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

Abstract

The present invention provides an adaptive cross-damping flutter suppression method for offshore wind turbine blades, belonging to the technical field of wind power generation based on computer data processing. First, an aeroelastic model containing non-diagonal damping terms is established, and the heave and pitch motions are coupled through the cross-damping coefficient; secondly, an adaptive control law based on the differential Riccati equation is designed, and the damping parameters are dynamically adjusted to compensate for the time-varying aerodynamic force; finally, the closed-loop stability is proved by the Lyapunov theory, and the control effect is verified by numerical simulation. The present invention does not require an external pneumatic actuator, has a simple structure, and fast response. At a wind speed of 8m / s, the vibration convergence time can be shortened to within 4 seconds, and the steady-state error approaches zero. It is suitable for flutter suppression of large offshore wind turbine blades.

Description

Technical Field

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

[0002] As offshore wind turbine blades continue to grow in length, blade flexibility increases, and the aeroelastic coupling effect intensifies, leading to an increased risk of blade flutter. Flutter is a self-excited vibration phenomenon caused by aerodynamic coupling of blades under the action of aerodynamic forces. In severe cases, it can cause 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 changes in angle of attack. In addition, the damping parameters are fixed and have poor adaptability. Aerodynamic trimming control relies on external aerodynamic actuators (such as trailing edge flaps), which have complex structures, susceptibility to salt spray corrosion, and high maintenance costs. It is often prone to failure in highly turbulent environments. Although fixed-gain LQR control can optimize state feedback, it is limited by the assumption of a time-invariant system and has difficulty compensating for periodic time-varying aerodynamic loads, resulting in low control accuracy.

[0003] Published technologies include using variable pitch systems to adjust flap angles, piezoelectric ceramics to adjust blade stiffness, and stepper motors to control flap swing. However, these control methods rely on the assumption of quasi-steady-state aerodynamic forces, making them difficult to adapt to unsteady aerodynamic disturbances. Furthermore, the motor and ball screw structures suffer from mechanical friction and response lag, resulting in wear under extreme loads, poor durability, and difficulty in maintaining accurate control. Cross-damping control technology, on the other hand, eliminates the need for external pneumatic actuators. Instead, it dynamically adjusts the cross-damping coefficient based on the differential Riccati equation, compensating for periodic, time-varying aerodynamic forces, adapting to wind speed fluctuations and nonlinear disturbances, and offering improved environmental adaptability. Summary of the Invention

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

[0005] The present invention provides a method for suppressing flutter of offshore wind turbine blades with adaptive cross damping.

[0006] Controllable distributed piezoelectric chips are embedded in key locations inside wind turbine blades, including the heaving motion sensitive area and the pitching motion actuation area. That is, piezoelectric chips are arranged near the elastic axis of the blade. The cross damping coefficient is adjusted by voltage, and the following process is involved:

[0007] S1, based on the two-dimensional airfoil model, combined with the physical parameters of the blade section and the offshore wind parameters, establishes the second-order dynamic equations for the blade's heave and pitch motions, including the mass matrix, stiffness matrix, and damping matrix. Non-diagonal cross damping is introduced into the damping matrix for reconstruction to obtain the coupled damping matrix. The aerodynamic coefficients are dynamically updated to generate the time-varying stiffness matrix and time-varying damping matrix.

[0008] S2, based on the second-order dynamic equation in S1, combined with the mass matrix, time-varying stiffness matrix and time-varying damping matrix, converts the system into a state space form to obtain the state space equation. According to the time-varying system matrix and input matrix in the state space equation, an adaptive feedback control law is designed. The adaptive feedback control law is composed of a state vector and a feedback gain matrix. The system matrix and input matrix are brought into the Riccati equation for solution to obtain a feedback gain matrix. This matrix is ​​used to generate a control input to drive the piezoelectric piece to adjust the cross damping coefficient through voltage.

[0009] S3, construct a Lyapunov function that includes the blade state energy and the gain error energy, calculate the time derivative of the Lyapunov function under the adaptive feedback control law designed in S2, and verify whether the derivative of the Lyapunov function is negative definite;

[0010] S4, performs conditional judgment. If the time derivative of the Lyapunov function output by S3 is negative along the system trajectory, it means that the system is stable. The cross damping coefficient is obtained based on the feedback gain matrix expression and applied to the offshore wind turbine blades.

[0011] If the time derivative of the Lyapunov function is positive along the system trajectory, then return to S2 for adjustment and enter S3 until the time derivative of the Lyapunov function is negative, and output the corresponding cross damping coefficient.

[0012] Preferably, the key positions inside the wind turbine blades are the blade heaving motion sensitive area and the pitching motion actuation area, that is, near the blade elastic axis;

[0013] Input offshore wind turbine blade physical parameters include: cross-sectional mass m , pitching moment of inertia around the elastic axis I θ , distance from center of mass to elastic axis x θ b , buoyancy stiffness k h , pitch stiffness k θ , buoyancy damping coefficient c h , pitch damping coefficient c θ , half chord lengthb ;

[0014] Offshore wind parameters include: air density ρ , wind speed U , blade rotation angular frequency ω;

[0015] The basic values ​​of aerodynamic coefficients include: average aerodynamic lift coefficient C l, θ and aerodynamic moment coefficient C m, θ .

[0016] Preferably, the specific process of S1 includes:

[0017] S11, based on the two-dimensional airfoil model, defines the second-order dynamic equations for heaving and pitching motions as:

[0018] ;

[0019] in, θ is the pitch angle, M ( t ) is the aerodynamic moment, which is related to the lift distribution and blade geometry parameters; m is the blade cross-sectional mass, I θ is the pitching moment of inertia 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 torque;

[0020] S12, introduces the cross damping coefficient, and introduces the cross damping term into the non-diagonal term of the damping matrix of S11 c 21 、 c 12 , reconstruct the damping matrix to form the coupled damping matrix:

[0021] ;

[0022] in, c 21 、 c 12is the cross damping coefficient, which represents the contribution of pitching velocity to heaving damping and the contribution of heaving velocity to pitching damping respectively;

[0023] S13, calculate the unsteady aerodynamic force caused by the offshore wind field in S11 L ( t ) and aerodynamic torque M ( t ):

[0024] ;

[0025] ;

[0026] in, ρ is Air density, U is the wind speed, ω is the blade rotation angular frequency;

[0027] S14, the unsteady aerodynamic force in S13 L ( t ) and aerodynamic torque M ( t ) in the aerodynamic lift coefficient C l, θ and aerodynamic moment coefficient C m, θ Modeled as a periodic time-varying function, specifically:

[0028] ;

[0029] ;

[0030] in, C l, 0 is the average aerodynamic lift coefficient, C m, 0 is the mean aerodynamic moment coefficient, C l, θ is the fluctuation amplitude of the aerodynamic lift coefficient, C m, θ is the fluctuation amplitude of the aerodynamic moment coefficient, ω is the blade rotation angular frequency;

[0031] S15, based on blade physical parameters and time-varying aerodynamic coefficients C l, θ 、 C m, θ , combining steps S11-S14, construct the time-varying stiffness matrix K0(t) and the time-varying damping matrix C0(t) including the cross damping term;

[0032] The expression of the time-varying stiffness matrix is:

[0033] ;

[0034] The expression of the time-varying damping matrix C0(t) including the cross damping term is: ;

[0035] in, a is the dimensionless distance from the center of the chord to the elastic axis.

[0036] Preferably, the specific process of S2 includes:

[0037] 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 the non-diagonal cross damping terms, the second-order dynamic equation is converted into a matrix form:

[0038] ;

[0039] Define the state vector as:

[0040] ;

[0041] in, h is the displacement of the blade, θ is the pitch angle of the blade, converting the system equation into state space form, then the state space equation of the system is:

[0042] ;

[0043] Among them, the control input u (t) is the adjustment amount of cross damping, A(t) is the time-varying system matrix, and the input matrix B is a constant matrix;

[0044] S22, based on the state space equation of S21, decomposes the system matrix A(t) into a constant component A0 and a periodic time-varying component A1(t):

[0045] ;

[0046] S23, based on the state space equation of S21, designs the adaptive feedback control rate u (t), the control input is:

[0047] ;

[0048] Where K0 is the fixed gain matrix, K1 is the time-varying adaptive gain matrix, and K(t) is obtained by solving the differential Riccati equation;

[0049] S24, updating the feedback gain matrix K(t) in step S23 online by solving the differential Riccati equation.

[0050] Preferably, in S24, the differential Riccati equation is:

[0051] ;

[0052] Among them, 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 Newton iteration method is used to solve the differential Riccati equation in real time online to obtain the time-varying matrix P(t); and the adaptive feedback gain matrix is ​​obtained by numerical method:

[0053] ;

[0054] K(t) is the obtained adaptive feedback gain matrix.

[0055] Preferably, the specific process of S3 is:

[0056] The specific process of S3 is as follows:

[0057] The stability of the closed-loop system is proved using Lyapunov stability theory. Based on the designed adaptive feedback control law and the output current moment feedback gain matrix K(t), a Lyapunov function containing the blade state energy and gain error energy is constructed:

[0058] ;

[0059] 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;

[0060] Evaluate this function and substitute it into the system of equations to show that:

[0061] ;

[0062] Check that the time derivative of the Lyapunov function is negative along the system trajectory, that is:

[0063] ;

[0064] Is it correct?

[0065] Preferably, the step S4 returns to step S2 for adjustment, specifically including:

[0066] Increase the weight elements corresponding to the pitch angle or heave displacement in the state weight matrix Q in the differential Riccati equation; reduce 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. Repeat this process until the time derivative of the constructed Lyapunov function is negative along the system trajectory to ensure the dynamic stability of the blade closed loop.

[0067] Preferably, the closed-loop system equation is constructed based on the feedback gain matrix output by S2:

[0068] ;

[0069] The fourth-order Runge-Kutta method is used to numerically integrate the closed-loop system differential equations. By updating the aerodynamic coefficients, the system matrix A(t), the feedback gain matrix K(t) and the closed-loop system equations, real-time simulation of the entire adaptive control loop is achieved. The specific expression of the gain matrix K(t) is obtained by simulation, and the cross-damping coefficient is obtained based on the specific expression of K(t). The cross-damping coefficient corresponds to the first row and fourth column and the second row and third column of K(t), respectively.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] Compared to traditional pneumatic trimmers that require flaps and hydraulic drives, the present invention uses piezoelectric plates to directly adjust the cross damping coefficient by changing the voltage. Piezoelectric plates have low power consumption and are suitable for the long-term operation requirements of offshore wind power.

[0072] The system updates the gain matrix in real time through the differential Riccati equation, adapting to the periodic, time-varying aerodynamic forces in complex offshore wind conditions. It offers strong anti-interference capabilities, with a fast convergence time of less than 4 seconds for heave and float displacement at an average wind speed of 8 m / s. It can be expanded to multi-degree-of-freedom models (such as bending-torsion-shimmy coupling), and complex modal energy can be controlled by adding cross-damping terms, ensuring excellent compatibility. It is suitable for large offshore wind turbines and unsteady wind farms, offering low maintenance costs and excellent safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions of the present invention or the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, what is described below is only one embodiment of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0074] Figure 1 It is a flow chart of the overall process of the present invention.

[0075] Figure 2 It is a flow chart of the adaptive control law design of the present invention.

[0076] Figure 3 Schematic diagram of the sinking and floating displacement response of the open-loop system under a wind speed of 8 m / s in the embodiment.

[0077] Figure 4 8m / s wind speed under the open-loop system of the embodiment of the pitch angle response curve diagram.

[0078] Figure 5 Schematic diagram of the sinking and floating displacement response of the closed-loop system under a wind speed of 8 m / s in the embodiment.

[0079] Figure 6 8m / s wind speed under the closed-loop system of the embodiment of the pitch angle response curve diagram. DETAILED DESCRIPTION

[0080] To increase the output power of wind turbine blades, blades are becoming increasingly slender. Increasing blade length captures more wind energy, but it also increases the risk of aeroelastic instability. Blade flutter is a self-excited vibration phenomenon caused by aerodynamic forces, resulting from aeroelastic coupling. In severe cases, it can damage or even break the blade. In marine environments, the challenges of blade aeroelastic flutter are particularly pronounced due to the influence of dynamic wind speeds such as turbulence and gusts in actual wind fields.

[0081] Traditional flutter suppression methods, such as passive damping control, assume static aerodynamic loads and are difficult to handle due to time-varying aerodynamic disturbances caused by wind speed fluctuations. Furthermore, damping parameters are fixed and cannot be dynamically adjusted. External mechanism control, on the other hand, requires complex external pneumatic actuators, resulting in high maintenance costs and low reliability in complex environments. These methods suffer from limitations such as insufficient adaptability, complex structures, and slow convergence. Therefore, a flutter suppression method that does not require external actuators, can adapt to time-varying aerodynamic loads, and converges rapidly is needed to improve the operational safety and reliability of offshore wind turbine blades.

[0082] In response to the shortcomings of the existing flutter suppression methods, the present invention proposes a flutter suppression method for offshore wind turbine blades 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, and designing the control law based on the Lyapunov theory to ensure the stability of the closed-loop system. The stability is verified by numerical simulation, thereby achieving rapid flutter suppression.

[0083] To achieve the above object, the present invention provides the following scheme, the specific process is as follows Figure 1 shown.

[0084] A method for adaptive cross-damping flutter suppression of offshore wind turbine blades, comprising: defining a second-order dynamic equation based on a binary airfoil model, blade cross-section physical parameters, and offshore wind condition parameters; calculating a mass matrix M0 and its inverse matrix; constructing an initial stiffness matrix K0 and a damping matrix C0; and dynamically updating aerodynamic coefficients. C l, θ 、 C m, θ Generate the time-varying stiffness matrix K0(t) and damping matrix C0(t). Design a feedback controller using the LQR method, solve the Riccati equation to obtain the gain matrix, extract the cross-damping coefficient, and obtain a new coupling damping matrix. Construct the closed-loop system equations, construct the Lyapunov function, and prove whether the derivative of the function is negative definite. If not, adjust the control parameters and numerically integrate the closed-loop system using the Runge-Kutta method. Determine the state response at each time step and output the time-domain response curves of the heave displacement and pitch angle.

[0085] Step A: Establish an aeroelastic model of offshore wind turbine blades with off-diagonal damping terms, introduce cross terms into the damping matrix, and couple heave and pitch motions.

[0086] The traditional damping matrix is ​​a diagonal matrix, which only contains the sinking and floating damping c h and pitch damping c θ , introducing off-diagonal terms c 21 and c 12 Forming the coupling damping matrix, c 21 is the contribution of the heaving and floating velocity to the pitching damping force, c 12 It is the contribution of pitch velocity to the heave damping force, which regulates the transmission path of pitch motion energy to the heave mode. The coupling damping matrix formed by introducing non-diagonal terms in the damping matrix can be expressed as: .

[0087] Based on the two-dimensional airfoil model, a nonlinear aeroelastic equation including the heave and pitch degrees of freedom is established. The heave motion equation is:

[0088] ;

[0089] in, h is the sinking displacement, L ( t ) is the time-varying aerodynamic lift, which is calculated using the unsteady aerodynamic formula. The pitch motion equation is:

[0090] ;

[0091] in, 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 cross-sectional mass, I θ is the pitching moment of inertia 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.

[0092] Considering the actual wind conditions at sea and the periodic changes in the angle of attack caused by blade rotation, the unsteady aerodynamic force and aerodynamic moment acting on the system can be expressed as:

[0093] ;

[0094] ;

[0095] in, ρ is the air density, U is the wind speed, b is the half-chord length, and a is the dimensionless distance from the mid-chord to the elastic axis.

[0096] As the blades rotate, the dynamic lift and moment coefficients should change with the periodic change of the angle of attack. The coefficient relationship can be determined by fitting experimental data or deriving from aeroelastic theory. C l, θ 、 C m, θ is a sinusoidal curve with the same blade rotation frequency, then the aerodynamic coefficient is:

[0097] ;

[0098] Aerodynamic moment coefficient:

[0099] ;

[0100] in, C l, 0 is the average aerodynamic lift coefficient, C m, 0 is the mean aerodynamic moment coefficient, C l, θ is the fluctuation amplitude of the aerodynamic lift coefficient, C m, θ is the fluctuation amplitude of the aerodynamic moment coefficient, ω is the blade rotation angular frequency;

[0101] By adjusting c 21 、 c 12 , realizing the interactive energy control of sinking and pitching motion.

[0102] Step B, state space equation transformation and adaptive control law design: construct the system matrix and input matrix at the initial time, design the feedback controller by LQR method, solve the Riccati equation to obtain the gain matrix, and extract the cross damping coefficient. Figure 2 shown.

[0103] Define the state vector , convert the second-order differential equation into state-space form:

[0104] ;

[0105] The control input u is the cross-damping adjustment. The system matrix A(t) contains the time-varying aerodynamic coefficients; the input matrix B is associated with the control input u(t), which is the cross-damping adjustment.

[0106] The system matrix A(t) can be expressed as:

[0107] ;

[0108] The input matrix B can be expressed as:

[0109] ;

[0110] The expression of the initial mass matrix is:

[0111] ;

[0112] in, x θ is the dimensionless distance from the center of mass to the elastic axis.

[0113] The expression of the time-varying stiffness matrix is:

[0114] ;

[0115] The expression of the matrix after the introduction of cross damping control is: ;

[0116] in, a is the dimensionless distance from the center of the chord to the elastic axis.

[0117] The control law is designed using a linear quadratic regulator (LQR) with the goal of minimizing the performance index and using an approximate or simplified method to solve the feedback gain matrix. Define the quadratic performance index:

[0118] .

[0119] Where Q is the state weight matrix, which penalizes state deviations, and R is the control input weight matrix, which penalizes control energy. Both are positive definite matrices. LQR (Low-Q Response) solves for the optimal feedback gain by balancing state deviations with control energy consumption. The weight matrices Q and R adjust the state convergence speed and control input amplitude, respectively. The feedback gain matrix K(t) is determined by solving the algebraic Riccati equation (ARE) to minimize J, at which point the closed-loop system is stable.

[0120] Since LQR control cannot handle time-varying aerodynamic forces, adaptive LQR control is used to compensate for the periodic variation of A(t), and A(t) is expressed as the sum of a constant term and a periodic term, that is:

[0121] ;

[0122] in, A 0 is the DC component of the aerodynamic coefficient, A 1 is the AC component of the aerodynamic coefficient.

[0123] Design feedback control input based on adaptive control law:

[0124] ;

[0125] Among them, K0 is a fixed gain matrix, which is determined by offline optimization; K1 is a time-varying gain matrix, which is updated online by the differential Riccati equation.

[0126] Design state weight matrix:

[0127] ;

[0128] Focus on pitch angle and heave displacement; control input weight matrix:

[0129] ;

[0130] Limits the cross damping gain.

[0131] design K 0 、K 1 makes:

[0132] A m = A 0 +BK 0, 0= A 1 +BK1

[0133] in A m is the desired stable reference model matrix.

[0134] Decompose the time-varying matrix and update the gain matrix online through the differential Riccati equation to compensate for periodic disturbances:

[0135] ;

[0136] Construct the residual function:

[0137] ;

[0138] If the residual F(P)≈0, the equation is balanced.

[0139] Using Newton-Kandrovitch iteration:

[0140] ;

[0141] Then iterate and optimize.

[0142] Initialize P by taking the solution of the static Riccati equation 0 .

[0143] In P (k) Linearize the differential Riccati equation: .

[0144] Solving linear equations , where the Jacobi operator It is a matrix composed of Kronecker products, reflecting the impact of small changes in P on the residual.

[0145] Calculating derivatives , which is a continuous-time Lyapunov equation and can be solved using the Bartels-Stewart algorithm. ,in, is the Riccati matrix correction.

[0146] renew , α is the step size.

[0147] when The iteration is terminated when , ensuring that the accuracy of P(t) reaches 10 -6 .

[0148] Solve in real time using numerical methods (such as iterative methods) to update the feedback gain matrix:

[0149] .

[0150] 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 along the system trajectory to ensure the stability of the closed-loop system. If not, return to adjust the control parameters.

[0151] Computes the time derivative of a Lyapunov function.

[0152] Define state error:

[0153] e =XX m；

[0154] Where e is the actual system state vector X and the reference model state vector X m The difference, X m It is obtained from the ideal closed-loop dynamic equation.

[0155] Construct the Lyapunov function:

[0156] ;

[0157] Where e is the state error, P(t) is the solution to 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.

[0158] Adaptive learning rate matrix:

[0159] ;

[0160] γ is the maximum learning rate, γ>0, when When it is much larger than 1, Г also becomes larger, and the maximum learning rate accelerates convergence; when When it is much smaller than 1, Г also becomes smaller and the parameters converge quickly.

[0161] calculate Substitute into the system equation and prove: .

[0162] According to Lyapunov stability theorem, the adaptive law: .

[0163] pass Ensure that the closed-loop system is stable.

[0164] Step D: numerical simulation and performance verification;

[0165] The wind conditions exceeding the critical flutter speed are selected as the design parameters, and the simulation parameters are set using the parameters in Table 1 for numerical experiments:

[0166] The blade motion equations need to be solved numerically. The Euler method has large errors, so the fourth-order Runge-Kutta method is used to solve the closed-loop system equations. The iterative steps are as follows:

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] .

[0172] Set the time step to 0.001 seconds to ensure computational accuracy (ε = 1e-3). Set the system initial state and solve the differential equation in the time interval [0, 15] seconds to obtain the state response.

[0173] The feedback gain matrix is ​​obtained through LQR design and the closed-loop system characteristics are analyzed.

[0174] The stability of the closed-loop system is verified by eigenvalue analysis to ensure that the real parts of all eigenvalues ​​are negative.

[0175] The simulation results in a specific expression for the feedback gain matrix K(t). Based on this specific expression for K(t), the cross-damping coefficient can be derived. Applying the cross-damping coefficient to offshore wind turbine blades can clearly demonstrate rapid suppression of offshore blade flutter. The open-loop system's heave displacement and pitch angle diverge over time, indicating system instability when uncontrolled. By adjusting the cross-damping, the closed-loop system's heave displacement and pitch angle rapidly converge to a steady state within 4 seconds, with the real parts of the eigenvalues ​​all negative, demonstrating stability. This demonstrates that the method of the present invention effectively suppresses aeroelastic flutter in offshore wind turbine blades, ensuring safe blade operation.

[0176] The present invention will be further described below with reference to specific embodiments.

[0177] Step 1: Establish a second-order dynamic model with cross damping terms

[0178] The blade is simplified into a two-dimensional airfoil model, whose motion equation consists of the heave and pitch degrees of freedom:

[0179] ;

[0180] Introduce cross damping terms: Add non-diagonal terms to the damping matrix to form a coupled damping matrix: ;

[0181] The mechanism of cross damping is: c 21 represents the contribution of pitch velocity to heave damping, c 12 represents the contribution of the heave velocity to the pitch damping;

[0182] Time-varying aerodynamic modeling: Considering the periodic changes in aerodynamic coefficients caused by blade rotation, the lift coefficient and moment coefficient are expressed as:

[0183] .

[0184] Step 2: State-space equation transformation

[0185] Define the state vector , convert the second-order dynamics equation into state space form:

[0186] ;

[0187] Among them, the system matrix and input matrix are:

[0188] ;

[0189] .

[0190] Step 3: Adaptive control law design

[0191] Decompose the system matrix into constant and time-varying components ;

[0192] Design the adaptive feedback control input as: ;

[0193] Solve the differential Riccati equation and update the gain matrix by solving the following equation online:

[0194] , where Q and R are weight matrices, which adjust the state convergence speed and control energy consumption respectively.

[0195] Step 4: Proof of Closed-Loop System Stability

[0196] Construct the Lyapunov function: ;

[0197] 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; by derivation, we can get Ensure the global asymptotic stability of the closed-loop system.

[0198] Step 5: Numerical simulation and result analysis

[0199] The fourth-order Runge-Kutta method is used to perform numerical integration on the closed-loop system. The simulation parameters are shown in Table 1:

[0200] Table 1 Simulation parameters

[0201]

[0202] Dynamic response simulation:

[0203] Initial conditions: h(0)=0.1m, θ(0)=10°, h'(0)=0, θ'(0)=0;

[0204] Time range: t∈[0,15]s;

[0205] Calculate the initial LQR feedback gains: K1=0.56, K2=0.33;

[0206] Calculate the eigenvalues ​​of the closed-loop system at the initial time: λ 1 = -1.581±18.041j, λ 2 = -1.363±11.858j. The real parts are all negative, indicating that the system is stable;

[0207] Response curve and result analysis: Figures 3 to 6 As shown in the figure, the displacement decays rapidly from 0.1m to 0m, with a convergence time of about 4 seconds, and the steady-state error approaches zero. The initial angle converges from 10 degrees to the equilibrium position of 0 degrees with no overshoot, and the convergence time is about 4 seconds.

[0208] The present invention uses cross damping control to dynamically adjust the cross damping coefficient inside the blade ( c 12 , c 21 ) achieves active control of modal energy and updates the feedback gain matrix K(t) online by solving the differential Riccati equation to accurately compensate for time-varying aerodynamic forces at sea. Lyapunov theory and eigenvalue verification ensure closed-loop stability, and ultimately output dynamically optimized cross-damping coefficient instructions, enabling rapid convergence of blade displacement and pitch angle after encountering disturbances, thereby achieving rapid suppression of offshore wind turbine blade flutter. Compared to traditional methods, this solution offers advantages such as simple structure, fast response, and excellent stability. At a wind speed of 8 m / s, it can shorten the vibration convergence time to within 4 seconds, with steady-state error approaching zero, providing reliable protection for the safe operation of large offshore wind turbines.

[0209] The foregoing description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are readily apparent to those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

[0210] Although the above describes the specific implementation methods of the present invention, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for suppressing flutter of offshore wind turbine blades with adaptive cross damping, characterized by: Controllable distributed piezoelectric sheets are embedded in key locations inside wind turbine blades, including the heave motion sensitive area and the pitch motion actuation area, and include the following processes: S1, based on the two-dimensional airfoil model, combined with the physical parameters of the blade section and the offshore wind parameters, establishes the second-order dynamic equations for the blade's heave and pitch motions, including the mass matrix, stiffness matrix, and damping matrix. Non-diagonal cross damping is introduced into the damping matrix for reconstruction to obtain the coupled damping matrix. The aerodynamic coefficients are dynamically updated to generate the time-varying stiffness matrix and time-varying damping matrix. S2, based on the second-order dynamic equation in S1, combined with the mass matrix, time-varying stiffness matrix and time-varying damping matrix, converts the system into a state space form to obtain the state space equation. According to the time-varying system matrix and input matrix in the state space equation, an adaptive feedback control law is designed. The adaptive feedback control law is composed of a state vector and a feedback gain matrix. The system matrix and input matrix are brought into the Riccati equation for solution to obtain a feedback gain matrix. This matrix is ​​used to generate a control input to drive the piezoelectric piece to adjust the cross damping coefficient through voltage. S3, construct a Lyapunov function that includes the blade state energy and the gain error energy, calculate the time derivative of the Lyapunov function under the adaptive feedback control law designed in S2, and verify whether the derivative of the Lyapunov function is negative definite; S4, performs conditional judgment. If the time derivative of the Lyapunov function output by S3 is negative along the system trajectory, it means that the system is stable. The cross damping coefficient is obtained based on the feedback gain matrix expression and applied to the offshore wind turbine blades. 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, and output the corresponding cross damping coefficient.

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

3. The method for suppressing flutter of offshore wind turbine blades with adaptive cross damping according to claim 1, characterized in that: The specific process of S1 includes: S11, based on the two-dimensional airfoil model, defines the second-order dynamic equations for heaving and pitching motions as: ； in, θ is the pitch angle, M ( t ) is the aerodynamic moment, which is related to the lift distribution and blade geometry parameters; m is the blade cross-sectional mass, I θ is the pitching moment of inertia 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 torque; S12, introduces the cross damping coefficient, and introduces the cross damping term into the non-diagonal term of the damping matrix of S11 c 21 、 c 12 , reconstruct the damping matrix to form the coupled damping matrix: ； in, c 21 、 c 12 is the cross damping coefficient, which represents the contribution of pitching velocity to heaving damping and the contribution of heaving velocity to pitching damping respectively; S13, calculate the unsteady aerodynamic force caused by the offshore wind field in S11 L ( t ) and aerodynamic torque M ( t ): ； ； in, ρ is Air density, U is the wind speed, ω is the blade rotation angular frequency; a is the dimensionless distance from the center of the chord to the elastic axis, b is half the chord length; S14, the unsteady aerodynamic force in S13 L ( t ) and aerodynamic torque M ( t ) in the aerodynamic lift coefficient C l, θ and aerodynamic moment coefficient C m, θ Modeled as a periodic time-varying function, specifically: ； ； in, 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 mean aerodynamic moment coefficient, C l, θ is the fluctuation amplitude of the aerodynamic lift coefficient, C m, θ is the fluctuation amplitude of the aerodynamic moment coefficient, ω is the blade rotation angular frequency; S15, based on blade physical parameters and time-varying aerodynamic coefficients C l, θ 、 C m, θ , combining steps S11-S14, construct the time-varying stiffness matrix K0(t) and the time-varying damping matrix C0(t) including the cross damping term; 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: ; in, a is the dimensionless distance from the center of the chord to the elastic axis.

4. The method for suppressing flutter of offshore wind turbine blades with adaptive cross damping 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, the time-varying stiffness matrix K0(t) and the time-varying damping matrix C0(t) containing the non-diagonal cross damping terms, the second-order dynamic equation is converted into a matrix form: ； in, F aero Unsteady aerodynamic force L ( t ) and aerodynamic torque M ( t ) is the aerodynamic matrix, which is expressed as: ； Define the state vector as: ； in, h is the displacement of the blade, θ is the pitch angle of the blade, converting the system equation into state space form, then 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 the time-varying system matrix, and the input matrix B is a constant matrix; S22, based on the state space equation of S21, decomposes 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, designs the adaptive feedback control rate u (t), the control input is: ； Where K0 is the fixed gain matrix, K1 is the time-varying adaptive gain matrix, and K(t) is obtained by solving the differential Riccati equation; S24, updating the feedback gain matrix K(t) in step S23 online by solving the differential Riccati equation.

5. The method for suppressing flutter of offshore wind turbine blades with adaptive cross damping according to claim 4, characterized in that: In S24, the differential Riccati equation is: ； Among them, 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 Newton iteration method is used to solve the differential Riccati equation in real time online to obtain the time-varying matrix P(t). P(t) is the solution of the differential Riccati equation; and the adaptive feedback gain matrix is ​​obtained by numerical method: ； K(t) is the obtained adaptive feedback gain matrix.

6. The method for suppressing flutter of offshore wind turbine blades with adaptive cross damping according to claim 4, characterized in that: The specific process of S3 is as follows: The specific process of S3 is as follows: The stability of the closed-loop system is proved using Lyapunov stability theory. Based on the designed adaptive feedback control law and the output current moment feedback gain matrix K(t), a Lyapunov function containing the blade state energy and gain error energy is constructed: ； 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; Evaluate this function and substitute it into the system of equations to show that: ； Check that the time derivative of the Lyapunov function is negative along the system trajectory, that is: ； Is it correct? 7. The method for suppressing flutter of offshore wind turbine blades with adaptive cross damping according to claim 6, characterized in that: The step S4 returns to step S2 for adjustment, specifically including: Increase the weight elements corresponding to the pitch angle or heave displacement in the state weight matrix Q in the differential Riccati equation; reduce 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. Repeat this process until the time derivative of the constructed Lyapunov function is negative along the system trajectory to ensure the dynamic stability of the blade closed loop.

8. The method for suppressing flutter of offshore wind turbine blades with adaptive cross damping according to claim 1, characterized in that: The closed-loop system equation is constructed based on the feedback gain matrix output by S2: ； The fourth-order Runge-Kutta method is used to numerically integrate the closed-loop system differential equations. By updating the aerodynamic coefficients, the system matrix A(t), the feedback gain matrix K(t) and the closed-loop system equations, real-time simulation of the entire adaptive control loop is achieved. The specific expression of the gain matrix K(t) is obtained by simulation, and the cross-damping coefficient is obtained based on the specific expression of K(t). The cross-damping coefficient corresponds to the first row and fourth column and the second row and third column of K(t), respectively.

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