Finite-time air-gap synchronization control method for a wind turbine nacelle suspension system

Abstract

The present invention relates to a finite-time air-gap synchronous control method for a wind turbine nacelle suspension system. It analyzes the time-varying wind disturbance characteristics suffered by the wind turbine nacelle suspension system, constructs a suspension model with two degrees of freedom for the pitch and axial directions of the wind turbine nacelle, designs a fast terminal sliding mode suspension air-gap tracking controller to achieve the global finite-time convergence of the tracking error of the wind turbine nacelle suspension system with a relatively small suspension air-gap tracking error (much less than 1); designs a fractional-order adaptive controller with terminal sliding mode convergence characteristics to achieve fast and accurate estimation of the singular term of the fast terminal sliding mode, external time-varying disturbances, and unknown system parameters; designs a finite-time state observer to achieve real-time observation of differential signals that are difficult to obtain; the present invention improves the suspension stability and interference suppression ability of the wind turbine nacelle suspension system, ensures the optimal air-gap synchronous performance throughout the operation process, and comprehensively improves the transient performance of the wind turbine nacelle suspension synchronization.

Description

Technical Field

[0001] The present invention relates to a control method, in particular to a finite-time air-gap synchronization control method for a wind turbine nacelle suspension system, belonging to the technical field of electrical engineering. Background Art

[0002] In the actual working environment, the wind turbine nacelle suspension system is affected by wind disturbances whose magnitude and direction often change. In such a harsh environment, for this unstable system of a maglev wind turbine nacelle, the front and rear ends are easily affected by pitching moments and become unstable, and may even fall, resulting in serious disaster accidents.

[0003] Regarding the research on the problem of multi-variable synchronization control of the air-gap synchronization of the wind turbine nacelle suspension system, some adopt SMC control, which can achieve suspension under a constant reference air-gap, but there is no more detailed research on the synchronization problem; some design a sliding mode disturbance observer, and the synchronization effect is obvious, but the observation speed of the disturbance is slow, affecting the dynamic performance of the system; some adopt a method combining cross-coupling and SMC to achieve multi-point synchronization; some design a synchronous error PD tracking controller based on the synchronous error of a multi-axis system, effectively improving the tracking and synchronization performance of the multi-axis motion system; some achieve the motion synchronization of the front and rear systems through the control of the virtual main system and sub-system, improving the anti-disturbance ability and riding comfort; some propose a method including inverse system compensation, virtual suspension control, and hybrid decoupling control to effectively cope with pitching interference and the stability of suspension, achieving good tracking and synchronization effects; some design a distributed adaptive controller for the uncertainties in the system, effectively solving the synchronization problem of non-linear multi-agent systems; some design an adaptive robust controller with synchronous compensation, effectively solving the stable suspension of the nacelle and pitching suppression.

[0004] However, it is worth pointing out that the existing research on the air-gap synchronization problem of the wind turbine nacelle suspension system almost only focuses on the air-gap synchronization problem in the steady state stage, without overly emphasizing the transient performance of the synchronization control, and it is difficult to ensure the optimal comprehensive performance of the entire parallel system. In fact, the transient performance of the synchronization control has a more serious impact on the stability of the suspension and cannot be ignored. Summary of the Invention

[0005] The main objective of the present invention is: aiming at the deficiencies and gaps in the existing technology, the present invention provides a finite-time air-gap synchronization control method for a wind turbine nacelle suspension system. A fast terminal sliding mode controller is designed for a wind turbine nacelle suspension system with a relatively small suspension air-gap tracking error (much less than 1) to achieve global finite-time convergence of the tracking error. For the singular term of the fast terminal sliding mode, external time-varying disturbances, and unknown system parameters, a fractional-order adaptive accurate estimation with the convergence characteristics of the terminal sliding mode is designed. For the differential signal that is difficult to obtain, a finite-time state observer is designed to observe the system state in real time, so as to comprehensively improve the transient performance of the wind turbine nacelle suspension, enhance the suspension stability and interference suppression ability of the wind turbine nacelle suspension system, and ensure the optimal air-gap synchronization performance throughout the operation process.

[0006] To achieve the above objectives, a finite-time air-gap synchronization control method for a wind turbine nacelle suspension system of the present invention includes the following steps:

[0007] Step 1, analyze the time-varying wind disturbance characteristics suffered by the wind turbine nacelle suspension system;

[0008] Step 2, construct a two-degree-of-freedom linearized suspension model for pitch and axial directions of the wind turbine nacelle for finite-time control;

[0009] Step 3, design a parameter adaptive nacelle global finite-time terminal sliding mode tracking controller with singularity elimination;

[0010] Step 4, design a fractional-order adaptive law for axial and pitch uncertain disturbances in the finite-time air-gap synchronization controller;

[0011] Step 5, design a finite-time state observer for the pitch angle differential signal in the finite-time air-gap synchronization controller.

[0012] The analysis of the time-varying wind disturbance characteristics suffered by the wind turbine nacelle suspension system in the said Step 1 is as follows:

[0013] Based on the boundary element theory of the "momentum theory" and the "blade element theory", analyze and calculate the aerodynamic loads on the wind turbine blades, and the pitching moment M acting on the wind turbine can be obtained p 、axial moment M y :

[0014]

[0015] where i is the i-th blade, i = 1, 2, 3, M p 、M y are the pitching moment and the axial moment, v fli is the relative wind speed acting on the i-th blade, β i is the pitch angle of the i-th blade, ρ is the air density, C is the chord length of the blade element, W is the incoming flow velocity, CL , C D is the lift - drag coefficient of the airfoil, φ is the angle between the relative flow velocity and the blade chord length, L0 is the equivalent blade radius, ψ i is the azimuth angle of the ith blade, i = 1, 2, 3.

[0016] The two - degree - of - freedom linearized suspension model of the wind turbine nacelle for finite - time control in step 2 is constructed as

[0017]

[0018] where θ is the pitch angle, μ0 is the vacuum permeability, N is the number of turns of the suspension windings on both sides, S is the pole area, i A , i B are the currents on both sides respectively, δ1 and δ2 are the front - and - rear suspension air - gaps respectively, J is the pitch moment of inertia of the nacelle, m is the mass of the wind turbine nacelle; g is the acceleration due to gravity; δ is the suspension height; f d is the axial disturbance of the nacelle; T r is the pitch moment of the nacelle, R is the rotor radius;

[0019] Linearize the two - degree - of - freedom suspension model of the wind turbine nacelle for pitch and axial directions:

[0020]

[0021] where, is the system parameter, i0 is the current reference value, δ0 is the air - gap reference value, h A , h B are the suspension heights on both sides respectively, k is the system parameter, Δf1, Δf2 are the high - order terms of the Taylor expansion.

[0022] The design of the parameter - adaptive nacelle global finite - time terminal - sliding - mode tracking controller with singularity elimination in step 3 is as follows,

[0023] First step, according to the linearized model, design the suspension air - gap tracking controllers for axial and pitch directions respectively, and then calculate the current reference values of the inner loop through the current reference distribution mechanism. First, take the pitch controller as an example. Let the pitch - angle tracking error e4 = θ ref - θ, the derivative of the tracking error Design the fast terminal - sliding - mode surface:

[0024]

[0025] where e4 is the tracking error, s4 is the fast terminal - sliding - mode surface, 0 < r < 1, α > 0, β > 0 are adjustable parameters, θ ref is the reference pitch angle, θ is the pitch angle;

[0026] In the second step, taking the first derivative of Equation (4) gives:

[0027]

[0028] where Δu = i A -i B , and T r is the pitch interference;

[0029] In the third step, ignoring the lumped interference T r of the maglev system and setting the derivative of the sliding mode surface to zero gives the equivalent control law u eq as follows:

[0030]

[0031] In the fourth step, for the sign term in the traditional constant-speed reaching law, the severe chattering seriously affects the non-stable maglev system. The reaching law in the form of the terminal sliding mode is used to replace it, and the fast terminal sliding mode control law is designed as follows:

[0032]

[0033]

[0034] where u is the output of the fast terminal sliding mode controller, u eq is the equivalent control law, u sw is the reaching control law, τ > 0, υ > 0 are adjustable parameters; ΔJ, ΔR, Δk h , Δm are the offsets of the system parameters; J0, R0, m0 are the reference values of the system parameters; is the upper bound of the parameter uncertainty, Φ = J / k i is the system parameter, is the coefficient that generates singularity; ξ is the uncertain system parameter;

[0035] For the situation in Equation (7) where e4 = 0 but r - 1 < 0 generates a singularity problem, a virtual variable is defined, and the adaptive law for the adaptive control of the singularity controller parameters is designed as:

[0036]

[0037] where y p is the defined virtual variable, η1, η2 > 0 are adjustable parameters, p0, q0 > 0, 0 < p0 / q0 < 1 are adjustable parameters, η1, η2 > 0 are adjustable parameters, are positive control parameters respectively.

[0038] In the step 4, the fractional - order adaptive laws for the axial and pitch uncertain disturbances in the finite - time air - gap synchronous controller are designed as

[0039]

[0040] where are the estimated values of ξ and T respectively r ; are the first - order derivatives of the estimated values of ξ and T respectively r ; are positive control parameters respectively

[0041] In the step 5, the finite - time state observer for the pitch - angle differential signal in the finite - time air - gap synchronous controller is designed as

[0042]

[0043] where are the observed values of the pitch angle, pitch - angle derivative and pitch disturbance respectively; c1, c2, c3 > 0 are adjustable controller parameters; A, B are system parameters

[0044] Finally, the finite - time air - gap synchronous controller integrating fractional - order adaptation and finite - time state observer is designed as:

[0045]

[0046] Similarly, the control output of the axial controller is:

[0047]

[0048] where u′ is the output of the axial controller; e5 is the suspension - height tracking error; Φ B is a system parameter are the estimated values of the axial uncertain - system parameter ξ′, the coefficient χ′ that generates singularity and the axial disturbance f d respectively

[0049] The beneficial effects of the present invention are:

[0050] 1) A finite - time air - gap synchronous control method for a wind - turbine nacelle suspension system is proposed to ensure that the nacelle can achieve stable suspension and effectively suppress pitch and axial disturbances, comprehensively improving the transient performance of the system

[0051] 2) An adaptive control of the fast terminal sliding mode singular term coefficient for a wind turbine nacelle suspension system with relatively small suspension air gap tracking error (much less than 1) is designed. While avoiding the influence of chattering of the non-singular terminal sliding mode surface on the system, it realizes the globally finite-time convergence of the tracking error, greatly improving the nacelle suspension performance;

[0052] 3) A fractional-order adaptive control for external time-varying disturbances and uncertain system parameters is designed, which can quickly and accurately estimate them within a finite time, improving the anti-interference ability of the system;

[0053] 4) A finite-time state observer is designed to realize the real-time observation of differential signals that are difficult to obtain, reducing the influence of noise interference on the system stability. Description of the Drawings

[0054] Appendix Figure 1 It is a schematic diagram of the wind turbine nacelle suspension system of the present invention.

[0055] Appendix Figure 2 It is a comparison diagram of the suspension air gap tracking performance under variable reference conditions of the present invention.

[0056] Appendix Figure 3 It is a comparison diagram of the suspension air gap tracking under the AC pitch interference condition of the present invention.

[0057] In the figure: 1 - wind turbine blade, 2 - wind turbine nacelle, 3 - yaw stator, 4 - front side winding, 5 - rear side winding, 6 - tower. Detailed Embodiment

[0058] The present invention will be further described in detail below with reference to the drawings.

[0059] The parameters of the wind turbine nacelle suspension system are as follows: the suspension weight of the nacelle is 484 kg, the total number of turns of the suspension winding is 930 turns, the number of turns of the front and rear side windings is 465 turns, the rotation radius of the nacelle is 350 mm, the power of each of the two suspension converters is 1 kW, and the suspension air gap sensor uses an eddy current displacement sensor with an accuracy of 0.27 v / mm. Variable air gap tracking experiments and AC pitch moment application experiments are respectively carried out to illustrate the effective effect of the present invention.

[0060] For the variable air gap tracking experiment, the reference air gap is 13 mm from t = 0 to 4 s, 13.5 mm from t = 4 to 15 s, and 13 mm from t = 15 to 20 s. The ripples of the suspension air gap of the traditional PID controller are 0.0125 mm, 0.006 mm, and 0.007 mm respectively, and the ripples of the suspension air gap of the present invention are 0.004 mm, 0.0035 mm, and 0.004 mm respectively. The detailed performance comparison is shown in Table 1.

[0061] Table 1 Comparison Table of Suspension Synchronization Performance

[0062]

[0063] Attached Figure 2 Comparison chart of the suspension air-gap tracking performance. During the start-up stage, the variable air-gap stage at t = 4 s, and the air-gap return stage at t = 15 s, the suspension air-gap tracking effects of the traditional PID control, the RBF interference compensation control, and the decoupling control under the model reference RBF are slower in convergence speed compared with the present invention; the maximum air-gap overshoots of the traditional PID controller are 0.117 mm, 0.36 mm, and 0.25 mm respectively, and the maximum air-gap overshoots of the present invention are 0.112 mm, 0.18 mm, and 0.2 mm respectively; the convergence times of the suspension air-gap of the RBF interference compensation control are 0.43 s, 0.37 s, and 0.44 s respectively, the convergence times of the suspension air-gap of the decoupling control under the model reference RBF are 0.2 s, 0.2 s, and 0.18 s respectively, and the convergence times of the suspension air-gap of the present invention are 0.12 s, 0.15 s, and 0.1 s respectively; when the present invention tracks the variable reference air-gap, it has a faster settling time and a smaller overshoot, verifying that the present invention has a strong air-gap tracking ability and good transient performance. The detailed performance comparison is shown in Table 2.

[0064] Table 2 Comparison table of suspension tracking performance

[0065]

[0066] AC pitch moment application experiment. The initial suspension height of the wind turbine nacelle is 13 mm. At t = 4 s, a downward pressure interference of T r = 800 + 500sin(2πt) N / m is applied to the tail wing side to simulate the pitch moment generated by the external time-varying wind disturbance on the wind turbine nacelle, and the downward pressure interference is removed at t = 15. Attached Figure 3Comparison chart of the floating air-gap tracking performance. Compared with Strategy 1, Strategy 2, Strategy 3, and TT-PID-AC control, the present invention has obvious advantages when facing time-varying pitch disturbances. The convergence speed in the start-up stage is fast and the maximum air-gap drop value is small, which ensures that the fan can operate stably in suspension quickly when facing complex working conditions. When applying disturbances, the synchronization error of Strategy 1 is 0.079 mm and the tracking error is 0.0125 mm; the synchronization error of Strategy 2 is 0.08 mm and the tracking error is 0.0132 mm; the synchronization error of Strategy 3 is 0.079 mm and the tracking error is 0.7 mm; the synchronization error of TT-PID-AC is 0.118 mm and the tracking error is 0.5 mm; the synchronization error of the present invention is 0.059 mm and the tracking error is 0.009 mm. When applying periodic pitch disturbances, the synchronization error of Strategy 1 is 0.01 mm, the synchronization error of Strategy 2 is 0.02 mm, the synchronization error of Strategy 3 is 0.028 mm, the synchronization error of TT-PID-AC is 0.032 mm, and the synchronization error of the present invention is 0.005 mm, verifying that the present invention has stronger advantages in the face of complex and changeable actual working conditions. The detailed performance comparison is shown in Table 3 below.

[0067] Table 3 Comparison table of the synchronization performance of the nacelle against AC pitch disturbances

[0068]

Claims

1. A finite-time air-gap synchronization control method for a wind turbine nacelle suspension system, characterized in that: Including the following steps: Step 1, analyze the time-varying wind disturbance characteristics suffered by the wind turbine nacelle suspension system The boundary element theory based on the "momentum theory" and the "blade element theory" analyzes and calculates the aerodynamic loads on the wind turbine blades, and the pitching moment M acting on the wind turbine can be obtained. p , the axial moment M y : where i is the i-th blade, i = 1, 2, 3, …, M p , …, M y are the pitching moment and the axial moment, v fli is the relative wind speed acting on the i-th blade, β i is the pitch angle of the i-th blade, ρ is the air density, C is the chord length of the blade element, W is the oncoming flow velocity, C L , C D is the lift-drag coefficient of the airfoil, φ is the angle between the relative flow velocity and the blade chord length, L0 is the equivalent blade radius, ψ i is the azimuth angle of the i-th blade, i = 1, 2, 3; Step 2, construct a two-degree-of-freedom linearized suspension model for the pitch and axial directions of the wind turbine nacelle for finite-time control as where θ is the pitch angle, μ0 is the magnetic permeability of vacuum, N is the number of turns of the suspension windings on both sides, S is the pole area, i A and i B are the currents on both sides respectively, δ1 and δ2 are the front and rear suspension air gaps respectively, J is the pitch moment of inertia of the nacelle, m is the mass of the wind turbine nacelle, g is the acceleration due to gravity, δ is the suspension height, f d is the axial interference of the nacelle, T r is the pitch moment of the nacelle, and R is the radius of the rotor; Linearize the two-degree-of-freedom suspension model of the pitch and axial directions of the wind turbine nacelle: Among them, is a system parameter, i0 is the current reference value, δ0 is the air gap reference value, h A , h B are the suspension heights on both sides respectively, k is a system parameter, and Δf1 and Δf2 are the high-order terms of the Taylor expansion respectively; Step 3, design a parameter adaptive nacelle global finite-time terminal sliding mode tracking controller with singularity elimination Step 1: According to the linearized model, design the suspension air-gap tracking controllers for axial and pitch respectively, and then calculate the current reference values of the inner loop through the current reference distribution mechanism. First, take the pitch controller as an example. Let the pitch angle tracking error be e4 = θ ref -θ, the derivative of the tracking error Design the fast terminal sliding mode surface: Among them, e4 is the tracking error, s4 is the fast terminal sliding mode surface, 0 < r < 1, α > 0, β > 0 are adjustable parameters, θ ref is the reference pitch angle, and θ is the pitch angle; Second step, taking the first derivative of Equation (4) gives: where, Δu = i A -i B , T r is the pitch interference; Step 3: Ignore the lumped disturbance T of the maglev system r , and let the derivative of the sliding mode surface be zero to obtain the equivalent control law u of the system eq as follows: Step 4. For the sign term in the traditional constant velocity reaching law, which seriously affects the instability of the maglev system, a reaching law in the form of terminal sliding mode is used to replace it, and the fast terminal sliding mode control law is designed as follows: ​ where \(u\) is the output of the fast terminal sliding mode controller, \(u\) eq is the equivalent control law, \(u\) sw is the reaching control law, \(\tau>0,\upsilon>0\) are adjustable parameters, \(\Delta J\), \(\Delta R\), \(\Delta k\) h , \(\Delta m\) are the offsets of the system parameters, \(J_0\), \(R_0\), \(m_0\) are the reference values of the system parameters, is the upper bound of the parameter uncertainty, \(\varPhi = J / k\) i is the system parameter, is the coefficient that generates singularity, \(\xi\) is the uncertain system parameter; For the formula (7), there exists e4 = 0, but r - 1 < 0 causes a singularity problem. Define a virtual variable The adaptive law for adapting the singularity controller parameters is designed as follows: where y p is a defined dummy variable, η1, η2 > 0 are adjustable parameters, p0, q0 > 0, 0 < p0 / q0 < 1 are adjustable parameters, η1, η2 > 0 are adjustable parameters, are positive control parameters respectively; Step 4, design the fractional-order adaptive law for the axial and pitch uncertain disturbances in the finite-time air gap synchronization controller as Among them, are the estimated values of ξ and T respectively, r and are the first-order derivatives of the estimated values of ξ and T respectively, r and are positive control parameters respectively; Step 5, design a finite-time state observer for the pitch angle differential signal in the finite-time air gap synchronization controller where, are the observed values of pitch angle, pitch angle derivative, and pitch disturbance respectively, c1, c2, c3 > 0 are adjustable controller parameters, and A, B are system parameters; Finally, the finite-time air gap synchronization controller integrating the fractional-order adaptive and finite-time state observer is designed as: Similarly, the control output of the axial controller can be obtained as: where u′ is the output of the axial controller, e5 is the suspension height tracking error, and Φ B is the system parameter, which are the estimated values of the axial uncertain system parameter ξ′, the coefficient χ′ that generates singularity, and the estimated value of the axial disturbance f d respectively.

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