A method for tracking a specified time and a specified performance of a wind power generator in a variable speed mode

Abstract

The application discloses a tracking control method for specified time and specified performance of a wind driven generator under variable speed mode, comprising: establishing a dynamic double-mass block drive dynamics model of the wind driven generator under variable speed mode; converting the dynamic double-mass block drive dynamics model into an equivalent mathematical model; adopting a backstepping method for the equivalent mathematical model to complete the design of an actual controller; performing stability analysis on a closed loop system formed by the equivalent mathematical model of the wind driven generator under variable speed mode and the designed actual controller; and giving a tracking control semi-physical simulation experiment for specified time and specified performance of the wind driven generator under variable speed mode. The application can model the wind driven generator under variable speed mode, realize tracking control of the wind driven generator under variable speed mode within specified time, ensure no overshoot tracking response of the wind driven generator during operation, and improve the safety, reliability and steering stability of the wind driven generator operation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wind turbine control, and relates to a specified time and specified performance tracking control method for a wind turbine in variable speed mode. BACKGROUND

[0002] As a key device for capturing wind energy, wind turbines play a key role in reducing the use of fossil fuels. Notably, wind turbines have a serious dependence on meteorological conditions, are structurally large, and operate in a harsh and complex environment. Today, modern wind turbines are usually operated in variable speed mode, which enables the wind turbine to operate at the best aerodynamic efficiency for as long as possible and withstand smaller power fluctuations and operating loads than in constant speed mode.

[0003] Wind turbines operating in variable speed mode have more complex structural, dynamic and environmental characteristics than wind turbines operating in constant speed mode, and their main features include a large operating range, complex system dynamics, and more components, thus having strong nonlinear characteristics. These factors make the modeling and control of wind turbines extremely scientific and challenging. When a wind turbine operates in variable speed mode, there are multiple control levels. At the highest control level, the supervisory control system detects the rotor speed and wind speed of the turbine to determine when to start the turbine and when to stop the turbine due to excessively high wind speed to ensure safety; the middle layer control is turbine control, including generator torque control, pitch control and yaw control. Internal engines, power electronics and pitch actuator controllers are at the lowest control level.

[0004] Currently, for wind turbines operating in variable speed mode, researchers have carried out a series of modeling, regulation and control work, including: robust nonlinear control without wind speed measurement, noise suppression, wind turbine control based on adaptive fuzzy logic, finite time control of wind turbines operating in variable speed mode. However, due to the inherent limitations and deficiencies of traditional finite time stability theory, existing finite time tracking control techniques need to rely on the accurate initial state of the wind turbine to estimate the convergence time. In fact, wind turbines usually operate in a noisy environment, so it is difficult to obtain accurate initial states, which will have a significant negative impact on the control effect of the wind turbine, so it cannot meet the control requirements well. In addition, existing tracking control techniques cannot monitor the transient behavior of wind turbine output, including the constraints on rotor speed during tracking and the overshoot response of rotor speed tracking error, which leads to the inability to guarantee the safety and maneuvering stability of wind turbine operation. SUMMARY

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a tracking control method for a wind turbine in variable speed mode at a specified time and with a specified performance. This method can model the complex dynamics of the wind turbine in variable speed mode, realize the tracking control of the wind turbine in variable speed mode at a specified time without requiring a precise initial state, ensure that the rotor speed of the wind turbine is subject to time-varying constraints and that there is no overshoot in the rotor speed tracking error during operation, and improve the safety, reliability and operational stability of the wind turbine.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution.

[0007] A tracking control method for a wind turbine generator in variable speed mode for a specified time and specified performance includes the following steps:

[0008] Step 1: First, establish the wind energy model and electrical energy model of the wind turbine in variable speed mode, and then obtain the wind energy model, electrical energy model, and rotor torque T. a The relationship between them; by using the wind energy model and electrical energy model of the wind turbine in variable speed mode, and with the help of the dual-mass block drive model of the wind turbine in variable speed mode, a dynamic dual-mass block drive dynamic model of the wind turbine in variable speed mode is established.

[0009] Step 2: By subtracting the high-speed shaft rotor angle and the low-speed shaft rotor angle and introducing a clever coordinate transformation, the dynamic dual-mass block drive dynamics model of the wind turbine in variable speed mode is transformed into an easily controllable dual-mass block drive equivalent mathematical model.

[0010] Step 3: For the dual-mass block drive equivalent mathematical model of the wind turbine under the established variable speed mode, the actual controller is designed by using the back-reasoning method, the piecewise continuous time scale function related to the specified time and the time-varying barrier Lyapunov function, and designing virtual control signals and actual control signals, thereby forming the corresponding closed-loop system.

[0011] Step 4: For the closed-loop system formed by the dual-mass block driven equivalent mathematical model of the wind turbine in variable speed mode and the actual controller designed in Step 3, a stability analysis is performed: Based on the Lyapunov function and the form of its derivative, using Lyapunov stability theory, it is first proven that the tracking error of the wind turbine rotor speed in variable speed mode converges to 0 within a specified time T and is always equal to 0 when the time is greater than or equal to T. Then, using L'Hopital's theorem and the forced convergence principle, it is proven that the controller u(t) is continuous at a specified time t = T, and further proven that the controller u(t) is continuous on the interval [0, +∞). Then, it is proved by contradiction that the rotor speed of the wind turbine in variable speed mode will not experience overshoot during the tracking of the ideal reference signal. Finally, the difference in rotor angle between the high and low speed shafts is directly calculated. the expression, to prove the boundedness on the interval [0, +∞).

[0012] Specifically, in the step 1:

[0013] The wind energy model of the wind turbine in variable speed mode is:

[0014]

[0015] The electric energy model of the wind turbine in variable speed mode is:

[0016]

[0017] where ρ represents the air density, r w represents the tip radius, v ω represents the wind speed, C p represents the power coefficient, which is a function of the pitch angle and the tip speed ratio , and ω is the rotor speed;

[0018] The model of the electric energy, the torque and the rotor speed generated by the wind turbine in variable speed mode is:

[0019]

[0020] The dynamic double mass block drive dynamics model of the wind turbine in variable speed mode is:

[0021]

[0022] where the mechanical torque T a (t) is the driving force, J r , J g , T ls (t), T hs (t), T g (t) respectively represent the rotor inertia, the generator inertia, the low-speed shaft torque, the high-speed shaft torque and the generator torque; b r , b g , C s , K s respectively represent the damping coefficient and the torsion coefficient, θ(t) represents the high-speed shaft angle, θ ls (t) represents the low-speed shaft angle, n g (t) represents the gear box reduction ratio, ω g (t) represents the high-speed shaft speed, w ls (t) represents the low-speed shaft speed.

[0023] Specifically, the process of the step 2 includes:

[0024] Step 2-1, Introduce a new high-low speed shaft rotor angle difference variable by differencing the high speed shaft rotor angle and the low speed shaft rotor angle The transformation simplifies the dynamic dual-mass drive dynamics model of the wind turbine in the variable speed mode given by equation (4) to:

[0025]

[0026]

[0027]

[0028] Step 2-2, Introduce a new coordinate transformation in combination with the geometric control method to further simplify the dynamic dual-mass drive dynamics model of the wind turbine in the variable speed mode, introduce the coordinate transformation as follows:

[0029]

[0030] In combination with equation (8), the dynamic dual-mass drive dynamics model (5)-(7) of the wind turbine in the variable speed mode is further simplified to:

[0031]

[0032] Define the control signal as: Define the output as: y = x1, where,

[0033] Step 2-3, Further introduce a new coordinate transformation in combination with the nonlinear system control method and control requirements to convert the dynamic dual-mass drive dynamics model of the wind turbine in the variable speed mode into an easy-to-control dual-mass drive equivalent mathematical model, introduce the coordinate transformation as follows:

[0034]

[0035] Where, Apply the coordinate transformation (10), the dynamic dual-mass drive dynamics model (9) of the wind turbine in the variable speed mode is equivalent to the following dual-mass drive equivalent mathematical model:

[0036]

[0037] Where,

[0038] Specifically, the process of the step 3 includes:

[0039] Step 3-1, two new error variables are introduced: error variable z1 is the difference between the output signal and the reference signal, and error variable z2 is the difference between the second state signal and the virtual control signal:

[0040]

[0041] Considering the relationship between the initial value of the wind turbine output and the initial value of the ideal reference signal in variable speed mode, two cases can be designed (1) If β1(0) < y(0)≤y d (0), then (2) If y d (0)≤y(0)<β2(0), α1, are continuous differentiable functions;

[0042] Step 3-2, combine the virtual control law designed in the above (1) or (2) two cases respectively Introduce a positive definite Lyapunov function V, design the actual controller, so that the derivative of the Lyapunov function V is negative, so as to realize the specified time and specified performance tracking control of the wind turbine in variable speed mode; Select the positive definite Lyapunov function as:

[0043]

[0044] Where, if β1(0) < y(0)≤y d (0), then If y d (0)≤y(0)<β2(0), then According to equations (16) and (18), the derivative of the Lyapunov function C is:

[0045]

[0046] Where, if β1(0) < y(0)≤y d (0), then If y d (0)≤y(0)<β2(0), then Next, the state feedback law is designed as:

[0047]

[0048] Where, γ2 is a normal number, therefore, the actual controller is:

[0049]

[0050] Where, Substituting (20) into (19), the derivative of Lyapunov function V satisfies:

[0051]

[0052] where, So far, the design of the actual controller for the tracking control of the specified time and specified performance of the wind turbine in variable speed mode is completed.

[0053] Specifically, in the following case in step 3, the process of designing is as follows:

[0054] (1) If the initial value of the wind turbine output is between the initial value of the lower bound of the output constraint β1(0) and the initial value of the ideal reference signal y d (0) tracked, i.e. β1(0) < y(0)≤ y d (0); introduce the difference variable δ1(t) = y d (t) - ω(t) of the ideal reference signal y d (t) tracked and the lower bound of the output constraint β1(t), further introduce the time-varying barrier Lyapunov function V1, and combine the backstepping method to design the virtual control law; the introduced time-varying barrier Lyapunov function is:

[0055]

[0056] where p≥1 is an integer; according to (11) and (12), the derivative of the time-varying barrier Lyapunov function V1 is:

[0057]

[0058] The virtual control law is designed as α1, and the expression is:

[0059]

[0060] where v, σ, and γ1 are normal numbers, and satisfy:

[0061]

[0062] Considering that the following formula is true:

[0063]

[0064] The derivative of the time-varying barrier Lyapunov function V1 satisfies:

[0065]

[0066] where,

[0067] Specifically, in the following case in the step 3, the virtual control law is designed as The process of the step 4 is as follows:

[0068] (2) If the initial value of the wind power generator output is between the upper initial value β2(0) of the output constraint and the initial value y d (0) of the ideal reference signal tracked, i.e. y d (0)≤y(0)<β2(0); introduce the difference variable δ2(t) of the ideal reference signal y d (t) tracked and the lower limit β2(t) of the output constraint, δ2(t)=ω(t)-y d (t), and further introduce the time-varying barrier Lyapunov function In combination with the backstepping method, the virtual control law is designed as The time-varying barrier Lyapunov function introduced is as follows:

[0069]

[0070] The virtual control law is designed as The expression of the virtual control law is as follows:

[0071]

[0072] Therefore, the derivative of the time-varying barrier Lyapunov function V1 satisfies:

[0073]

[0074] Wherein,

[0075] Specifically, the process of the step 4 includes:

[0076] Step 4-1, according to the form of the Lyapunov function and the derivative of the Lyapunov function, by using the Lyapunov stability theory, the tracking error of the rotor speed of the wind power generator in the variable speed mode is proved to converge to 0 within a specified time T by integrating the derivative of the Lyapunov function from 0 to t; if t∈[0,T), the following inequality holds:

[0077]

[0078] Integrating both sides of equation (23) from 0 to t, the following inequality can be obtained:

[0079]

[0080] Equation (24) shows that lim t→T -V(t)=0, i.e. the limit of the Lyapunov function V(t) when t tends to the time T is equal to 0; therefore,​ holds; according to equation (24) and the definition of, the following inequality holds:

[0081]

[0082] Therefore, according to the boundedness of δ1(yu) and δ2(yu) on the interval [0, T), it can be obtained that the limit of the tracking error z1(t) of the wind turbine rotor speed in the variable speed mode when t approaches the moment T is equal to 0;

[0083] Step 4-2, use the form of the Lyapunov function and the derivative of the Lyapunov function, and the tracking error of the wind turbine rotor speed in the variable speed mode converges to 0 within the specified time T, to prove that the tracking error z1(t) of the wind turbine rotor speed in the variable speed mode is always equal to 0 when the time is greater than or equal to T; if t ∈ [T, +∞), according to equation (22) and the following equation can be obtained:

[0084]

[0085] The above equation and the limit of the Lyapunov function V(t) when t approaches T - is equal to 0, making the Lyapunov function V(t) always equal to 0 when t ≥ T; therefore, according to the definition of the Lyapunov function, it is proved that for t ∈ [T, +∞), the tracking error z1(t) of the wind turbine rotor speed in the variable speed mode is identically equal to 0;

[0086] Step 4-3, use L'Hopital's rule and the squeezing principle, combined with the fact that the tracking error of the wind turbine rotor speed in the variable speed mode converges to 0 within the specified time T and is always equal to 0 when the time is greater than or equal to T, to prove that the controller u(t) is continuous at the specified moment t = T, and further prove that the controller u(t) is continuous on the interval [0, +∞); actually, according to equations (20) and (21), to prove the continuity of u(t) on the interval [0, +∞), it only needs to prove and the continuity on the interval [0, +∞);

[0087] Considering that σ > 2p, the following limit holds:

[0088]

[0089] Using the squeezing principle, the following limit holds:

[0090]

[0091] Through equations (14) and (17), the virtual control law can be obtained At time t = T is continuous; further, the continuity of the derivative of the virtual control law depends only on According to the L'Hopital's rule, the following holds:

[0092]

[0093] Using equations (25) and (26), the following limit holds:

[0094]

[0095] Therefore, the virtual control law is continuous differentiable at time t = T, the derivative of the virtual control law is continuous on the interval [0, +∞); according to the definition of the Lyapunov function V(t) and equation (24), the following holds: According to σ > 2 p , the following holds:

[0096]

[0097] This shows that z2(t) is continuous on the interval [0, +∞); further, according to equations (10) and (20), it can be proved that the controller u(t) is continuous at the specified time t = T, and further that the controller u(t) is continuous on the interval [0, +∞);

[0098] Step 4-4, using the proof by contradiction, it is proved that the rotor speed of the wind turbine in variable speed mode will not change the sign of the tracking error of the rotor speed of the wind turbine in variable speed mode in the process of tracking the ideal reference signal; It also shows that there is no overshoot phenomenon of the tracking error of the rotor speed of the wind turbine in variable speed mode, that is, the output of the wind turbine in variable speed mode, i.e. the rotor speed, can only track the ideal reference signal from one direction; If β1(0) < y(0) ≤ y d (0), z1(0) < 0 and Both hold; according to the selected γ1in equation (15), the following holds:

[0099]

[0100] According to equations (12) and (20), the following equation holds:

[0101]

[0102] Thus the following equation holds:

[0103]

[0104] According to equations (27) and (28), z2(t) < 0, t ∈ [0, T); using equations (11), (12), (14) and (17), the following equation can be obtained:

[0105]

[0106] Because and a(t) > 0 for all t ∈ [0, T) can be obtained; using the proof by contradiction, it is proved that the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode is less than or equal to 0 for all t ∈ [0, T); it is assumed that there is a time t * ∈ (0, T) such that z1(t * ) > 0 is true, which, combined with z1(0) < 0, indicates that there must be a time t1 ∈ (0, t * ) such that z1(t1) = 0, and z1(t) < 0 for all t ∈ [0, t1); therefore, the following equation is true:

[0107]

[0108] For some τ1 > 0, equation (30) and the continuity of the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode indicate that z1(t) is monotonously decreasing in the interval [t1, t1+ τ1]; therefore, the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode is less than or equal to 0 for all t ∈ [0, t1+ τ1]; once the boundary of the compact set S = {t ∈ [0, T) | z1(t) = 0} is reached, another time t2 ∈ (t1+ τ, t * ) such that is found, thereby ensuring that the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode is monotonously decreasing in the interval [t2, t2+ τ2] for some τ2 > 0; thus, the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode is less than or equal to 0 for all t ∈ [0, t2+ τ2]; performing the same rule, it can be concluded that the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode is less than or equal to 0 for all t ∈ [0, t * ], which will form a contradiction with the assumed z1(t * ) > 0; if y d (0) ≤ y(0) < β2(0), at this time, the initial value z1(0) of the tracking error of the rotor speed of the wind power generator in the variable speed mode is greater than 0 and is true; repeating the analysis of equations (27)-(29), it can be proved by contradiction that the tracking error z1(t) of the rotor speed of the wind power generator in the variable speed mode is greater than or equal to 0 for all t ∈ [0, T).

[0109] Step 4-5, directly calculate the high and low speed shaft rotor angle difference The expression of the high and low speed shaft rotor angle difference, prove The boundedness on the interval [0, +∞);By using formula (12), (14) and (17), it can be derived that the limit of the tracking error z1(t) of the rotor speed of the wind turbine under the variable speed mode when t tends to T - is equal to 0, and is equal to 0 when t is greater than or equal to T, and the limit of ξ2(t) when t tends to T - is equal to 0, and is equal to 0 when t is greater than or equal to T, and thus there is a normal number M such that According to formula (11), the following inequality holds:

[0110]

[0111] According to the boundedness of the states z1(t) and ξ2(t) and formula (31), it can be proved that the high and low speed shaft rotor angle difference is bounded on the interval t∈[0, ∞).

[0112] Further, in the step 4, the design parameter selection in the time control design is specified as: γ1=0.8, γ2=0.54, ν=0.55, σ=2, p=1.

[0113] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0114] 1. According to the double mass block driving model of the wind turbine under the variable speed mode shown in the formula, the dynamic double mass block driving dynamics model of the wind turbine under the variable speed mode with complex dynamic torsional properties and nonlinear characteristics is established. Figure 5 Through defining the high and low speed shaft rotor angle difference and introducing a series of coordinate transformations, the dynamic double mass block driving dynamics model of the wind turbine under the variable speed mode is converted into an equivalent mathematical model of double mass block driving, which is easy to control. This modeling method can accurately describe the dynamic properties of the torsional effect of the wind turbine under the variable speed mode and the influence of the torsional effect on the power change and the communication mode of the wind turbine and the power grid, and at the same time, it opens up a new way for using the backstepping method to control the wind turbine under the variable speed mode.

[0115] 2. The present invention is directed to the equivalent mathematical model of the wind turbine in variable speed mode, i.e., the double mass drive equivalent mathematical model. A continuous state feedback control strategy is designed by using the backstepping method, the piecewise continuous time scale function related to the specified time, and the time-varying barrier Lyapunov function related to the constraint boundary. This control strategy can achieve the specified time tracking control of the wind turbine in variable speed mode without the accurate initial state, and improves the reliability of the wind turbine operation, and ensures that the wind turbine can capture the maximum wind energy.

[0116] 3. According to the requirements of the safety and stability of the wind turbine in variable speed mode, a tracking control scheme is designed by using the proof by contradiction method, the piecewise continuous time scale function, and the time-varying barrier Lyapunov function, and is directed to the equivalent mathematical model of the wind turbine in variable speed mode, i.e., the double mass drive equivalent mathematical model. This control scheme ensures that the rotor speed of the wind turbine in variable speed mode satisfies the time-varying constraint and the tracking error has no overshoot. This feature not only prevents the deterioration of the wind turbine structure, but also ensures the safety of the wind turbine in variable speed mode and prolongs the service life of the wind turbine.

[0117] 4. The present invention is directed to the tracking control problem of the specified time and the specified performance of the wind turbine in variable speed mode. Novel mathematical tools are used, including a series of state transformations and coordinate changes, the proof by contradiction method, the L'Hopital's rule, and the squeeze lemma. The use of these mathematical tools simplifies the stability analysis process and can accurately capture the torsional effect of the wind turbine. BRIEF DESCRIPTION OF DRAWINGS

[0118] Figure 1 A method flowchart for an embodiment of the present invention.

[0119] Figure 2 A rotor speed operation mode diagram of the wind turbine in variable speed mode for an embodiment of the present invention.

[0120] Figure 3 An output power diagram of the wind turbine in variable speed mode at different wind speed regions for an embodiment of the present invention.

[0121] Figure 4 A typical power coefficient curve diagram of the wind turbine in variable speed mode for an embodiment of the present invention.

[0122] Figure 5 A two-mass drive model diagram of the wind turbine in variable speed mode for an embodiment of the present invention.

[0123] Figure 6Output tracking response of a wind power generator at different initial values in analog variable speed mode of an embodiment of the invention.

[0124] Figure 7 Tracking error response of a wind power generator at different initial values in analog variable speed mode of an embodiment of the invention.

[0125] Figure 8 Generator torque of a wind power generator at different initial values in analog variable speed mode of an embodiment of the invention.

[0126] Figure 9 Output tracking response of a wind power generator at different specified times in analog variable speed mode of an embodiment of the invention.

[0127] Figure 10 Tracking error response of a wind power generator at different specified times in analog variable speed mode of an embodiment of the invention.

[0128] Figure 11 Generator torque of a wind power generator at different specified times in analog variable speed mode of an embodiment of the invention. DETAILED DESCRIPTION

[0129] The structure of the wind power generator in variable speed mode of the invention comprises: a tower, a rotor, a low speed shaft, a brake, a gearbox, a blade, a yawer, a yaw machine, a generator, a high speed shaft, a controller, an anemometer, a nacelle, a wind vane. The generator works as follows: wind blows over the rotor, which makes it rotate. The low speed shaft transfers the captured energy to the high speed shaft through the gearbox. The high speed shaft makes the generator rotate, thus generating electricity. The yaw system is used to turn the nacelle to ensure that the rotor is directly facing the wind direction. The wind power generator in variable speed mode contains multiple control levels. At the highest control level, the supervisory control system monitors the turbine and the wind speed to determine when to start the turbine and when to stop due to excessive wind speed to ensure safety. For example, if the wind speed is too high, the turbine will be stopped to prevent damage. The supervisory control system also monitors the turbine and the wind speed to determine when to start the turbine and when to stop due to excessive wind speed to ensure safety. For example, if the wind speed is too high, the turbine will be stopped to prevent damage. Figure 2 and Figure 3As shown, the operating mode of the wind turbine in variable speed mode is divided into three regions related to wind speed, maximum allowable rotor speed and rated power. Among them, v1 represents the starting wind speed, at which the turbine starts to rotate; v2 represents the wind speed at which the maximum allowable rotor speed can be obtained; v3 represents the rated wind speed; for safety, the turbine must be shut down when the wind speed reaches v4. When v1 < v < v2, the wind turbine operates in region I, i.e. variable tip speed ratio operation; when v2 < v < v3, the wind turbine operates in region II, i.e. constant tip speed ratio operation; when v3 < v < v4, the wind turbine operates in region III, obtaining and maintaining its rated power. Due to the limitations of the physical structure and electrical characteristics of the wind turbine in variable speed mode, the absorbed energy cannot continue to increase even if there is higher wind speed. The middle control level is the turbine control, including generator torque control, blade pitch control and yaw control. In addition, the internal engine, power electronics and pitch execution control are the lowest control level, which works faster than the turbine control. The present application focuses on the turbine control in region II, where the pitch angle remains constant and only torque control works.

[0130] The present application will be further described in detail below with reference to the accompanying drawings.

[0131] Figure 1 A method flow chart of an embodiment of the present application. As shown, a specified time and specified performance tracking control method of a wind turbine in variable speed mode of the present application comprises the following steps: Figure 1

[0132] Step 1, according to the power curve of the wind turbine in variable speed mode, first establish the wind energy model and the electric energy model of the wind turbine in variable speed mode, and then obtain the relationship between the wind energy model, the electric energy model and the rotor torque T a Through the established wind energy model and electric energy model of the wind turbine in variable speed mode, and with the help of Figure 5 The double mass block drive model of the wind turbine in variable speed mode is shown, the dynamic double mass block drive dynamics model of the wind turbine in variable speed mode is established. In addition, Figures 2-4 The operating characteristics of the wind turbine in variable speed mode are shown intuitively: Figure 2 The speed operating mode of the wind turbine in variable speed mode is shown; Figure 3 The output power of the wind turbine in variable speed mode when working in different wind speed regions is shown; Figure 4 The typical power curve of the wind turbine in variable speed mode is shown.

[0133] The specific process of step 1 is as follows:

[0134] ​Step 1-1: Based on the power curve of the wind turbine in variable speed mode, establish the wind energy model and electrical energy model of the wind turbine in variable speed mode. As mentioned above, Figures 2-4 It intuitively demonstrates the operating characteristics of the wind turbine in variable speed mode.

[0135] The wind energy model of a wind turbine in variable speed mode is as follows:

[0136]

[0137] The electrical energy model of a wind turbine in variable speed mode is as follows:

[0138]

[0139] Where ρ represents air density, r w Represents the tip radius, v ω C represents the speed of the wind. p The power coefficient is the pitch angle. Compared to the tip speed The function is given by ω, where ω is the rotor speed. From formula (2), it can be seen that if the wind turbine in variable speed mode operates at a power coefficient C... p If the maximum value is reached, then the electrical energy generated will reach its peak value. Figure 3 In the operating area II shown, the pitch angle is maintained at the ideal set value, such as... Figure 4 The 1° shown. Therefore, υ w Changes can alter λ, C p and P m The value of . However, if w(t) can be determined according to v w By adjusting the change in λ, λ can be kept at its maximum value. Therefore, the relationship between the electrical energy, torque, and rotor speed of a wind turbine in variable speed mode is established as follows:

[0140]

[0141] Step 1-2: Based on the relationship between the electrical energy, torque, and rotor speed of the wind turbine in variable speed mode established in Step 1-1, and Figure 5 The dual-mass drive model of the wind turbine in variable speed mode is shown. A dynamic dual-mass drive dynamics model of the wind turbine in variable speed mode is then established. For example... Figure 5 As shown, the wind turbine rotor rotates at a speed w(t), and the mechanical torque T a (t) represents the driving force. During the process of the aero-turbine converting wind energy into mechanical energy, the gearbox can increase the rotational speed w(t), while simultaneously reducing the low-speed shaft torque and the high-speed shaft torque. The generator utilizes mechanical energy to produce electrical energy. The dynamic dual-mass block driving dynamics model of the wind turbine in variable speed mode is as follows:

[0142]

[0143] where J r , J g , T ls (t), T hs (t), T g (t) represent rotor inertia, generator inertia, low speed shaft torque, high speed shaft torque and generator torque respectively.b r , b g , C s , K s represent damping coefficient and torsional coefficient respectively. θ(t) represents high speed shaft angle, θ ls (t) represents low speed shaft angle, n g (t) represents gear box reduction ratio, ω g (t) represents high speed shaft speed, w ls (t) represents low speed shaft speed. In order to meet the safety of wind turbine operation in variable speed mode, the output of equation (4), i.e. rotor speed w(t) should meet time-varying output constraint. The present invention requires that the output of equation (4), i.e. rotor speed w(t) meets: where β1: R + → R and β2: R + → R are set continuous differentiable functions.

[0144] Step 2, by subtracting high speed shaft rotor angle and low speed shaft rotor angle and introducing a clever coordinate transformation, the dynamic double mass block drive dynamics model of wind turbine in variable speed mode is converted into an equivalent mathematical model, i.e. double mass block drive equivalent mathematical model, which is easy to control, and this method facilitates the application of geometric control method in wind turbine tracking control in variable speed mode.

[0145] The process of step 2 includes:

[0146] Step 2-1, by subtracting high speed shaft rotor angle and low speed shaft rotor angle, a new high-low speed shaft rotor angle difference variable The transformation makes the dynamic double mass block drive dynamics model of wind turbine in variable speed mode given by equation (4) simplified, and the simplified form is as follows:

[0147]

[0148]

[0149]

[0150] Step 2-2, combined with the geometric control method, a new coordinate transformation is introduced to further simplify the dynamic dual-mass block drive dynamics model of the wind turbine in the variable speed mode. The coordinate transformation is introduced as follows:

[0151]

[0152] Combined with equation (8), the dynamic dual-mass block drive dynamics model (5)-(7) of the wind turbine in the variable speed mode is further simplified as:

[0153]

[0154] The control signal is defined as: The output is defined as: y=x1. Wherein,

[0155] Step 2-3, combined with the nonlinear system control method and control requirements, a new coordinate transformation is further introduced to convert the dynamic dual-mass block drive dynamics model of the wind turbine in the variable speed mode into an equivalent mathematical model that is easy to control, i.e. the dual-mass block drive equivalent mathematical model. The coordinate transformation is introduced as follows:

[0156]

[0157] Wherein, By applying the coordinate transformation (10), the dynamic dual-mass block drive dynamics model (9) of the wind turbine in the variable speed mode is equivalent to the following dual-mass block drive equivalent mathematical model:

[0158]

[0159] Wherein,

[0160] Step 3, for the established dual-mass block drive equivalent mathematical model of the wind turbine in the variable speed mode, the backstepping method, the piecewise continuous time scale function related to the specified time and the time-varying barrier Lyapunov function are used to design the virtual control signal and the actual control signal, and the actual controller is designed, thereby forming the corresponding closed-loop system.

[0161] The process of step 3 includes:

[0162] Step 3-1, two new error variables are introduced, the error variable z1 is the difference between the output signal and the reference signal, and the error variable z2 is the difference between the second state signal and the virtual control signal, which prepares for the application of the backstepping method. The introduced error variables are as follows:

[0163]

[0164] Considering the relationship between the initial value of wind turbine output and the initial value of ideal reference signal, two cases are considered to design the controller (1) If β1(0) < y(0)≤y d (0), then (2) If y d (0)≤y(0)<β2(0), then α1, are continuous and differentiable functions. The design process of in the two cases is described as follows:

[0165] (1) If the initial value of wind turbine output is between the initial value of output constraint lower bound β1(0) and the initial value of ideal reference signal y d (0) to be tracked, i.e. β1(0) < y(0)≤y d (0). Introducing the difference variable δ1(t) = y d (t)-w(t) of the ideal reference signal y d (t) to be tracked and the output constraint lower bound β1(t), and further introducing the time-varying barrier Lyapunov function V1, the virtual control law is designed by combining backstepping method. The time-varying barrier Lyapunov function introduced is:

[0166]

[0167] where p≥1 is an integer. According to (11) and (12), the derivative of the time-varying barrier Lyapunov function V1 is:

[0168]

[0169] The virtual control law is designed as α1, and the expression is:

[0170]

[0171] where ν, σ, and γ1 are normal numbers, and satisfy:

[0172]

[0173] Considering that the following formula is true:

[0174]

[0175] The derivative of the time-varying barrier Lyapunov function V1 satisfies:

[0176]

[0177] where

[0178] (2) If the initial value of the wind power generator output is between the upper initial value β2(0) of the output constraint and the initial value y d (0) of the ideal reference signal being tracked, i.e. y d (0)≤y(0)<β2(0). Introduce the difference variable δ2(t)=w(t)-y d (t) of the ideal reference signal being tracked y d (t) and the lower limit β2(t) of the output constraint, and further introduce the time-varying barrier Lyapunov function In combination with the backstepping method, a virtual control law is designed The time-varying barrier Lyapunov function introduced is:

[0179]

[0180] The virtual control law is designed The expression is:

[0181]

[0182] Therefore, the derivative of the time-varying barrier Lyapunov function V1 satisfies:

[0183]

[0184] Wherein,

[0185] Step 3-2, in combination with the virtual control law designed in the above (1) or (2) Introduce a positive definite Lyapunov function V, and design an actual controller, so that the derivative of the Lyapunov function V is negative, thereby realizing the specified time and specified performance tracking control of the wind power generator in the variable speed mode. The positive definite Lyapunov function is selected as:

[0186]

[0187] Wherein, if β1(0)<y(0)≤y d (0), then If y d (0)≤y(0)<β2(0), then

[0188] According to the formula (16) and (18), the derivative of the Lyapunov function V is:

[0189]

[0190] ​​​where if β1(0) < y(0) ≤ y d (0), then if y d (0) ≤ y(0) < β2(0), then Next, the state feedback law is designed as:

[0191]

[0192] where γ2 is a positive constant. Thus, the actual controller is:

[0193]

[0194] where Substitute equation (20) into equation (19), the derivative of Lyapunov function V satisfies:

[0195]

[0196] where Up to now, the design of the actual controller for the specified time and specified performance tracking control of the wind turbine in variable speed mode has been completed.

[0197] Step 4, for the closed-loop system formed by the double-mass block drive equivalent mathematical model of the wind turbine in variable speed mode and the actual controller designed in step 3, stability analysis is performed. According to the form of Lyapunov function and the derivative of Lyapunov function, using Lyapunov stability theory, it is first proved that the tracking error of the rotor speed of the wind turbine in variable speed mode converges to 0 within the specified time T and is equal to 0 at time greater than or equal to T. Then, using L'Hopital's rule and the principle of forced convergence, it is proved that the controller u(t) is continuous at the specified time t = T, and further it is proved that the controller u(t) is continuous on the interval [0, +∞). Then, using proof by contradiction, it is proved that the rotor speed of the wind turbine in variable speed mode will not overshoot during the tracking of the ideal reference signal, that is, the output of the wind turbine in variable speed mode, i.e. the rotor speed, can only track the ideal reference signal from one direction. Finally, the expression of the high-low speed shaft rotor angle difference is directly calculated to prove its boundedness on the interval [0, +∞). Through the stability analysis of this step, it is proved that the designed controller can achieve a specified time and specified performance tracking control of the wind turbine in variable speed mode.

[0198] The process of step 4 includes:

[0199] Step 4-1, according to the form of Lyapunov function and the derivative of Lyapunov function, by using Lyapunov stability theory, the tracking error of wind turbine rotor speed in variable speed mode is proved to converge to 0 within a specified time T by integrating the derivative of Lyapunov function from 0 to t. If t ∈ [0, T), the following inequality holds:

[0200]

[0201] Integrating both sides of equation (23) from 0 to t, the following inequality can be obtained:

[0202]

[0203] Equation (24) shows that that is, the limit of Lyapunov function V(t) as t tends to time T - is equal to 0. Therefore, holds. According to equation (24) and the definition of , the following inequality holds:

[0204]

[0205] Therefore, according to the boundedness of δ1(t) and δ2(t) on the interval [0, T), it can be obtained that the limit of tracking error z1(t) of wind turbine rotor speed in variable speed mode as t tends to time T is equal to 0.

[0206] Step 4-2, by using the form of Lyapunov function and the derivative of Lyapunov function and the fact that the tracking error of wind turbine rotor speed in variable speed mode converges to 0 within a specified time T, it is proved that the tracking error z1(t) of wind turbine rotor speed in variable speed mode is equal to 0 for time greater than or equal to T. If t ∈ [T, +∞), according to equation (22) and , the following equation holds:

[0207]

[0208] The above equation and the limit of Lyapunov function V(t) as t tends to T - is equal to 0, so that for t ≥ T, Lyapunov function V(t) is equal to 0 for t greater than or equal to T. Therefore, according to the definition of Lyapunov function, it is proved that for t ∈ [T, +∞), the tracking error z1(t) of wind turbine rotor speed in variable speed mode is equal to 0.

[0209] Step 4-3, by using L'Hopital's rule and the principle of forced convergence, combined with the fact that the tracking error of the rotor speed of the wind turbine in variable speed mode converges to 0 in a specified time T and is equal to 0 for time greater than or equal to T, it is proved that the controller u(t) is continuous at the specified time t = T, and further that the controller u(t) is continuous on the interval [0, +∞). In fact, according to equations (20) and (21), to prove the continuity of u(t) on the interval [0, +∞), it is only necessary to prove that and are continuous on the interval [0, +∞).

[0210] Considering that σ > 2p, the following limit holds:

[0211]

[0212] Using the principle of forced convergence, the following limit holds:

[0213]

[0214] From equations (14) and (17), the virtual control law is continuous at time t = T. Furthermore, the continuity of the derivative of the virtual control law depends only on According to L'Hopital's rule, the following holds:

[0215]

[0216] Using equations (25) and (26), the following limit holds:

[0217]

[0218] Therefore, the virtual control law is continuous and differentiable at time t = T, and the derivative of the virtual control law is continuous on the interval [0, +∞). According to the definition of the Lyapunov function V(t) and equation (24), it follows that: According to σ > 2p, the following holds:

[0219]

[0220] This shows that z2(t) is continuous on the interval [0, +∞). Furthermore, according to equations (10) and (20), it can be proved that the controller u(t) is continuous at the specified time t = T, and further that the controller u(t) is continuous on the interval [0, +∞).

[0221] Step 4-4, by using the method of contradiction, it is proved that the sign of the tracking error of the rotor speed of the wind power generator in variable speed mode will not change in the process of tracking the ideal reference signal, which also shows that the overshoot phenomenon of the tracking error of the rotor speed of the wind power generator in variable speed mode will not occur, that is, the output of the wind power generator in variable speed mode, i.e. the rotor speed, can only track the ideal reference signal from one direction. If β1(0) < y(0) ≤ y d (0), z1(0) < 0 and are all true. According to the selected γ1in equation (15), the following equation is true:

[0222]

[0223] According to equations (12) and (20), the following equation is obtained:

[0224]

[0225] Thus, the following equation is obtained:

[0226]

[0227] According to equations (27) and (28), z2(t) < 0, t ∈ [0, T) is obtained. Further, by using equations (11), (12), (14) and (17), the following equation is obtained:

[0228]

[0229] Because and a(t) > 0 for all t ∈ [0, T) is obtained. Next, by using the method of contradiction, it is proved that the tracking error z1(t) of the rotor speed of the wind power generator in variable speed mode is less than or equal to 0 for all t ∈ [0, T). Assume that there exists a time t * ∈ (0, T) such that z1(t * ) > 0 is true. This point combined with z1(0) < 0 shows that there must be a time t1∈ (0, t * ) such that z1(t1) = 0, and z1(t) < 0 for all t ∈ [0, t1). Therefore, the following equation is true:

[0230]

[0231] For some τ1> 0, the continuity of z1(t) in (30) and the tracking error of the rotor speed of the wind generator in the variable speed mode implies that z1(t) is monotonically decreasing on the interval [t1, t1+τ1]. Therefore, the tracking error of the rotor speed of the wind generator in the variable speed mode is less than or equal to zero for all t∈[0, t1+τ1]. Once the boundary of the compact set S = {t∈[0, T) | z1(t) = 0} is reached, another time instant t2∈(t1+τ, t * ) will be found such that This will guarantee that for some τ2> 0, the tracking error of the rotor speed of the wind generator in the variable speed mode is monotonically decreasing on the interval [t2, t2+τ2]. Thus, the tracking error of the rotor speed of the wind generator in the variable speed mode is less than or equal to zero for all t∈[0, t2+τ2]. By performing the same rule, it can be concluded that the tracking error of the rotor speed of the wind generator in the variable speed mode is less than or equal to zero for all t∈[0, t * ]. This will contradict the assumption that z1(t * )> 0. If y d (0)≤y(0)<β2(0), then the initial value of the tracking error of the rotor speed of the wind generator in the variable speed mode z1(0) is greater than zero and By repeating the analysis of (27)-(29), it can be proved by contradiction that the tracking error of the rotor speed of the wind generator in the variable speed mode z1(t) is greater than or equal to zero for all t∈[0, T).

[0232] Step 4-5, directly calculate the expression of the rotor angle difference between the high speed shaft and the low speed shaft , and prove its boundedness on the interval [0, +∞), which greatly simplifies the traditional process of proving the boundedness of the rotor angle difference between the high speed shaft and the low speed shaft on the interval [0, +∞) by Lyapunov analysis theory, and is more intuitive. By using (12), (14) and (17), it can be derived that the limit of ξ2(t) as t tends to T - is equal to zero, and is equal to zero for all t≥T, according to the limit of the tracking error of the rotor speed of the wind generator in the variable speed mode z1(t) as t tends to T - is equal to zero, and is equal to zero for all t≥T. Therefore, there exists a positive number M such that Further, according to (11), the following inequality holds:

[0233]

[0234] According to the boundedness of the states z1(t) and z2(t) and equation (31), it can be proved that the difference between the high-speed shaft rotor angle and the low-speed shaft rotor angle is bounded on the interval t∈[0,∞).

[0235] Simulation verification of the present application:

[0236] Step F1, the parameters of the permanent magnet wind power simulation system are as follows: (1) three-phase permanent magnet synchronous motor (simulating wind turbine): rated power is 4.5KW, rated voltage is 380V, rated speed is 1500rpm, simulating wind turbine blade tip radius is 1.2897m, pitch angle is 0, air density is 1.225kg / m 3 (2) three-phase generator (load motor): rated power is 3KW, rated voltage is 380V, rated speed is 1500rpm. (3) torque / speed sensor DYN-200: supports RS485 communication, the fastest communication rate can reach 1000 times per second, 24-bit AD acquisition chip, acquisition speed is 1200 times per second. (4) frequency converter GD350: rated power is 7.5KW, input power voltage is 380V, input frequency is 50Hz. (5) generator controller DY3H: rated power is 5.5KW, output voltage is 380V, output current is 0-10A, output frequency is 0-100Hz. The following gives the adjustment parameters of the specified time and specified performance tracking control of the wind turbine in the simulation variable speed mode: γ1=0.8, γ2=0.54, ν=0.55, σ=2, p=1. Set the time-varying upper bound of the rotor speed constraint in the specified time and specified performance tracking control of the wind turbine in the simulation variable speed mode as Set the time-varying lower bound of the rotor speed constraint in the specified time and specified performance tracking control of the wind turbine in the simulation variable speed mode as First, set the specified time as T=2.

[0237] Step F2, for the specified time and specified performance tracking control model of the wind turbine in the simulation variable speed mode, a virtual control signal and an actual controller u are designed. Then two groups of initial values are selected: The output tracking response of the wind turbine in the simulation variable speed mode under different initial values is shown in Figure 6 , the tracking error response curve of the wind turbine in the simulation variable speed mode under different initial values is shown in Figure 7 , and the generator torque of the wind turbine in the simulation variable speed mode under different initial values is shown in Figure 8 It can be seen from Figure 6 that the rotor speed of the wind turbine in the simulation variable speed mode under different initial values tracks the ideal reference signal without overshoot within the specified time T=2; from Figure 7It can be seen that the tracking error of the wind power generator under different initial values in the simulation variable speed mode does not have overshoot phenomenon. Figure 8 It can be seen that the control input of the wind power generator under different initial values in the simulation variable speed mode is a continuous and bounded signal.

[0238] Step F3, the fixed initial value is Then select different specified times as T=1, T=2 respectively. The output tracking response of the wind power generator under different specified times in the simulation variable speed mode is as shown in Figure 9 The tracking error response curve of the wind power generator under different specified times in the simulation variable speed mode is as shown in Figure 10 The generator torque of the wind power generator under different specified times in the simulation variable speed mode is as shown in Figure 11 It can be seen that the rotor speed of the wind power generator in the simulation variable speed mode does not have overshoot tracking ideal reference signal in different specified times; it can be seen that the tracking error of the wind power generator under different specified times in the simulation variable speed mode does not have overshoot phenomenon; it can be seen that the control input of the wind power generator under different specified times in the simulation variable speed mode is a continuous and bounded signal. Figure 9 Figure 10 Figure 11

[0239] Step F4, the output tracking response and the tracking error response of the wind power generator in the simulation variable speed mode show that the method proposed in the application is superior to the adaptive tracking control method and the nonlinear asymptotic tracking control method.​​​

Claims

1. A tracking control method for a wind turbine generator in variable speed mode for a specified time and specified performance, characterized in that, Includes the following steps: Step 1: First, establish the wind energy model and electrical energy model of the wind turbine in variable speed mode, and then obtain the wind energy model, electrical energy model, and rotor torque T. a The relationship between them; by using the wind energy model and electrical energy model of the wind turbine in variable speed mode, and with the help of the dual-mass block drive model of the wind turbine in variable speed mode, a dynamic dual-mass block drive dynamic model of the wind turbine in variable speed mode is established. Step 2: By subtracting the high-speed shaft rotor angle and the low-speed shaft rotor angle and introducing a clever coordinate transformation, the dynamic dual-mass block drive dynamics model of the wind turbine in variable speed mode is transformed into an easily controllable dual-mass block drive equivalent mathematical model. Step 3: For the dual-mass block drive equivalent mathematical model of the wind turbine under the established variable speed mode, the actual controller is designed by using the back-reasoning method, the piecewise continuous time scale function related to the specified time and the time-varying barrier Lyapunov function, and designing virtual control signals and actual control signals, thereby forming the corresponding closed-loop system. Step 4: For the closed-loop system formed by the dual-mass block driven equivalent mathematical model of the wind turbine in variable speed mode and the actual controller designed in Step 3, a stability analysis is performed: Based on the Lyapunov function and the form of its derivative, using Lyapunov stability theory, it is first proven that the tracking error of the wind turbine rotor speed in variable speed mode converges to 0 within a specified time T and is always equal to 0 when the time is greater than or equal to T. Then, using L'Hopital's theorem and the forced convergence principle, it is proven that the controller u(t) is continuous at a specified time t = T, and further proven that the controller u(t) is continuous on the interval [0, +∞). Then, it is proved by contradiction that the rotor speed of the wind turbine in variable speed mode will not experience overshoot during the tracking of the ideal reference signal. Finally, the difference in rotor angle between the high and low speed shafts is directly calculated. The expression is used to prove... Boundedness on the interval [0, +∞); In step 1: The wind energy model of a wind turbine in variable speed mode is as follows: The electrical energy model of a wind turbine in variable speed mode is as follows: Where ρ represents air density, r ω Represents the tip radius, v ω Represents the speed of the wind. The power coefficient is the pitch angle. Compared to the tip speed The function, where ω is the rotor speed; The model for the electrical energy, torque, and rotor speed generated by a wind turbine in variable speed mode is as follows: The dynamic dual-mass drive dynamics model of the wind turbine in variable speed mode is as follows: Among them, mechanical torque T a (t) is the driving force, J r J g ,T ls (t),T hs (t),T g (t) represent rotor inertia, generator inertia, low-speed shaft torque, high-speed shaft torque, and generator torque, respectively; b r ,b g C s ,K s These represent the damping coefficient and torsional coefficient, respectively, and θ(t) represents the high-speed shaft angle. ls (t) represents the low-speed shaft angle, n g (t) represents the gearbox reduction ratio, ω g (t) represents the high-speed shaft speed, ω ls (t) represents the low-speed shaft speed; Step 2 includes the following process: Step 2-1: By subtracting the high-speed shaft rotor angle from the low-speed shaft rotor angle, a new variable for the high-speed and low-speed shaft rotor angle difference is derived. This transformation simplifies the dynamic dual-mass drive dynamics model of the wind turbine in variable speed mode given in equation (4) to: Step 2-2: Combining geometric control methods, a new coordinate transformation is introduced to further simplify the dynamic dual-mass block drive dynamics model of the wind turbine in the above variable speed mode. The coordinate transformation is as follows: Combining equation (8), the dynamic dual-mass block drive dynamics model (5)-(7) of the wind turbine in variable speed mode is further simplified to: Define the control signal as: The output is defined as: y = x1, where, Steps 2-3: Combining nonlinear system control methods and control requirements, a new coordinate transformation is further introduced to transform the dynamic dual-mass block drive dynamics model of the wind turbine in variable speed mode into an easily controllable equivalent mathematical model of dual-mass block drive. The coordinate transformation is as follows: in, Applying coordinate transformation (10), the dynamic dual-mass block drive dynamics model (9) of the wind turbine in variable speed mode is equivalent to the following dual-mass block drive equivalent mathematical model: in, Step 3 includes the following process: Step 3-1: Introduce two new error variables: error variable z1 is the difference between the output signal and the reference signal, and error variable z2 is the difference between the second state signal and the virtual control signal. Considering the relationship between the initial value of the wind turbine output and the initial value of the ideal reference signal in variable speed mode, the design can be divided into two cases. (1) If β1(0) <y(0)≤y d (0), then (2) If y d (0)≤y(0)<β2(0), α1, They are all continuously differentiable functions; Step 3-2: Combine the virtual control laws designed in cases (1) or (2) above. Introducing a positive definite Lyapunov function V, designing a practical controller such that the derivative of the Lyapunov function V... Negative definite, thus enabling tracking control of the wind turbine generator at specified times and with specified performance in variable speed mode; positive definite Lyapunov function is selected as: Where, if β1(0) <y(0)≤y d (0), then If y d If (0)≤y(0)<β2(0), then According to equations (16) and (18), the derivative of the Lyapunov function V is: Where, if β1(0)<y(0)≤y d (0), then If y d If (0)≤y(0)<β2(0), then Next, the design state feedback law is as follows: Where γ2 is a positive constant, therefore, the actual controller is: in, Substituting equation (20) into equation (19), the derivative of the Lyapunov function V satisfies: in, This completes the design of the actual controller for tracking and controlling the wind turbine generator at specified times and with specified performance in variable speed mode.

2. The tracking control method for a wind turbine generator in variable speed mode at a specified time and with specified performance according to claim 1, characterized in that, In step 3, design The process is as follows: (1) If the initial value of the wind turbine output is within the lower bound of the output constraint initial value β1(0) and the initial value of the ideal reference signal being tracked is y d Between (0), i.e., β1(0) <y(0)≤y d (0); Introduce the ideal reference signal y for tracking. d The difference variable δ1(t) between y(t) and the lower bound of the output constraint β1(t) is y. d (t)-ω(t), further introducing the time-varying barrier Lyapunov function V1, and combining it with the backstepping method, a virtual control law is designed; the introduced time-varying barrier Lyapunov function is: Where p≥1 is an integer; according to (11) and (12), the derivative of the time-varying barrier Lyapunov function V1 is: Design virtual control law Let α1 be the expression: Where v, σ, and γ1 are all positive constants and satisfy: Considering that the following formula holds true: The derivative of the time-varying barrier Lyapunov function V1 satisfies: in, 3. The tracking control method for a wind turbine generator in variable speed mode for a specified time and specified performance according to claim 1, characterized in that, In step 3, design The process is as follows: (2) If the initial value of the wind turbine output is within the upper bound of the output constraint initial value β2(0) and the initial value of the ideal reference signal being tracked is within the range of the initial value y2(0) and the initial value of the ideal reference signal being tracked is within the range of the initial value β ...). d (0) and above, i.e., y d (0)≤y(0)<β2(0); Introduce an ideal reference signal y for tracking. d The difference between δ2(t) and the lower bound of the output constraint β2(t) is δ2(t) = ω(t) - y. d (t), further introducing the time-varying barrier Lyapunov function By combining the backstepping method, a virtual control law is designed. Introduced time-varying barrier Lyapunov function for: Design virtual control law for Its expression is: Therefore, the derivative of the time-varying barrier Lyapunov function V1 satisfies: in, 4. The tracking control method for a wind turbine generator in variable speed mode at a specified time and with specified performance according to claim 1, characterized in that, Step 4 includes the following process: Step 4-1: Based on the Lyapunov function and the form of its derivative, and using Lyapunov stability theory, by integrating the derivative of the Lyapunov function from 0 to t, prove that the tracking error of the wind turbine rotor speed in variable speed mode converges to 0 within a specified time T; if t∈[0,T), the following inequality holds: Integrating both sides of equation (23) from 0 to t, we obtain the following inequality: Equation (24) shows that lim t→T -V(t) = 0, meaning the limit of the Lyapunov function V(t) as t approaches time T- is equal to 0; therefore, Established; according to equation (24) and By definition, the following inequalities hold: Therefore, based on the boundedness of δ1(t) and δ2(t) in the interval [0, T), it can be obtained that the limit of the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is equal to 0 when t approaches time T-. Step 4-2: Using the Lyapunov function and the form of its derivative, and the fact that the tracking error of the wind turbine rotor speed in variable speed mode converges to 0 within a specified time T, prove that the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is always equal to 0 when the time is greater than or equal to T; if t∈[T, +∞), according to equation (22) and The following equation holds true: The above equation and the limit of the Lyapunov function V(t) as t approaches T- are equal to 0, such that for t≥T, the Lyapunov function V(t) is always equal to 0 when t is greater than or equal to T; therefore, according to the definition of the Lyapunov function, it is proved that for t∈[T,+∞), the tracking error z1(t)≡z2(t) of the wind turbine rotor speed in variable speed mode is always equal to 0. Step 4-3: Using L'Hôpital's theorem and the forced convergence principle, combined with the fact that the tracking error of the wind turbine rotor speed in variable speed mode converges to 0 within a specified time T and is always equal to 0 when the time is greater than or equal to T, prove that the controller u(t) is continuous at the specified time t = T, and further prove that the controller u(t) is continuous on the interval [0, +∞). In fact, according to equations (20) and (21), to prove the continuity of u(t) on the interval (0, +∞), it is only necessary to prove that... and Continuity on the interval [0, +∞); Considering σ > 2p, the following limit holds: Using the forced convergence principle, the following limits hold: The virtual control law can be obtained through equations (14) and (17). The function is continuous at time t = T; therefore, the derivative of the virtual control law... The continuity depends only on According to L'Hôpital's rule, the following equation holds: Using equations (25) and (26), the following limits hold: Therefore, virtual control law The derivative of the virtual control law is continuously differentiable at time t=T. It is continuous on the interval [0, +∞); according to the definition of the Lyapunov function V(t) and equation (24), we can obtain: According to σ>2p, the following equation holds: This shows that z2(t) is continuous on the interval [0, +∞); furthermore, according to equations (10) and (20), it can be proved that the controller u(t) is continuous at the specified time t = T, and it can be further proved that the controller u(t) is continuous on the interval [0, +∞); Step 4-4: Using proof by contradiction, prove that in the process of the wind turbine rotor speed tracking the ideal reference signal in variable speed mode, the sign of the tracking error of the wind turbine rotor speed in variable speed mode will not change; it also shows that there will be no overshoot phenomenon of the tracking error of the wind turbine rotor speed in variable speed mode, that is: the output of the wind turbine in variable speed mode, i.e., the rotor speed, can only track the ideal reference signal in one direction; if β1(0) <y(0)≤y d (0), z1(0)<0 and All of these hold true; based on the γ1 selected in equation (15), the following equation holds true: Based on equations (12) and (20), the following equation can be obtained: Therefore, we can obtain the following formula: According to equations (27) and (28), z2(t) < 0, t ∈ [0, T); using equations (11), (12), (14) and (17), the following equation can be obtained: because and Therefore, we can conclude that a(t) > 0 holds for all t ∈ [0, T). We can prove by contradiction that for all t ∈ [0, T), the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is less than or equal to 0. We assume there exists a time t... * ∈(0,T) such that z1(t) * The statement that z1 > 0 holds true, combined with z1(0) < 0, indicates that there must exist a time t1 ∈ (0, t * (e.g., z1(t1) = 0, and for all t ∈ [0, t1), z1(t) < 0; therefore, the following equation holds:) For some τ1>0, the continuity of equation (30) and the tracking error z1(t) of the wind turbine rotor speed in variable speed mode indicates that z1(t) is monotonically decreasing on the interval [t1, t1+τ1]. Therefore, the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is less than or equal to 0 for all t∈[0, t1+τ1]. Once the boundary of the compact set S={t∈[0, T)|z1(t)=0} is reached, another time t2∈(t1+τ, t1+τ1) will be found. * ) makes This ensures that for some τ2 > 0, the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is monotonically decreasing on the interval [t2, t2 + τ2]. Therefore, for all t ∈ [0, t2 + τ2], the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is less than or equal to 0. Applying the same rule, we can conclude that for all t ∈ [0, t2 + τ2], the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is less than or equal to 0. * The tracking error z1(t) of the wind turbine rotor speed in variable speed mode is less than or equal to 0, which contradicts the assumed z1(t) * )>0 creates a contradiction; if y d (0)≤y(0)<β2(0), at this time the initial value of the tracking error of the wind turbine rotor speed in variable speed mode is greater than 0 and The following is true; the analysis of repeated formulas (27)-(29) can be proved by contradiction: for all t∈[0,T], the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is greater than or equal to 0. Steps 4-5: Directly calculate the rotor angle difference between high and low speed shafts. The expression, proof Boundedness on the interval [0, +∞); using equations (12), (14) and (17), it can be deduced that the limit of the tracking error z1(t) of the wind turbine rotor speed in variable speed mode is equal to 0 when t approaches T- and is always equal to 0 when t is greater than or equal to T, and that the limit of ξ2(t) is equal to 0 when t approaches T- and is always equal to 0 when t is greater than or equal to T; therefore, there exists a positive constant M such that According to equation (11), the following inequalities hold: Based on the boundedness of states z1(t) and ξ2(t) and equation (31), it can be proved that the angle difference between the high-speed and low-speed shaft rotors... It is bounded on the interval t∈[0,∞).

5. The tracking control method for a wind turbine generator in variable speed mode for a specified time and specified performance according to claim 4, characterized in that, In step 4, the design parameters selected in the specified time control design are: γ1 = 0.8, γ2 = 0.54, v = 0.55, σ = 2, p = 1.

Images