation. Increase the damping of the transmission chain to suppress torsional vibration when performing torque control on the generator converter.

[0005] Optionally, in step S103, the angular velocity components under the two torsional vibration modes are... and The total compensation torque is obtained by extracting the compensation torque under two torsional vibration modes through a sliding mode controller and then summing them by weight. The function expression is: ; in, and These represent the compensation torque weights for the two torsional vibration modes, respectively. and These are the compensation torques for two torsional vibration modes, respectively. and The weighting coefficient for the angular velocity component. and To switch the gain in the auxiliary items, and These are the sliding mode variables under two torsional vibration modes, and sgn is the sign function.

[0006] Optionally, the functional expressions for the sliding mode variables under the two torsional vibration modes are: , ; in, and These are disturbance signals for the torsional angle of the connecting shaft under two torsional vibration modes, respectively.

[0007] Optionally, the torsional angular velocity of the wind turbine is obtained in step S101. The function expression is: ; in, The angular velocity of the fan. Let ω be the generator angular velocity, and N be the ratio of the ideal gearbox.

[0008] Optionally, step S102 involves calculating the torsional angular velocity of the wind turbine. The resonant frequencies of the two torsional vibration modes are combined using bandpass filters. and The function expression for bandpass filtering is: , ; in, and These represent the torsional angular velocity components under two torsional vibration modes. and Let be the transfer functions of the bandpass filters under two torsional vibration modes, respectively, and we have: ; , ; in, and These represent the bandpass filter gains for two torsional vibration modes. and These are the damping coefficients for two torsional vibration modes, respectively. and These are the bandpass filter center angular frequencies for two different torsional vibration modes. It is a complex variable.

[0009] Optionally, the functional expression for the gain of the bandpass filter is: ; in, For the bandpass filter gain, and These are the transmission chain dampings before and after applying resistance, respectively. Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. Let be the moment of inertia of the generator.

[0010] Optionally, the resonant frequencies of the wind turbine drive train blades under two torsional vibration modes—the symmetrical mode and the inherent mode of the drive train—can be obtained. and The function expression is: ; ; ; in, The equivalent stiffness weighting term of the system, For the system inertial coupling product term, For the effective stiffness of the blade, For the total stiffness of the low-speed and high-speed shafts of the transmission chain, Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. Let be the moment of inertia of the generator.

[0011] In addition, the present invention provides a multimodal torsional vibration sliding mode control system for wind turbine drive train, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the multimodal torsional vibration sliding mode control method for wind turbine drive train.

[0012] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the wind turbine drivetrain multimodal torsional vibration sliding mode control method via a processor.

[0013] In addition, the present invention also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the wind turbine drivetrain multimodal torsional vibration sliding mode control method via a processor.

[0014] Compared with existing technologies, the present invention mainly achieves the following beneficial effects: The invention includes obtaining the resonant frequency and torsional angular velocity of two torsional vibration modes: the symmetrical mode of the wind turbine drivetrain blades and the inherent mode of the drivetrain. The torsional angular velocity is bandpass filtered in combination with the resonant frequency of the two torsional vibration modes to extract the torsional angular velocity components of the two torsional vibration modes. Then, the compensation torque of the two torsional vibration modes is extracted by an improved sliding mode controller and weighted summed to obtain the total compensation torque. The total compensation torque is added to the reference torque based on the maximum power point tracking algorithm as the compensated reference torque for torque control of the generator converter. This can suppress the torsional vibration problem of the two torsional vibration modes: the symmetrical mode of the wind turbine drivetrain blades and the inherent mode of the drivetrain, achieve directional torsional vibration suppression under different modes, and improve the robustness of the system. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0016] Figure 2 This is a schematic diagram illustrating the control principle of the method in an embodiment of the present invention.

[0017] Figure 3 This is a schematic diagram of the "three-mass model" in an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram illustrating the control principle of the improved sliding mode controller in an embodiment of the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0020] like Figure 1 and Figure 2 As shown, the multi-mode torsional vibration sliding mode control method for wind turbine drive train in this embodiment includes the following steps: S101, Obtain the resonant frequencies of the wind turbine drivetrain blades under two torsional vibration modes: the symmetrical mode and the inherent mode of the drivetrain. and Obtain the torsional angular velocity of the wind turbine. ; S102, the torsional angular velocity of the wind turbine The resonant frequencies of the two torsional vibration modes are combined using bandpass filters. and Bandpass filtering was performed to extract the torsional angular velocity components under the two torsional vibration modes. and ; S103, torsional angular velocity components under two torsional vibration modes and The compensation torque under two torsional vibration modes is extracted by improving the sliding mode controller and then weighted and summed to obtain the total compensation torque. The total compensation torque The reference torque applied to the maximum power point tracking (MPPT) algorithm The above serves as the reference torque after compensation. Increase the damping of the transmission chain to suppress torsional vibration when performing torque control on the generator converter.

[0021] In this embodiment, the resonant frequencies of two torsional vibration modes are obtained: the symmetrical mode of the wind turbine drivetrain blades and the inherent mode of the drivetrain. and The function expression is: ; ; ; in, This is a weighted term for the system's equivalent stiffness (system equivalent stiffness weighted by inertia). This is the system inertial coupling product term (the joint action term in the calculation of the system's natural frequency). For the effective stiffness of the blade, For the total stiffness of the low-speed and high-speed shafts of the transmission chain, Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. Let be the moment of inertia of the generator.

[0022] Figure 2 This is a schematic diagram illustrating the principle of the method in this embodiment, where V windWhere β is the wind speed and β is the pitch angle output by the pitch controller. T a For the aerodynamic torque of the wind turbine, The angular velocity of the fan. The torsional angular velocity of the wind turbine. T m The mechanical torque of the generator is used for analysis. The resonant frequencies of the wind turbine drivetrain blades under two torsional vibration modes—the symmetrical mode and the inherent mode of the drivetrain—are obtained. and The process is as follows: Since in-plane bending of wind turbine blades occurs far from the hub, the blade can be divided into rigid and flexible parts. The inertia of the rigid part of the blade is included in the hub inertia, and the hub inertia and the blade flexible inertia are connected by springs, representing the effective stiffness of the blade. When the inherent modes of the drive train are excited or the in-plane symmetrical modes of the blade are indirectly excited, torsional vibration of the wind turbine drive shaft will occur. Figure 3 As shown, the flexible part of the blade, the hub, the rigid part of the blade, and the generator are regarded as three mass blocks with rotational inertia, defined as the first, second, and third mass blocks, respectively. The mass blocks are connected by a transmission shaft with torsional stiffness and damping to describe the torsional coupling dynamics between the wind turbine and the generator. The dynamic characteristic equations of the wind turbine and the low-speed shaft under the "three-mass model" are established: ; in, Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. The moment of inertia of the generator; For the effective stiffness of the blade, For the total stiffness of the low-speed and high-speed shafts of the transmission chain, D 1. D 2 represents the damping coefficient; T a , T m These correspond to the aerodynamic torque of the wind turbine and the mechanical torque of the generator, respectively. The angular velocity of the fan. The generator's angular velocity, , , These represent the torsional angles of the flexible blade section, the rigid hub and blade section, and the connecting shaft of the generator; N is the ratio of the ideal gearbox, specifically as follows: Figure 3 As shown.

[0023] The dynamic characteristic equations can be written as state-space equations under the "three-mass model" of the shaft system: ; in, θ 1. θ 2 represents the torsion angles of the connecting shafts of the first and second mass blocks, and the connecting shafts of the second and third mass blocks, respectively. Based on this, the resonant frequencies of the wind turbine drive train blades under two torsional vibration modes—the symmetrical mode and the inherent mode of the drive train—can be obtained. and The function expression: ; ; ; in, This is a weighted term for the system's equivalent stiffness (system equivalent stiffness weighted by inertia). This is the system inertial coupling product term (the joint action term in the calculation of the system's natural frequency). For the effective stiffness of the blade, For the total stiffness of the low-speed and high-speed shafts of the transmission chain, Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. Let be the generator's moment of inertia. A frequency spectrum analysis of the low-speed shaft was performed using the simulation software GH Bladed, and the two resonant frequencies of the low-speed shaft were obtained from the Campbell plot of the simulation results. and Combining the above formula, we obtain the parameters of the three mass modules, including: the moment of inertia of the flexible part of the blade. Moment of inertia of the rigid parts of the hub and blades and the effective stiffness of the blades .

[0024] like Figure 4 As shown, in step S103 of this embodiment, the angular velocity components under the two torsional vibration modes are... and The total compensation torque is obtained by extracting the compensation torque under two torsional vibration modes through a sliding mode controller and then summing them by weight. The function expression is: ; in, and These represent the compensation torque weights for the two torsional vibration modes, respectively. and These are the compensation torques for two torsional vibration modes, respectively. and The weighting coefficient for the angular velocity component. and To switch the gain in the auxiliary items, and These are the sliding mode variables under two torsional vibration modes, and sgn is the sign function.

[0025] The torsional vibration modes of the wind turbine drivetrain blades, namely the symmetrical mode and the inherent mode of the drivetrain, are denoted as the first mode and the second mode, respectively. Since controlling the main modes, such as the first and second modes, can significantly reduce the torque vibration of the drivetrain, and the sliding mode control design used in this patent has a limited frequency range, the torsional vibration suppression technology proposed in this embodiment is based on the motion equations of the main modes of the drivetrain. ; in, and These are disturbance signals for the drive shaft torsion angle and torsional angular velocity, respectively. ; , For disturbance signals of aerodynamic torque and electromagnetic torque; The term can be rewritten as compensating torque. u ( T comp The sum of the unknown disturbance and the equation of motion is rewritten as: ; in, This is considered an unknown disturbance. Disturbances caused by aerodynamics and the power grid can be classified as unknown disturbances in the equations of motion and compensated for in subsequent control algorithms. Torsional vibration suppression is involved at two modal frequencies; therefore, sliding surfaces are designed for each of the two torsional vibration modes, the sliding mode variable s is added to the system's state variables, and the extracted torsional angular velocity components under the two torsional vibration modes are... and Substituting these values, we obtain the functional expressions for the sliding mode variables under the two torsional vibration modes in this embodiment: , ; in, and The disturbance signals are the torsional angles of the connecting shaft under two torsional vibration modes, and the functional expressions of the derivatives of the sliding mode variable s under the two torsional vibration modes are as follows: ; in, and These are the derivatives of the sliding mode variables under the two torsional vibration modes, respectively. and represent the compensation torques under two torsional vibration modes, respectively. and These are the unknown disturbances under two torsional vibration modes (obtaining the unknown disturbances through an extended state observer is a well-known existing method), among which The time of the disturbance signal.

[0026] In this embodiment, the Lyapunov function is selected. as follows: ; Then the derivative of the Lyapunov function is... for: ; Assume the control rate is: ; in, To compensate for torque, It is a positive gain coefficient. For torsional angular velocity disturbance signal, To switch between auxiliary options, we have: ; in, and These represent the unknown disturbances under two torsional vibration modes. and These are the switching auxiliary terms for the two torsional vibration modes. To compensate for unknown disturbances and ensure convergence, the switching auxiliary terms are determined. v， Two sliding mode control rates were designed as follows: ; in, To switch the gain, let sgn be the sign function and s be a complex variable, then we have: ; ; in, and These are the compensation torques for two torsional vibration modes, respectively. and The weighting coefficient for the angular velocity component. and The switching gain is used in the switching auxiliary term; assuming the disturbance term satisfies: ; in, For the unknown disturbance in the i-th torsional vibration mode, The maximum upper bound of the disturbance term under the i-th torsional vibration mode is given by , where The value is either 1 or 2, representing the two torsional vibration modes of the wind turbine drive train blades: the symmetrical mode and the inherent mode of the drive train, respectively. Therefore: ; in, Let be the sliding mode variable under the i-th torsional vibration mode; therefore: , It is evident that ensuring ,but The sliding surface gradually stabilizes. The switching gain is the switching auxiliary term for the i-th torsional vibration mode.

[0027] In step S101 of this embodiment, the torsional angular velocity of the wind turbine is obtained. The function expression is: ; in, The angular velocity of the fan. Let ω be the generator angular velocity, and N be the ratio of the ideal gearbox.

[0028] like Figure 4 As shown, BPF1 and BPF2 are bandpass filters for two torsional vibration modes in this embodiment. In step S102 of this embodiment, the torsional angular velocity of the wind turbine is... The resonant frequencies of the two torsional vibration modes are combined using bandpass filters. and The function expression for bandpass filtering is: , ; in, and These represent the torsional angular velocity components under two torsional vibration modes. and Let be the transfer functions of the bandpass filters under two torsional vibration modes, respectively, and we have: ; , ; in, and These represent the bandpass filter gains for two torsional vibration modes. and These are the damping coefficients for two torsional vibration modes, respectively. and These represent the resonant periods under two torsional vibration modes. It is a complex variable.

[0029] In this embodiment, the functional expression for the bandpass filter gain is: ; in, For the bandpass filter gain, and These are the transmission chain dampings before and after applying resistance, respectively. Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. This represents the generator's moment of inertia. For example... Figure 4 As shown, due to the total compensation torque The reference torque applied to the maximum power point tracking (MPPT) algorithm The above serves as the reference torque after compensation. Used to increase the damping of the drive train; the original damping of the drive train before applying resistance. That is, to use the reference torque Directly used as reference torque Damping of the transmission chain, damping of the transmission chain after applying resistance Let the total compensation torque be denoted as Added to reference torque Used as reference torque afterward The transmission chain damping.

[0030] Furthermore, this embodiment also provides a multimodal torsional vibration sliding mode control system for a wind turbine drivetrain, including a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the multimodal torsional vibration sliding mode control method for the wind turbine drivetrain. Additionally, this embodiment also provides a computer-readable storage medium storing a computer program or instructions programmed or configured to execute the multimodal torsional vibration sliding mode control method for the wind turbine drivetrain via a processor. Furthermore, this embodiment also provides a computer program product, including a computer program or instructions programmed or configured to execute the multimodal torsional vibration sliding mode control method for the wind turbine drivetrain via a processor.

[0031] Those skilled in the art will understand that the technical solutions provided by this invention may take the form of a method, system, or computer program product. Therefore, this invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this invention may take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, produce an implementation of the flowchart... Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0032] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for multi-mode torsional vibration sliding mode control of a wind turbine drive train, characterized in that, Includes the following steps: S101, Obtain the resonant frequencies of the wind turbine drivetrain blades under two torsional vibration modes: the symmetrical mode and the inherent mode of the drivetrain. and To obtain the torsional angular velocity of the wind turbine; S102, the torsional angular velocity of the wind turbine The resonant frequencies of the two torsional vibration modes are combined using bandpass filters. and Bandpass filtering was performed to extract the torsional angular velocity components under the two torsional vibration modes. and ; S103, torsional angular velocity components under two torsional vibration modes and The compensation torque under two torsional vibration modes is extracted by improving the sliding mode controller and then weighted and summed to obtain the total compensation torque. The total compensation torque Reference torque attached to the maximum power point tracking algorithm The above serves as the reference torque after compensation. Increase the damping of the transmission chain to suppress torsional vibration when performing torque control on the generator converter.

2. The multi-mode torsional vibration sliding mode control method for wind turbine drive train according to claim 1, characterized in that, In step S103, the angular velocity components under the two torsional vibration modes are... and The total compensation torque is obtained by extracting the compensation torque under two torsional vibration modes through a sliding mode controller and then summing them by weight. The function expression is: ； in, and These represent the compensation torque weights for the two torsional vibration modes, respectively. and These are the compensation torques for two torsional vibration modes, respectively. and The weighting coefficient for the angular velocity component. and To switch the gain in the auxiliary items, and These are the sliding mode variables under two torsional vibration modes, and sgn is the sign function.

3. The multi-mode torsional vibration sliding mode control method for wind turbine drive train according to claim 2, characterized in that, The functional expressions for the sliding mode variables under the two torsional vibration modes are as follows: ， ； in, and These are disturbance signals for the torsional angle of the connecting shaft under two torsional vibration modes, respectively.

4. The multi-mode torsional vibration sliding mode control method for wind turbine drive train according to claim 1, characterized in that, In step S101, the torsional angular velocity of the wind turbine is obtained. The function expression is: ； in, The angular velocity of the fan. Let ω be the generator angular velocity, and N be the ratio of the ideal gearbox.

5. The multi-mode torsional vibration sliding mode control method for wind turbine drive train according to claim 1, characterized in that, Step S102: The torsional angular velocity of the wind turbine unit The resonant frequencies of the two torsional vibration modes are combined using bandpass filters. and The function expression for bandpass filtering is: ， ； in, and These represent the torsional angular velocity components under two torsional vibration modes. and Let be the transfer functions of the bandpass filters under two torsional vibration modes, respectively, and we have: ； ， ； in, and These represent the bandpass filter gains for two torsional vibration modes. and These are the damping coefficients for two torsional vibration modes, respectively. and These are the bandpass filter center angular frequencies for two different torsional vibration modes. It is a complex variable.

6. The multi-mode torsional vibration sliding mode control method for wind turbine drive train according to claim 5, characterized in that, The functional expression for the gain of the bandpass filter is: ； in, For the bandpass filter gain, and These are the transmission chain dampings before and after applying resistance, respectively. Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. Let be the moment of inertia of the generator.

7. The multi-mode torsional vibration sliding mode control method for wind turbine drive train according to claim 1, characterized in that, Obtain the resonant frequencies of two torsional vibration modes: the symmetrical mode of the wind turbine drivetrain blades and the natural mode of the drivetrain. and The function expression is: ； ； ； in, The equivalent stiffness weighting term of the system, For the system inertial coupling product term, For the effective stiffness of the blade, For the total stiffness of the low-speed and high-speed shafts of the transmission chain, Let be the moment of inertia of the flexible part of the blade. Let be the moment of inertia of the rigid components of the hub and blades. Let be the moment of inertia of the generator.

8. A multi-mode torsional vibration sliding mode control system for a wind turbine drive train, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the multimodal torsional vibration sliding mode control method for wind turbine drive train according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute the multimodal torsional vibration sliding mode control method for the wind turbine drive train according to any one of claims 1 to 7 via a processor.

10. A computer program product, comprising a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute the multimodal torsional vibration sliding mode control method for the wind turbine drive train according to any one of claims 1 to 7 via a processor.

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