Self-adaptive cross damping flutter suppression method for blades of offshore wind turbine

Abstract

The invention provides a self-adaptive cross damping flutter suppression method for blades of an offshore wind turbine, and belongs to the technical field of wind power generation based on computer data processing. The method comprises the following steps: firstly, establishing an aeroelastic model containing a non-diagonal damping item, and coupling sinking and floating motion and pitching motion through a cross damping coefficient; secondly, designing a self-adaptive control law based on a differential Riccati equation, and dynamically adjusting a damping parameter to compensate the time-varying aerodynamic force; and finally, proving closed-loop stability through a Lyapunov theory, and verifying a control effect by utilizing numerical simulation. An external pneumatic executing mechanism is not needed, the structure is simple, response is fast, the vibration convergence time can be shortened to be within 4 seconds at the wind speed of 8 m / s, the steady-state error approaches zero, and the method is suitable for flutter suppression of the blades of the large offshore wind turbine.

Description

Technical Field

[0001] The present invention belongs to the technical field of wind power generation based on computer data processing, and particularly relates to a method for suppressing the adaptive cross-damping flutter of an offshore wind turbine blade. Background Art

[0002] With the continuous increase in the length of offshore wind turbine blades, the blade flexibility increases, and the aeroelastic coupling effect intensifies, resulting in an increased risk of blade flutter. Flutter is a self-excited vibration phenomenon of aeroelastic coupling formed by a blade under the action of aerodynamic forces. In severe cases, it can lead to blade damage or even fracture. Traditional passive damping control is based on the assumption of static aerodynamic loads and cannot cope with unsteady disturbances such as sudden changes in offshore wind speed and dynamic angle of attack. Moreover, the damping parameters are fixed, and the adaptability is poor. The pneumatic trim tab control relies on external pneumatic actuators (such as trailing-edge flaps), which has problems such as complex structure, susceptibility to salt spray corrosion, and high maintenance costs. In a strong turbulence environment, it is often prone to failure. Although the fixed-gain LQR control can optimize the state feedback, it is limited by the assumption of a time-invariant system and is difficult to compensate for periodic time-varying aerodynamic loads, resulting in low control accuracy.

[0003] The disclosed technologies include using a pitch system to adjust the flap angle, piezoelectric ceramics to adjust the blade rigidity, and a stepper motor to control the flap swing to control flutter. However, the above control methods rely on the assumption of quasi-steady aerodynamic forces and are difficult to meet the requirements of unsteady aerodynamic disturbances. Moreover, the motor and ball screw structure have problems such as mechanical friction and response lag, are prone to wear under extreme loads, have poor durability, and it is difficult to control the accuracy problem. The cross-damping control technology does not require external pneumatic actuators and dynamically adjusts the cross-damping coefficient based on the differential Riccati equation, can compensate for periodic time-varying aerodynamic forces, adapt to wind speed fluctuations and nonlinear disturbances, and has better environmental adaptability. Summary of the Invention

[0004] To address the above problems, the present invention introduces cross-damping control. By dynamically adjusting the non-diagonal terms of the damping matrix, it breaks through the limitations of traditional passive damping and mechanical pitch, and has the advantages of rapidity, self-adaptability, and structural simplification, providing a more competitive solution for suppressing the flutter of large wind turbine blades.

[0005] The present invention provides a method for suppressing the adaptive cross-damping flutter of an offshore wind turbine blade, Embedding controllable distributed piezoelectric wafers at key positions inside the wind turbine blade, including a heave motion sensitive area and a pitch motion actuation area, that is, arranging piezoelectric wafers near the elastic axis of the blade, adjusting the cross-damping coefficient through voltage, and including the following processes: S1. Based on the binary airfoil model, establish the second-order dynamic equations for the heaving and pitching motions of the blade by combining the physical parameters of the blade cross-section and the offshore wind conditions parameters, including the mass matrix, stiffness matrix, and damping matrix; introduce non-diagonal cross-damping in the damping matrix for reconstruction to obtain the coupled damping matrix, dynamically update the aerodynamic coefficients, and generate the time-varying stiffness matrix and time-varying damping matrix; S2. Based on the second-order dynamic equations in S1, combine the mass matrix, time-varying stiffness matrix, and time-varying damping matrix to convert the system into the state-space form, obtain the state-space equation, design an adaptive feedback control law according to the time-varying system matrix and input matrix in the state-space equation. The adaptive feedback control law consists of the state vector and the feedback gain matrix. Substitute the system matrix and input matrix into the Riccati equation for solution to obtain the feedback gain matrix, which is used to generate the control input to drive the piezoelectric sheet to adjust the cross-damping coefficient through voltage; S3. Construct a Lyapunov function containing the blade state energy and the gain error energy, calculate the time derivative of this Lyapunov function under the adaptive feedback control law designed in S2, and verify whether the derivative of the Lyapunov function is negative definite; S4. Make a conditional judgment. If the time derivative of the Lyapunov function output in S3 is negative along the system trajectory, it indicates that the system is stable. Obtain the cross-damping coefficient based on the feedback gain matrix expression and apply the cross-damping coefficient to the offshore wind turbine blade; If the time derivative of the Lyapunov function is positive along the system trajectory, return to S2 for adjustment and then enter S3 until the time derivative of the Lyapunov function is negative definite, and output the corresponding cross-damping coefficient.

[0006] Preferably, the key positions inside the wind turbine blade are the heaving motion sensitive area and the pitching motion actuator area, that is, near the elastic axis of the blade; The input physical parameters of the offshore wind turbine blade include: the cross-sectional mass m 、the pitching moment of inertia about the elastic axis I θ 、the distance from the center of mass to the elastic axis x θ b 、the heaving stiffness k h 、the pitching stiffness k θ 、the heaving damping coefficient c h 、the pitching damping coefficient c θ 、the semi-chord length b ; The offshore wind conditions parameters include: the air density ρ 、the wind speedU , the blade rotational angular frequency ω; The base values of the aerodynamic coefficients include: the average aerodynamic lift coefficient C l, θ and the aerodynamic moment coefficient C m, θ .

[0007] Preferably, the specific process of S1 includes: S11, based on the two-dimensional airfoil model, define the second-order dynamic equations of heaving motion and pitching motion as: ; Among them, θ is the pitch angle, M ( t ) is the aerodynamic moment, related to the lift distribution and blade geometric parameters; m is the blade section mass, I θ is the inertial pitch moment about the elastic axis, x θ b is the distance from the center of mass to the elastic axis, c h , c θ are the heaving and pitching damping coefficients, k h , k θ is the spring stiffness; L ( t ) represents the unsteady aerodynamic force and M ( t ) represents the aerodynamic moment; S12, introduce the cross-damping coefficient, and introduce the cross-damping term c 21 , c 12 in the non-diagonal terms of the damping matrix in S11 to reconstruct the damping matrix and form a coupled damping matrix: ; Among them, c 21 , c 12 are the cross-damping coefficients, respectively representing the contribution of the pitch velocity to the heaving damping and the contribution of the heaving velocity to the pitch damping; S13, calculate the unsteady aerodynamic force L ( t ) and the aerodynamic moment M ( t ) received in S11 caused by the offshore wind field: ; ; Wherein, ρ is the air density, U is the wind speed, and ω is the blade rotational angular frequency; S14. The unsteady aerodynamic force L ( t ) and the aerodynamic moment M ( t ) in the aerodynamic lift coefficient C l, θ and the aerodynamic moment coefficient C m, θ are modeled as periodic time-varying functions, specifically: ; ; Wherein, C l, 0 is the average aerodynamic lift coefficient, C m, 0 is the average aerodynamic moment coefficient, C l, θ is the amplitude of the aerodynamic lift coefficient fluctuation, C m, θ is the amplitude of the aerodynamic moment coefficient fluctuation, and ω is the blade rotational angular frequency; S15. Based on the blade physical parameters and the time-varying aerodynamic coefficients C l, θ , C m, θ , combined with the steps of S11 - S14, construct the time-varying stiffness matrix K0(t) and the time-varying damping matrix C0(t) containing cross-damping terms; The expression of the time-varying stiffness matrix is: ; The expression of the time-varying damping matrix C0(t) containing cross-damping terms is: ; Wherein, a is the dimensionless distance from the chord center to the elastic axis.

[0008] Preferably, the specific process of S2 includes: S21. According to the second-order dynamic equation and the mass matrix M0, the time-varying stiffness matrix K0(t), and the time-varying damping matrix C0(t) containing non-diagonal cross-damping terms, convert the second-order dynamic equation into matrix form: ; Define the state vector as: ; Wherein,h is the sinking and floating displacement of the blade, θ is the pitch angle of the blade. Converting the system equation into the state space form, the state space equation of the system is: ; where the control input u (t) is the adjustment amount of the cross damping, A(t) is a time-varying system matrix, and the input matrix B is a constant matrix; S22. Based on the state space equation of S21, decompose the system matrix A(t) into a constant component A0 and a periodic time-varying component A1(t): ; S23. Based on the state space equation of S21, design the adaptive feedback control law u (t), and the control input is: ; where K0 is a fixed gain matrix, K1 is a time-varying adaptive gain matrix, and K(t) is obtained by solving the differential Riccati equation; S24. Update the feedback gain matrix K(t) in step S23 online by solving the differential Riccati equation.

[0009] Preferably, in S24, the differential Riccati equation is: ; where Q is the state weight matrix, which penalizes the state deviation, and R is the control input weight matrix, which penalizes the control energy. Both matrices are positive definite matrices. The differential Riccati equation is solved in real time online using the Newton iteration method to obtain the time-varying matrix P(t); and the adaptive feedback gain matrix is obtained by numerical methods: ; K(t) is the obtained adaptive feedback gain matrix.

[0010] Preferably, the specific process of S3 is: The specific process of S3 is: Use the Lyapunov stability theory to prove the stability of the closed-loop system. Based on the designed adaptive feedback control law and the current moment feedback gain matrix K(t) of the output, construct a Lyapunov function that includes the blade state energy and the gain error energy: ; where e is the state error, P(t) is the solution of the differential Riccati equation in S24, K(t) - K* is the gain error matrix, K* is the ideal gain, and Γ is the adaptive learning rate matrix; Calculate the function and substitute it into the system equation to prove that: ; Check that the time derivative of the Lyapunov function is negative definite along the system trajectory, that is: ; Is it correct?

[0011] Preferably, in S4, return to S2 for adjustment, which specifically includes: Increase the weight element corresponding to the pitch angle or heave displacement in the state weight matrix Q in the differential Riccati equation; decrease the control input weight matrix R in the differential Riccati equation, and increase the elements of the adaptive learning rate matrix Γ; use the adjusted parameters (Q, R, Γ) to recalculate the feedback gain matrix K(t) at the current moment, and then return to S2 to reconstruct the Lyapunov function for stability judgment. Loop this process until the time derivative of the constructed Lyapunov function is negative definite along the system trajectory to ensure the closed-loop dynamic stability of the blade.

[0012] Preferably, construct a closed-loop system equation based on the feedback gain matrix output by S2: ; Use the fourth-order Runge-Kutta method to numerically integrate the differential equation of the closed-loop system. By updating the aerodynamic coefficient, system matrix A(t), feedback gain matrix K(t) and closed-loop system equation, realize the real-time simulation of the entire adaptive control loop; obtain the specific expression of the gain matrix K(t) through simulation, and obtain the cross-damping coefficient according to the specific expression of K(t). The cross-damping coefficients correspond to the fourth element in the first row and the third element in the second row of K(t) respectively.

[0013] Compared with the prior art, the present invention has the following beneficial effects: Compared with traditional pneumatic trim tabs that require the installation of flaps, hydraulic drive devices, etc., the present invention directly adjusts the cross-damping coefficient by changing the voltage of the piezoelectric sheet. The piezoelectric sheet has low power consumption and is suitable for the long-term operation requirements of offshore wind power.

[0014] The gain matrix is updated in real time through the differential Riccati equation to adapt to the periodic time-varying aerodynamic force under complex offshore wind conditions, with strong anti-interference ability. At an average wind speed of 8 m / s, the convergence time of the heave displacement is less than 4 seconds, and the convergence speed is fast. It can be extended to a multi-degree-of-freedom model (such as bending-torsion-oscillation coupling), and the complex modal energy is regulated by increasing the cross-damping term, with good compatibility. It is applicable to large offshore wind turbines and unsteady wind fields, with low maintenance costs and good safety. Description of the Drawings [[ID=3?]]

[0015] To more clearly illustrate the technical solutions of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following description is only one embodiment of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0016] Figure 1 is the overall process flow chart of the present invention.

[0017] Figure 2 is the design flow chart of the adaptive control law of the present invention.

[0018] Figure 3 is the schematic diagram of the heave displacement response of the open-loop system at a wind speed of 8 m / s in the embodiment.

[0019] Figure 4 is the pitch angle response curve of the open-loop system at a wind speed of 8 m / s in the embodiment.

[0020] Figure 5 is the schematic diagram of the heave displacement response of the closed-loop system at a wind speed of 8 m / s in the embodiment.

[0021] Figure 6 is the pitch angle response curve of the closed-loop system at a wind speed of 8 m / s in the embodiment. Detailed implementation manners

[0022] In order to increase the output power of wind turbine blades, the blade size is gradually developing towards being slender. Increasing the blade length can capture more wind energy, but it is more likely to have problems of aeroelastic instability. Blade flutter is a self-excited vibration phenomenon of aeroelastic coupling formed by the blade under the action of aerodynamic forces. In severe cases, it will cause blade damage or even fracture. Especially in the marine environment, affected by dynamic wind speeds such as turbulence and gusts in the actual wind field, the challenge of blade aeroelastic flutter is more prominent.

[0023] Traditional flutter suppression methods such as passive damping control are based on the assumption of static aerodynamic loads, and it is difficult to cope with the time-varying aerodynamic disturbances caused by wind speed fluctuations. Moreover, the damping parameters are fixed and cannot be dynamically adjusted, while external mechanism control requires complex external aerodynamic actuators, with high maintenance costs and low reliability in complex environments. There are defects such as insufficient adaptability, complex structure, and slow convergence speed. Therefore, it is necessary to design a flutter suppression method that does not require external actuators, can adapt to time-varying aerodynamic loads, and converges rapidly to improve the operation safety and reliability of offshore wind turbine blades.

[0024] In view of the deficiencies of the existing flutter suppression methods in the prior art, the present invention proposes a method for suppressing the flutter of the blades of an offshore wind turbine based on the combination of cross-damping control and adaptive law. By introducing an asymmetric damping matrix to reconstruct the energy transfer path between modes, combining the adaptive law of time-varying aerodynamic parameters with the differential Riccati equation, updating the control gain online, designing the control law based on the Lyapunov theory to ensure the stability of the closed-loop system, and verifying the stability through numerical simulation, the rapid suppression of flutter is achieved.

[0025] To achieve the above object, the present invention provides the following scheme, and the specific process is as Figure 1 shown.

[0026] An adaptive cross-damping flutter suppression method for the blades of an offshore wind turbine, including: defining a second-order dynamic equation based on the two-dimensional airfoil model, the physical parameters of the blade cross-section, and the offshore wind condition parameters, calculating the mass matrix M0 and its inverse matrix, constructing the stiffness matrix K0 and the damping matrix C0 at the initial moment, and dynamically updating the aerodynamic coefficients C l, θ 、 C m, θ , generating the time-varying stiffness matrix K0(t) and damping matrix C0(t), designing a feedback controller by the LQR method, solving the Riccati equation to obtain the gain matrix, extracting the cross-damping coefficient, obtaining a new coupled damping matrix, constructing the closed-loop system equation, constructing a Lyapunov function, and proving whether the derivative of the function is negative definite. If not satisfied, return to adjust the control parameters, numerically integrate the closed-loop system using the Runge-Kutta method, solve the state response at each time step, and output the time-domain response curves of the heave displacement and pitch angle.

[0027] Step A: Establish an aeroelastic model of the offshore wind turbine blade with non-diagonal damping terms, introduce cross terms into the damping matrix, and couple the heave and pitch motions.

[0028] The traditional damping matrix is a diagonal matrix, only including the heave damping c h and the pitch damping c θ . By introducing non-diagonal terms c 21 and c 12 to form a coupled damping matrix, c 21 is the contribution of the heave velocity to the pitch damping force, c 12 is the contribution of the pitch velocity to the heave damping force, and adjusts the energy transfer path from the pitch motion to the heave mode. The coupled damping matrix formed by introducing non-diagonal terms into the damping matrix can be expressed as: .

[0029] Based on the two-dimensional airfoil model, a nonlinear aeroelastic equation including heave and pitch degrees of freedom is established. The heave motion equation is: ; where, h is the heave displacement, L ( t ) is the time-varying aerodynamic lift, which is calculated by the unsteady aerodynamic force formula. The pitch motion equation is: ; where, θ is the pitch angle, M ( t ) is the aerodynamic moment, which is related to the lift distribution and blade geometric parameters. m is the mass of the blade section, I θ is the inertial pitch moment about the elastic axis, x θ b is the distance from the center of mass to the elastic axis, c h , c θ are the heave and pitch damping coefficients, k h , k θ is the spring stiffness.

[0030] Considering the actual sea wind conditions and the periodic change of the angle of attack caused by the blade rotation, the unsteady aerodynamic force and aerodynamic moment acting on the system can be expressed as: ; ; where, ρ is the air density, U is the wind speed, b is the semi-chord length, and a is the dimensionless distance from the mid-chord to the elastic axis.

[0031] As the blade rotates, the dynamic lift and moment coefficients should change with the periodic change of the angle of attack. The coefficient relationship is determined by fitting experimental data or deriving from aeroelastic theory. Assuming C l, θ , C m, θ are sine curves with the same blade rotation frequency, then the aerodynamic force coefficient: ; The aerodynamic moment coefficient: ; where, C l, 0is the average aerodynamic lift coefficient, C m, 0 is the average aerodynamic moment coefficient, C l, θ is the amplitude of the fluctuation of the aerodynamic lift coefficient, C m, θ is the amplitude of the fluctuation of the aerodynamic moment coefficient, ω is the angular frequency of blade rotation; By adjusting c 21 and c 12 the energy interaction control of heave and pitch motions is achieved.

[0032] Step B: State - space equation transformation and adaptive control law design: At the initial moment, construct the system matrix and input matrix, design a feedback controller by the LQR method, solve the Riccati equation to obtain the gain matrix, and extract the cross - damping coefficient. The adaptive control law design is as Figure 2 shown.

[0033] Define the state vector and transform the second - order differential equation into the state - space form: ; where the control input u is the adjustment amount of the cross - damping. The system matrix A(t) contains time - varying aerodynamic coefficients; the input matrix B is related to the control input u(t), that is, the adjustment amount of the cross - damping coefficient.

[0034] The system matrix A(t) can be expressed as: ; The input matrix B can be expressed as: ; The expression of the initial mass matrix is: ; where x θ is the dimensionless distance from the center of mass to the elastic axis.

[0035] The expression of the time - varying stiffness matrix is: ; The expression of the matrix after introducing cross - damping control is: ; where a is the dimensionless distance from the center of the chord to the elastic axis.

[0036] The linear quadratic regulator (LQR) is used to design the control law with the goal of minimizing the performance index, and an approximate or simplified method is used to solve the feedback gain matrix. Define the quadratic performance index: .

[0037] where Q is the state weight matrix that penalizes the state deviation, and R is the control input weight matrix that penalizes the control energy. Both are positive definite matrices. LQR solves for the optimal feedback gain by trading off the state deviation and control energy consumption. The weight matrices Q and R adjust the state convergence rate and the control input amplitude respectively. The feedback gain matrix K(t) is determined by solving the algebraic Riccati equation (ARE) to minimize J, and at this time the closed-loop system is stable.

[0038] Since the LQR control cannot handle the time-varying aerodynamic force, the adaptive LQR control is used to compensate for the periodic change of A(t). A(t) is expressed as the sum of a constant term and a periodic term, that is: ; where A 0 is the DC component of the aerodynamic coefficient, A 1 is the AC component of the aerodynamic coefficient.

[0039] Design the feedback control input based on the adaptive control law: ; where K0 is the fixed gain matrix determined by offline optimization; K1 is the time-varying gain matrix updated online through the differential Riccati equation.

[0040] Design the state weight matrix: ; Focus on the pitch angle and heave displacement; the control input weight matrix: ; Limit the cross-damping gain.

[0041] Design K 0 、K 1 such that: A m = A 0 +BK 0, 0= A 1 +BK 1 where A m is the desired stable reference model matrix.

[0042] Decompose the time-varying matrix and update the gain matrix online through the differential Riccati equation to compensate for the periodic disturbance: ; Construct the residual function: ; Make the residual F(P) ≈ 0, then the equation is balanced.

[0043] Adopt Newton-Kantorovich iteration: ; Subsequently, iterate and optimize.

[0044] Initialize P with the solution of the static Riccati equation 0 .

[0045] Linearize the differential Riccati equation at P (k) : .

[0046] Solve the linear equation , where the Jacobian operator is a matrix formed by the Kronecker product, reflecting the influence of the small change of P on the residual.

[0047] Calculate the derivative , which is in the form of a continuous-time Lyapunov equation and can be solved by the Bartels-Stewart algorithm. , where is the Riccati matrix correction.

[0048] Update , where α is the step size.

[0049] When , terminate the iteration to ensure that the accuracy of P(t) reaches 10 -6 .

[0050] Solve in real time through numerical methods (such as the iteration method) and update the feedback gain matrix: .

[0051] Step C: Modify the damping matrix, construct the closed-loop system matrix, construct the Lyapunov function for stability judgment, and verify that the time derivative of the Lyapunov function is negative definite along the system trajectory to ensure the stability of the closed-loop system. If not satisfied, return to adjust the control parameters.

[0052] Calculate the time derivative of the Lyapunov function.

[0053] Define the state error: e = X - X m； where e is the actual system state vectorX and the difference with the reference model state vector X m is obtained from the ideal closed-loop dynamics equation X m Construct the Lyapunov function:

[0054] ; ; where e is the state error, P(t) is the solution of the differential Riccati equation in step B, K(t) - K* is the gain error matrix, K* is the ideal gain, and Γ is the adaptive learning rate matrix; the first term of the Lyapunov function reflects the state energy, and the second term penalizes the gain error

[0055] Adaptive learning rate matrix: ; γ is the maximum learning rate, γ > 0. When is much greater than 1, Γ also becomes larger, and the maximum learning rate accelerates convergence; when is much less than 1, Γ also becomes smaller, and the parameters converge rapidly

[0056] Calculate and substitute it into the system equation to prove: .

[0057] According to the Lyapunov stability theorem, the adaptive law: .

[0058] Through ensure the stability of the closed-loop system

[0059] Step D: Numerical simulation and performance verification; Select the wind condition when exceeding the critical flutter speed as the design parameter, and use the parameters in Table 1 for numerical experiments with the simulation parameter settings: The blade motion equation needs to be numerically solved. The Euler method has a large error, so the fourth-order Runge-Kutta method is used to solve the closed-loop system equation. The iterative steps are as follows: ; ; ; ; .

[0060] Set the time step to 0.001 seconds to ensure the calculation accuracy (ε = 1e-3). Set the initial state of the system and solve the differential equation within the time interval [0, 15] seconds to obtain the state response

[0061] The feedback gain matrix is obtained through LQR design, and the characteristics of the closed-loop system are analyzed.

[0062] The stability of the closed-loop system is verified by eigenvalue analysis to ensure that the real parts of all eigenvalues are negative.

[0063] The specific expression of the feedback gain matrix K(t) is obtained through simulation. According to the specific expression of K(t), the cross-damping coefficient can be obtained. Applying the cross-damping coefficient to the blades of an offshore wind turbine can rapidly suppress the flutter of the offshore blades. The heave displacement and pitch angle of the open-loop system diverge with time, indicating that the system is unstable without control. The closed-loop system rapidly converges to the steady state within 4 seconds by adjusting the cross-damping, and the real parts of the eigenvalues are all negative, verifying the stability. This proves that the method of the present invention effectively suppresses the aeroelastic flutter of the blades of an offshore wind turbine and ensures the safe operation of the blades.

[0064] The solution of the present invention will be further described below in conjunction with specific embodiments.

[0065] Step 1: Establish a second-order dynamic model with a cross-damping term The blade is simplified into a two-dimensional airfoil model, and its motion equation consists of heave and pitch degrees of freedom: ; Introduce the cross-damping term: Add non-diagonal terms to the damping matrix to form a coupled damping matrix: ; The action mechanism of the cross-damping term is: c 21 represents the contribution of the pitch velocity to the heave damping, c 12 represents the contribution of the heave velocity to the pitch damping; Time-varying aerodynamic force modeling: Considering the periodic change of the aerodynamic coefficient caused by the rotation of the blade, the lift coefficient and moment coefficient are expressed as: .

[0066] Step 2: State-space equation transformation Define the state vector , and transform the second-order dynamic equation into the state-space form: ; Among them, the system matrix and the input matrix are respectively: ; .

[0067] Step 3: Adaptive control law design Decompose the system matrix into a constant component and a time-varying component ; The designed adaptive feedback control input is: ; Solve the differential Riccati equation and update the gain matrix by online solving the following equation: , where Q and R are weight matrices that respectively adjust the state convergence speed and control energy consumption.

[0068] Step 4: Proof of the stability of the closed-loop system Construct the Lyapunov function: ; where e is the state error, P(t) is the solution of the differential Riccati equation in Step 3, K(t) - K* is the gain error matrix, and Γ is the adaptive learning rate matrix; it is derived that Ensure the global asymptotic stability of the closed-loop system.

[0069] Step 5: Numerical simulation and result analysis Use the fourth-order Runge-Kutta method to perform numerical integration on the closed-loop system, and the simulation parameters are shown in Table 1: Table 1 Simulation parameters

[0070] Dynamic response simulation: Initial conditions: h(0) = 0.1m, θ(0) = 10°, h'(0) = 0, θ'(0) = 0; Time range: t ∈ [0, 15] s; Calculate the LQR feedback gain at the initial moment: K1 = 0.56, K2 = 0.33; Calculate the eigenvalues of the closed-loop system at the initial moment: λ 1 = -1.581 ± 18.041j, λ 2 = -1.363 ± 11.858j. The real parts are all negative, indicating that the system is stable; Response curve and result analysis: As Figures 3 to 6 shown, the heave displacement rapidly decays from 0.1 m to 0 m, the convergence time is about 4 s, and the steady-state error approaches zero. The initial angle converges from 10° to the equilibrium position of 0° without overshoot, and the convergence time is about 4 s.

[0071] The present invention uses cross-damping control to dynamically adjust the internal cross-damping coefficient of the blade ( c 12 , c 21)Modal energy active control is realized, and the feedback gain matrix K(t) is updated online by solving the differential Riccati equation to accurately compensate for the time-varying aerodynamic force at sea. Based on the Lyapunov theory and eigenvalue verification, the closed-loop stability is ensured. Finally, the dynamically optimized cross-damping coefficient command is output, enabling the heave displacement and pitch angle of the blade to quickly converge after encountering disturbances, thus achieving rapid suppression of blade flutter of offshore wind turbines. Compared with traditional methods, this solution has the advantages of simple structure, fast response, and good stability. At a wind speed of 8 m / s, the vibration convergence time can be shortened to within 4 seconds, and the steady-state error approaches zero, providing a reliable guarantee for the safe operation of large offshore wind turbines.

[0072] The above are only the preferred embodiments of the present application and are not intended to limit the present application. For those skilled in the art, various changes and modifications can be made to the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included within the protection scope of the present application.

[0073] Although the specific implementation manners of the present invention have been described above, they do not limit the protection scope of the present invention. Those skilled in the art should understand that various modifications or deformations that can be made without creative efforts on the basis of the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. An adaptive cross-damping flutter suppression method for an offshore wind turbine blade, characterized in that: Controllable distributed piezoelectric sheets are embedded at key positions inside the wind turbine blade, including a heave motion sensitive area and a pitch motion actuation area, and the method includes the following processes: S1. Based on the two-dimensional airfoil model, combined with the physical parameters of the blade section and the offshore wind conditions parameters, establish the second-order dynamic equations of the blade heave motion and pitch motion, including the mass matrix, stiffness matrix and damping matrix; introduce non-diagonal cross-damping into the damping matrix for reconstruction to obtain the coupled damping matrix, dynamically update the aerodynamic coefficients, and generate the time-varying stiffness matrix and time-varying damping matrix; S2. Based on the second-order dynamic equations in S1, combined with the mass matrix, time-varying stiffness matrix and time-varying damping matrix, convert the system into the state space form to obtain the state space equation, design an adaptive feedback control law according to the time-varying system matrix and input matrix in the state space equation, the adaptive feedback control law is composed of the state vector and the feedback gain matrix, substitute the system matrix and input matrix into the Riccati equation for solution to obtain the feedback gain matrix, and this matrix is used to generate the control input to drive the piezoelectric sheet to adjust the cross-damping coefficient through voltage; S3. Construct a Lyapunov function including the blade state energy and the gain error energy, calculate the time derivative of this Lyapunov function under the adaptive feedback control law designed in S2, and verify whether the derivative of the Lyapunov function is negative definite; S4. Make a conditional judgment. If the time derivative of the Lyapunov function output in S3 is negative along the system trajectory, it means the system is stable. Obtain the cross-damping coefficient based on the feedback gain matrix expression, and apply the cross-damping coefficient to the offshore wind turbine blade; If the time derivative of the Lyapunov function is positive along the system trajectory, return to S2 for adjustment, and then enter S3 until the time derivative of the Lyapunov function is negative definite, and output the corresponding cross-damping coefficient.

2. The adaptive cross-damping flutter suppression method for the blades of an offshore wind turbine according to claim 1, characterized in that: The key positions inside the wind turbine blade, namely the heave motion sensitive area and the pitch motion actuation area, are near the elastic axis of the blade; The input physical parameters of the offshore wind turbine blade include: sectional mass m , pitch moment of inertia about the elastic axis I θ , distance from the center of mass to the elastic axis x θ b , heave stiffness k h , pitch stiffness k θ , heave damping coefficient c h , pitch damping coefficient c θ , half chord length b ; Offshore wind conditions parameters include: air density ρ , wind speed U , and the blade rotational angular frequency ω; The basic values of the aerodynamic coefficients include: the average aerodynamic lift coefficient C l, θ and the aerodynamic moment coefficient C m, θ .

3. The adaptive cross-damping flutter suppression method for an offshore wind turbine blade according to claim 1, characterized in that: The specific process of S1 includes: S11. Based on the two-dimensional airfoil model, define the second-order dynamic equations of the heave motion and pitch motion as: ； wherein, θ is the pitch angle, M ( t ) is the aerodynamic moment, which is related to the lift distribution and blade geometric parameters; m is the blade section mass, I θ is the inertia pitch moment about the elastic axis, x θ b is the distance from the center of mass to the elastic axis, c h , c θ are the heave and pitch damping coefficients, k h , k θ is the spring stiffness; L ( t ) represents the unsteady aerodynamic force and M ( t ) represents the aerodynamic moment; S12. Introduce the cross-damping coefficient and introduce cross-damping terms into the off-diagonal terms of the damping matrix in S11. c 21 、 c 12 , reconstruct the damping matrix to form a coupled damping matrix: ； Among them, c 21 and c 12 are cross-damping coefficients, representing the contributions of pitch rate to heave damping and heave rate to pitch damping, respectively; S13, calculate the unsteady aerodynamic force L ( t ) and aerodynamic moment M ( t ) caused by the offshore wind farm in S11: ； ； Among them, ρ is the air density, U is the wind speed, ω is the angular frequency of blade rotation; a is the dimensionless distance from the chord center to the elastic axis, b is the semi-chord length; S14, model the unsteady aerodynamic force L ( t ) and the aerodynamic moment M ( t ) as periodic time-varying functions, specifically: C l, θ and the aerodynamic moment coefficient C m, θ as follows: ； ； wherein, C l, θ is the aerodynamic lift coefficient, C m, θ is the aerodynamic moment coefficient, C l, 0 is the average aerodynamic lift coefficient, C m, 0 is the average aerodynamic moment coefficient, C l, θ is the amplitude of the fluctuation of the aerodynamic lift coefficient, C m, θ is the amplitude of the fluctuation of the aerodynamic moment coefficient, ω is the angular frequency of blade rotation; S15, based on the physical parameters of the blade and the time-varying aerodynamic coefficients C l, θ 、 C m, θ , combining the steps of S11 - S14, construct the time-varying stiffness matrix K0(t) and the time-varying damping matrix C0(t) including cross-damping terms; The expression of the time-varying stiffness matrix is: ； The expression of the time-varying damping matrix C0(t) including the cross-damping term is: ； Among them, a is the dimensionless distance from the chord length center to the elastic axis.

4. The adaptive cross-damping flutter suppression method for an offshore wind turbine blade according to claim 3, characterized in that: The specific process of S2 includes: S21. According to the second-order dynamic equation and the mass matrix M0, time-varying stiffness matrix K0(t) and time-varying damping matrix C0(t) including non-diagonal cross-damping terms, convert the second-order dynamic equation into matrix form: ； Among them, F aero is the unsteady aerodynamic force L ( t ) and the aerodynamic moment M ( t ) form an aerodynamic force matrix, and its expression is: ； Define the state vector as: ； wherein, h is the floating and sinking displacement of the blade, θ is the pitch angle of the blade. Converting the system equation into the state space form, the state space equation of the system is: ； Among them, the control input u (t) is the adjustment amount of cross damping, A(t) is a time-varying system matrix, and the input matrix B is a constant matrix; S22. Based on the state space equation in S21, decompose the system matrix A(t) into a constant component A0 and a periodic time-varying component A1(t): ； S23. Design an adaptive feedback control law based on the state space equation of S21 u (t), and the control input is: ； Among them, K0 is a fixed gain matrix, K1 is a time-varying adaptive gain matrix, and K(t) is obtained by solving the differential Riccati equation; S24. Online update the feedback gain matrix K(t) in step S23 by solving the differential Riccati equation.

5. A method for suppressing the adaptive cross-damping flutter of an offshore wind turbine blade according to claim 4, characterized in that: In S24, the differential Riccati equation is as follows: ； where Q is the state weight matrix that penalizes state deviation, R is the control input weight matrix that penalizes control energy, and both matrices are positive definite matrices. The differential Riccati equation is solved online in real time using the Newton iteration method to obtain the time-varying matrix P(t), where P(t) is the solution of the differential Riccati equation; and the adaptive feedback gain matrix is obtained by numerical methods: ； K(t) is the obtained adaptive feedback gain matrix.

6. The adaptive cross-damping flutter suppression method for the blades of an offshore wind turbine according to claim 4, wherein: The specific process of S3 is as follows: The specific process of S3 is as follows: Use the Lyapunov stability theory to prove the stability of the closed-loop system. Based on the designed adaptive feedback control law and the current-time feedback gain matrix K(t) of the output, construct a Lyapunov function that includes the blade state energy and the gain error energy: ； where e is the state error, P(t) is the solution of the differential Riccati equation in S24, K(t) - K* is the gain error matrix, K* is the ideal gain, and Γ is the adaptive learning rate matrix; Calculate this function and substitute it into the system equation to prove: ； Check that the time derivative of the Lyapunov function is negative definite along the system trajectory, that is: ； Is it correct? 7. A method for suppressing the self-adaptive cross-damping flutter of an offshore wind turbine blade according to claim 6, characterized in that: In S4, return to S2 for adjustment, specifically including: Increase the weight element corresponding to the pitch angle or heave displacement in the state weight matrix Q in the differential Riccati equation; decrease the control input weight matrix R in the differential Riccati equation, and increase the elements of the adaptive learning rate matrix Γ; use the adjusted parameters (Q, R, Γ) to recalculate the feedback gain matrix K(t) at the current time, and then return to S2 to reconstruct the Lyapunov function for stability judgment. Repeat this process until the time derivative of the constructed Lyapunov function is negative definite along the system trajectory to ensure the closed-loop dynamic stability of the blade.

8. An adaptive cross-damping flutter suppression method for an offshore wind turbine blade according to claim 1, characterized in that: Construct a closed-loop system equation based on the feedback gain matrix output by S2: ； Use the fourth-order Runge-Kutta method to numerically integrate the differential equation of the closed-loop system. By updating the aerodynamic coefficient, the system matrix A(t), the feedback gain matrix K(t), and the closed-loop system equation, realize the real-time simulation of the entire adaptive control loop; obtain the specific expression of the gain matrix K(t) through simulation, and obtain the cross-damping coefficient according to the specific expression of K(t). The cross-damping coefficients correspond to the fourth element in the first row and the third element in the second row of K(t), respectively.

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