CN115437285A - Control method for inhibiting vibration of wind driven generator tower based on PDE model - Google Patents
Control method for inhibiting vibration of wind driven generator tower based on PDE model Download PDFInfo
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Abstract
The invention provides a control method for inhibiting vibration of a tower body of a wind driven generator based on a PDE model, which comprises the following steps: acquiring original parameters of a flexible tower body in a wind driven generator system; a plurality of sensors are distributed at the tower top of the flexible tower, and data information of real-time vibration of the tower body is obtained through the sensors; establishing a PDE model of a wind driven generator system according to the obtained original parameters of the tower body of the flexible tower and data information obtained by a sensor arranged at the top of the flexible tower, and constructing a fault observer for observing potential faults of the controller; and deducing a control algorithm according to the established PDE model and the established fault observer, calculating the control algorithm through software to obtain an output value, giving an actuator positioned at the top of the tower as an input signal in real time, and applying a control action on the tower top by the actuator so as to inhibit the vibration of the tower body. The method can greatly improve the fault-tolerant capability of the controller, reduce the influence of external load on the flexible tower and effectively inhibit the vibration of the tower body.
Description
Technical Field
The invention relates to the field of control for inhibiting vibration of a flexible tower, in particular to a control method for inhibiting vibration of a tower body of a wind driven generator based on a PDE model.
Background
With the increasing importance of the country on the development of renewable energy sources, the control problem of the wind driven generator is concerned more and more. The wind energy is used as a substitute of fossil fuel, has the characteristics of abundant resources, renewability, wide distribution, cleanness and the like, does not generate greenhouse gas emission during operation, and uses little land. The wind power generator can convert wind energy into mechanical energy and finally into electric energy. The basic components of a wind turbine include blades, hub, low and high speed shafts, gearbox, generator, nacelle, and tower. In modern wind power engineering, wind power generators are usually installed in areas with stronger and more stable wind power, such as at sea and high altitude areas. Due to the transportation cost and price limitation, the flexible tower is widely used, so that the wind energy has more competitiveness and economic benefit. The design of flexible tower makes the tower body become lighter, more nimble, and consequently, the tower body receives the influence of the external load in the environment more easily, like the mechanical vibration that can cause the tower of periodic turbulence, the stress fluctuation of tower body is caused to big vibration to lead to tower body metal fatigue, seriously probably make the tower body collapse.
For the control of the flexible tower, the design of the existing controller is mostly based on a set of finite dimensional ODEs obtained by performing spatial discretization on PDEs. Due to the infinite dimensional nature of distributed parametric systems, controllers based on finite dimensional models may cause system overflow instabilities, which should be avoided in the design of the controller.
Meanwhile, due to the complexity of the wind field environment, the controller is easy to have some unknown faults, when the faults occur, the controller still has an inhibiting effect on the vibration of the tower body, the safe operation of the generator set is guaranteed, and the fault-tolerant control problem is mostly not considered in the design of the existing flexible tower controller based on the model, so that the application of an actual control system is limited.
Therefore, a new control method for suppressing the tower vibration of the wind driven generator is urgently needed in the industry.
Disclosure of Invention
The invention aims to make up the defects of the prior art, and provides a control method for inhibiting the vibration of a tower body of a wind driven generator based on a Partial Differential Equation (PDE) model in order to avoid the possible overflow instability problem of a controller designed based on a discretization model and realize good inhibition effect on the vibration of the tower body.
The invention is realized by the following technical scheme:
a control method for inhibiting vibration of a tower body of a wind driven generator based on a PDE model comprises the following steps:
step 1: acquiring original parameters of a flexible tower body in a wind driven generator system;
and 2, step: the flexible tower is characterized in that a plurality of sensors are distributed at the tower top of the flexible tower, and data information of real-time vibration of the tower body is acquired through the sensors;
and step 3: according to the original parameters of the flexible tower body obtained in the step 1 and data information obtained by the sensor arranged at the top of the flexible tower in the step 2, a partial differential equation model of the wind driven generator system is established based on the kinetic potential energy conversion and the virtual work theorem of the structural mechanics;
and 4, step 4: constructing a fault observer for observing potential faults of the controller based on a Lyapunov stability analysis theory according to the original parameters of the flexible tower body obtained in the step 1 and data information obtained by the sensor arranged at the top of the flexible tower in the step 2;
and 5: deducing a control algorithm according to the partial differential equation model established in the step 3 and the fault observer established in the step 4, and embedding the control algorithm into a wind turbine controller;
the sensor monitors the vibration condition of the tower body in real time and transmits information to the controller, the output value of the controller is obtained through a software real-time calculation control algorithm in the controller, the output value of the controller is given to the actuator positioned at the top of the tower in real time to serve as an input signal, and the actuator exerts a control action on the top of the tower by receiving the input signal given by the controller, so that the vibration of the tower body is suppressed.
Further, the original parameters in step 1 include: the flexible tower comprises a flexible tower body, a flexible tower top, a flexible tower, a mass density of the flexible tower, an elastic modulus of the flexible tower body, an uneven moment of the flexible tower body, an uneven cross-sectional area of the flexible tower body and a vibration attenuation coefficient of the flexible tower body.
Further, in step 2, the sensor comprises a laser displacement sensor, an inclinometer and a shear force sensor which are arranged on the top boundary of the flexible tower; the laser displacement sensor is used for acquiring data information of deflection of the tower top, the inclinometer is used for acquiring data information of primary partial derivative of deflection of the tower top to space variation, and the shearing force sensor is used for acquiring data information of tertiary partial derivative of deflection of the tower top to space variation.
Further, according to the original parameters of the flexible tower body obtained in the step 1 and the data information obtained by the sensor arranged at the top of the flexible tower in the step 2, a partial differential equation model of the wind driven generator system is established based on the kinetic potential energy conversion and the virtual power theorem of the structural mechanics, and the method specifically comprises the following steps:
when the flexible tower body is subjected to a distributed load psi (tau, xi), analyzing the inherent vibration generated by the tower body under the action of the distributed load; one end of the bottom end of the tower body is fixed, virtual displacement omega (tau, xi) generated by vibration is defined, and the kinetic potential energy and the external force of the tower body are respectively obtained to do work;
according to the virtual work principle, the work of the external force on the virtual displacement is equal to the work of the internal force on the virtual displacement, and the following results are obtained:
E k (ξ)+E p (ξ)＝δW(ξ)
wherein, ek (xi) is the kinetic energy of the tower body, ep (xi) is the potential energy of the tower body, and delta W (xi) is the sum of the virtual work done to the tower body, including the virtual work done by the tower body damping, the virtual work done by the tower body distributed load, the virtual work done by the control action suppression tower body vibration and the virtual work produced by the controller due to the potential fault;
applying Hamilton principle, and considering the whole tower body to obtain a four-order heterogeneous partial differential equation of the dynamic characteristic of the tower body to obtain a PDE model of the wind driven generator system, wherein the four-order heterogeneous partial differential equation comprises the following specific steps:
wherein in the formula
Is a partial derivative symbol; tau is the space position of each position of the tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; rho is the mass density of the tower body, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the column body, m 2 ；
Is the transverse vibration of the tower body, m;
is the deflection distance at the top of the tower, m; mu is the damping coefficient of tower vibration, NS/m 2 (ii) a Δ (ξ) is the controller failure; psi (τ, ξ) is the unknown distributed load borne by the tower body; u ([ xi ]) is the given control force at the top of the column, N.
Further, since the sum of the virtual work generated at the tower top due to the control force distributed at the tower top and the potential fault of the controller and the kinetic potential energy of the tower top is equal to 0, the boundary conditions are obtained as follows:
wherein in the formula
Is a partial derivative symbol; tau is the space position of each tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; ρ is the mass of the tower bodyDensity, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the tower body, m 2 ；
Is the transverse vibration of the tower body, m;
is the tower top deflection distance, m; mu is the vibration attenuation coefficient of the tower body, NS/m 2 (ii) a Δ (ξ) is the controller failure; ψ (τ, ξ) is the unknown distributed load borne by the tower body; u ([ xi ]) is the given control force at the top of the column, N.
Further, a fault observer for observing potential faults of the controller is constructed based on the Lyapunov stability analysis theory according to the original parameters of the flexible tower body obtained in the step 1 and the data information obtained by the sensor arranged at the top of the flexible tower in the step 2,
wherein, the fault observer observes and compensates the potential fault of the controller, and the observation is represented as follows:
φ (ξ) is obtained from the differential equation:
wherein d is the sign of the full derivative;
is a partial derivative symbol;
an optional parameter that is positive; tau is the space position of each tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; rho is the towerMass density of the body, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the tower body, m 2 ；
Is the transverse vibration of the tower body, m;
is the tower top deflection distance, m;
a fault observed for the fault observer;
observing errors for a fault observer; u (ξ) is the control force given at the top of the column, N.
Further, a control algorithm is derived according to the PDE model established in step 3 and the fault observer established in step 4, and the design control algorithm is as follows:
wherein,
an optional parameter that is positive;
in the formula
Is a partial derivative symbol; i is the height of the column, m; q is the concentrated mass at the top of the column, kg; kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；
Is the transverse vibration of the tower body, m;
is the overhead deflection, m;
a fault observed for the fault observer; u ([ xi ]) is the given control force at the top of the column, N.
Further, in step 5, for different models of wind turbine generators, the actuators used include: and the hydraulic self-balancing gearbox, the pendulum damper, the liquid damper, the magnetorheological damper and the hydraulic variable pitch mechanism are arranged at the top of the tower.
Furthermore, when the actuator is a liquid damper, the liquid damper adjusts the damping of the tower body by adjusting the size of the hole in the water tank so as to reduce the vibration of the tower body;
when the actuator is a pendulum damper, the pendulum damper generates the swing opposite to the vibration direction in the tower body through a hydraulic mechanism so as to reduce the vibration of the tower body;
when the actuator is a hydraulic variable pitch mechanism, the hydraulic variable pitch mechanism reduces the influence of impact load by adjusting the angle of the blade.
The invention has the following beneficial effects:
1. the invention provides a control method for inhibiting vibration of a wind driven generator tower body based on a PDE model. Since the flexible tower may generate large vibration under the influence of distributed external loads, and the tower body may even collapse due to serious vibration, the vibration must be suppressed. The fault-tolerant control algorithm designed by the Lyapunov stability theory can ensure that the Lyapunov function energy is bounded, so that the potential energy and the kinetic energy of the flexible tower body of the wind driven generator are stabilized within a certain range, and the vibration of the flexible tower body is maintained within a certain range. Due to the complex operating environment of the wind turbine, the controller may potentially malfunction. Under the normal working condition of the controller, the real-time data measured by the sensor is acquired, the control algorithm implanted in the controller calculates the output value of the controller in real time, the output value is used as the input signal of the actuator positioned at the tower top, and after the actuator receives the signal given by the controller, the actuator generates corresponding control force according to the working principle of the actuator, so that the effect of inhibiting the vibration of the tower body is achieved, and the influence of external load on the flexible tower is reduced. When the unknown fault occurs in the controller, the fault observer is designed for observing the unknown fault and compensating the output of the controller, so that the fault tolerance of the controller is improved. The invention provides a complete solution of boundary control for the flexible tower under distributed external load, thereby reducing the influence of the external load on the flexible tower and inhibiting the vibration of the tower body.
2. The existing control method for suppressing vibration of the flexible tower is mostly based on a finite dimension ODEs model, and because the vibration state of the flexible tower is distributed, the finite dimension model cannot accurately describe the complete vibration characteristic of the flexible tower, and an infinite dimension PDE model is required to be adopted for accurate description, a controller designed based on the finite dimension model may cause instability of system overflow and failure in achieving vibration suppression. The control method designed by the invention is based on an infinite dimension PDE model, and the model can accurately describe the dynamic characteristic of the tower body vibration, so that compared with the existing control method, the control method has the advantages of no system overflow instability, higher reliability and higher practical value.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. In the drawings:
FIG. 1 is a schematic view of a wind turbine according to the present invention;
fig. 2 is a schematic diagram of the control force of the wind turbine, the distributed load, and the position of the sensor at the joint (1) between the nacelle (2) and the tower (3) according to the present invention;
FIG. 3 is a graph showing the deflection at the top of a tower controlled by the control method of the present invention;
FIG. 4 is a diagram of the lateral vibration generated at various positions of the tower top and the tower body by adopting the control method provided by the invention;
FIG. 5 is a graph of the control force applied to the top of the tower by the actuator of the present invention;
FIG. 6 is a signal diagram of a fault occurring in the controller of the present invention;
fig. 7 is a diagram of a fault signal observed by the fault observer of the present invention.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
Since the vibration of the tower body is closely related to space and time, a distributed parameter system described by partial differential equations must be adopted to accurately characterize the dynamic characteristics of the tower body. In order to avoid the possible overflow instability problem of a controller designed based on a discretization model, the invention provides a control method for inhibiting the tower body vibration of an offshore wind driven generator based on a Partial Differential Equation (PDE) model, simultaneously considers the problem of controller failure possibly caused under a complex environment, improves the fault tolerance of the controller, and provides a complete solution of boundary control for a flexible tower under distributed load, thereby reducing the influence of external load on the flexible tower and inhibiting the vibration of the tower body. Fig. 1 is a schematic view of a wind power generator, wherein, (2) is a wind power generator cabin, and (3) is a tower body of a flexible tower.
The invention provides a control method for inhibiting tower body vibration of a wind driven generator based on a PDE model, which comprises the following steps of establishing a mathematical model according to system parameters of the wind driven generator and deriving a control algorithm through the mathematical model:
step 1: and acquiring original parameters of a flexible tower body in the wind driven generator system.
Specifically, the original parameters include: the height of the flexible tower, the concentrated mass at the top of the flexible tower, the mass density of the flexible tower, the elastic modulus of the flexible tower body, the uneven moment of the flexible tower body, the uneven cross-sectional area of the flexible tower body, and the vibration attenuation coefficient of the flexible tower body.
And 2, step: a plurality of sensors are arranged at the top of the flexible tower, and data information of real-time vibration of the tower body is obtained through the sensors.
Specifically, the sensor comprises a laser displacement sensor, an inclinometer and a shear force sensor which are arranged on the top boundary of the flexible tower; the laser displacement sensor is used for collecting data information of the deflection quantity of the tower top, the inclinometer is used for collecting data information of the first partial derivative of the deflection quantity of the tower top to the space variation, and the shearing force sensor is used for collecting data information of the third partial derivative of the deflection quantity of the tower top to the space variation. As shown in fig. 2, (2) is a wind driven generator cabin, (3) is a tower body, and (1) is a joint of the wind driven generator cabin and the tower body, wherein the sensor is specifically arranged at the joint (1) of the cabin (2) and the tower body (3) on the top of the tower and is used for collecting data which is required by control and changes along with time.
And step 3: and (3) establishing a partial differential equation model (PDE) of the wind driven generator system based on the kinetic potential energy conversion and the virtual work theorem of the structural mechanics according to the original parameters of the flexible tower body obtained in the step (1) and the data information obtained by the sensor arranged at the top of the flexible tower in the step (2).
When the flexible tower body is subjected to distributed load psi (tau, xi), analyzing the natural vibration generated by the tower body under the action of the distributed load; one end of the bottom end of the tower body is fixed, virtual displacement omega (tau, xi) generated by vibration is defined, and the kinetic potential energy and the external force of the tower body are respectively obtained to do work;
wherein, the kinetic energy of tower body does:
the potential energy of the tower body is as follows:
the virtual work done by the tower damping is:
the virtual work done by the distributed load of the tower body is as follows:
the control function inhibits the virtual work done by the vibration of the tower body as follows: delta W u (ξ)＝u(ξ)δω(τ,ξ) τ＝I
Virtual work produced by the controller due to latent faults: delta W Δ (ξ)＝Δ(ξ)δω(τ,ξ) τ＝I
The sum of the virtual work done on the tower body is as follows: δ W (ξ) = δ W μ (ξ)+δW ψ (ξ)+δW u (ξ)+δW Δ (ξ)
According to the virtual work principle, the work of the external force on the virtual displacement is equal to the work of the internal force on the virtual displacement, and the following results are obtained:
E k (ξ)+E p (ξ)＝δW(ξ)
applying a Hamilton principle, considering the whole tower body to obtain a four-order non-homogeneous partial differential equation of the dynamic characteristic of the tower body, and obtaining a PDE model of the wind driven generator system, wherein the four-order non-homogeneous partial differential equation comprises the following specific components:
the boundary conditions obtained by fixing and deducing one end of the tower body are as follows:
because the sum of the virtual work generated at the tower top due to the control force distributed at the tower top and the potential fault of the controller and the kinetic potential energy of the tower top is equal to 0, the obtained boundary conditions are as follows:
data I, Q, rho, kappa, gamma (tau), theta adopted in the established model ξ (τ), μ are the original parameters determined in step one.
Wherein in the formula
Is a partial derivative symbol; delta is a variation sign; tau is the space position of each tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; rho is the mass density of the tower body, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the tower body, m 2 ；
Is the transverse vibration of the tower body, m;
is the tower top deflection distance, m; mu is the vibration attenuation coefficient of the tower body, NS/m 2 (ii) a Δ (ξ) is the controller failure; ψ (τ, ξ) is the unknown distributed load borne by the tower body; u (ξ) is the control force given at the top of the column, N.
And 4, step 4: and (3) constructing a fault observer for observing potential faults of the controller based on a Lyapunov stability analysis theory according to the original parameters of the flexible tower body obtained in the step (1) and the data information obtained by the sensor arranged at the top of the flexible tower in the step (2).
Specifically, the Lyapunov function is defined as follows:
v is an artificially designed energy function, represents the sum of the kinetic energy and potential energy of the tower body, the energy of a fault observation error of the controller and the energy of a positive definite term which is artificially designed, and the time of the Lyapunov function is subjected to derivation to obtain a derivative of the Lyapunov function
Substituting into the partial differential equation of the flexible tower. According to the Lyapunov stability theory, the V is always kept bounded, so that the kinetic energy, the potential energy and the controller fault observation error of the tower body can be kept within a certain range, and the vibration of the flexible tower body can be kept within a certain range under the condition that whether the controller has a fault or not. In order to keep V bounded all the time, a proper fault observer and a proper fault controller are designed to ensure that V is bounded all the time
Satisfy the requirement of
In the form of a constant λ > 0 and θ > 0 for any positive value. In order to maintain the vibration of the flexible tower within a certain range under the condition of controller failure, the following fault observer is designed to observe and compensate the controller failure:
φ (ξ) is obtained from the differential equation:
and 5: and (4) deducing a control algorithm according to the PDE partial differential equation model established in the step (3) and the fault observer established in the step (4), and embedding the control algorithm into a wind turbine generator controller.
The sensor monitors the vibration condition of the tower body in real time and transmits information to the controller, the output value of the controller is obtained through a software real-time calculation control algorithm in the controller, the output value of the controller is given to an actuator positioned at the top of the tower in real time to serve as an input signal, and the actuator exerts a control action on the top of the tower by receiving the input signal given by the controller, so that the vibration of the tower body is suppressed.
The control algorithm deduced in the step 5 is based on the Lyapunov stability analysis theory and the Lyapunov function in the step 4, and is designed as follows in order to keep V bounded all the time:
wherein
Wherein, the expression of the fault observer is used as a part of the control algorithm and is embedded in the controller, and the potential fault estimation value of the controller is provided for the controller and output compensation is carried out. The output value u (xi) of the controller is obtained through a software calculation control algorithm, the output value is given to an actuator positioned at the tower top in real time to serve as an input signal of the actuator, and the actuator generates a control force with the same size as the input signal u (xi) so as to inhibit the tower body vibration.
The control algorithm designed in the step 5 can be embedded into a wind driven generator controller, and physical quantities measured by the tower top laser displacement sensor, the inclinometer and the shearing force sensor are obtained in real time. Wherein, the inclinometer obtains and controls the algorithm
Information of (2), shear force sensor acquisition control algorithm
The laser displacement sensor acquires information of omega (I, xi) in the control algorithm and acquires information of omega (I, xi) in the control algorithm through a backward difference method
And
and (4) information. Selecting appropriate design parameters
A good control effect will be maintained. In the control algorithm, the control algorithm is,
the design parameters are positive design parameters which can be manually selected, and in practical application, manual selection and comparison are needed to select the optimal parameters, so that the control effect is optimal.
In the formula, I is the height of the tower, m; q is the concentrated mass at the top of the column, kg; rho is the mass density of the column, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the column body, m 2 ；
Is the transverse vibration of the tower body, m;
is the overhead deflection, m; μ is the attenuation coefficient, NS/m 2 (ii) a Δ (ξ) is the controller failure;
a fault observed by a fault observer;
observing errors for a fault observer; ψ (τ, ξ) is an unknown distributed load on the tower; u (ξ) is the control force given at the top of the column, N.
In step 5, aiming at different models of wind generating sets, the adopted actuators can be divided into: the hydraulic self-balancing gearbox, the pendulum damper, the liquid damper, the magnetorheological damper, the hydraulic variable pitch mechanism and the like are arranged at the top of the tower. The sensor monitors the vibration condition of the tower body in real time and transmits information to the control system, software in the control system calculates a control algorithm in real time to obtain an input signal of the actuator, and after the actuator receives the input signal, different actuators exert control action on the top of the tower according to the working principle of the actuators, so that the vibration of the tower body is restrained. For example: when the actuator is a liquid damper, the liquid damper adjusts the damping of the tower body by adjusting the size of the holes in the water tank so as to reduce the vibration of the tower body; when the actuator is a pendulum damper, the pendulum damper generates swing opposite to the vibration direction in the tower body through a hydraulic mechanism so as to reduce the vibration of the tower body; when the actuator is a hydraulic pitch-variable mechanism, the hydraulic pitch-variable mechanism reduces the influence of impact load and the like by adjusting the angle of the blade.
Based on the Lyapunov stability theory, the designed control algorithm and the fault observer can maintain the vibration kinetic energy and the vibration potential energy of the flexible tower body within a bounded range, so that the vibration amplitude of the flexible tower body caused by unknown load is maintained within a certain range, the fault-tolerant control can be performed on the tower body under the condition that the controller has an unknown fault, and the phenomenon that the tower body is fatigued or even collapsed possibly due to excessive vibration is avoided. The effectiveness of the proposed control method is explained with reference to fig. 3 to 7. Wherein, fig. 3 is a graph of deflection generated at the top of the tower by adopting the control method provided by the invention to control the top of the tower; FIG. 4 is a diagram of the lateral vibration generated at various positions of the tower top and the tower body by adopting the control method provided by the invention; FIG. 5 is a graph of the control force applied to the top of the tower by the actuator of the present invention; FIG. 6 is a graphical representation of a fault signal occurring in the controller of the present invention; FIG. 7 is a diagram of a fault signal observed by the fault observer of the present invention.
Fig. 3 shows that in the case of an unknown fault in the controller, the control algorithm calculates the control action that the actuator should give, and the deflection displacement of the tower top is finally kept within a small bounded range under the control action of the actuator. Fig. 4 shows that the deflection of each part of the tower under the control of the actuator is finally kept within a small, bounded range. Fig. 5 shows the control effect of the actuator on the tower top, and the actuator can still control the tower body in the case of various unknown faults of the controller. Fig. 6 and 7 show that under various fault conditions of the controller, the fault observer can accurately observe various faults occurring in the controller, and as can be known from the control algorithm expression in step 5, the expression of the fault observer is used as a part of the control algorithm, is calculated in the controller in real time, and compensates the output value of the controller in real time, so as to reduce adverse effects of the fault of the controller on the output of the controller.
In summary, the invention provides a control method for suppressing tower body vibration of a wind driven generator based on a PDE model, which establishes the PDE model of the flexible tower of the wind driven generator by measuring the original parameters of the flexible tower body of the wind driven generator and combining with the real-time data of the tower body vibration obtained by a sensor distributed at the joint of the tower body and an engine room. Since the flexible tower may generate large vibration under the influence of distributed external loads, and the tower body may even collapse due to serious vibration, the vibration must be suppressed. The fault-tolerant control algorithm designed by the Lyapunov stability theory can ensure that the energy of a Lyapunov function is bounded, so that the potential energy and the kinetic energy of the flexible tower body of the wind driven generator are stabilized within a certain range, and the vibration of the flexible tower body is maintained within a certain range. Due to the complex operating environment of the wind turbine, the controller may potentially malfunction. Under the normal working condition of the controller, the real-time data measured by the sensor is acquired, the control algorithm implanted in the controller calculates the output value of the controller in real time, the output value is used as the input signal of the actuator positioned at the tower top, and after the actuator receives the signal given by the controller, the actuator generates corresponding control force according to the working principle of the actuator, so that the effect of inhibiting the vibration of the tower body is achieved, and the influence of external load on the flexible tower is reduced. When the controller has unknown faults, the fault observer is designed for observing the unknown faults and compensating the output of the controller, so that the fault tolerance of the controller is improved. The invention provides a complete solution of boundary control for the flexible tower under distributed external load, thereby reducing the influence of the external load on the flexible tower and inhibiting the vibration of the tower body. In addition, the control method designed by the invention is based on an infinite dimension PDE model, and the model can accurately describe the dynamic characteristic of tower body vibration, so that compared with the existing control method, the control method has the advantages of no system overflow instability, higher reliability and higher practical value.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. The control method for inhibiting the tower body vibration of the wind driven generator based on the PDE model is characterized by comprising the following steps of:
step 1: acquiring original parameters of a flexible tower body in a wind driven generator system;
step 2: the flexible tower is characterized in that a plurality of sensors are distributed at the tower top of the flexible tower, and data information of real-time vibration of the tower body is acquired through the sensors;
and step 3: according to the original parameters of the flexible tower body obtained in the step 1 and data information obtained by the sensor arranged at the top of the flexible tower in the step 2, a partial differential equation model of the wind driven generator system is established based on the kinetic potential energy conversion and virtual work theorem of structural mechanics;
and 4, step 4: constructing a fault observer for observing potential faults of the controller based on a Lyapunov stability analysis theory according to the original parameters of the flexible tower body obtained in the step 1 and data information obtained by the sensor arranged at the top of the flexible tower in the step 2;
and 5: deducing a control algorithm according to the partial differential equation model established in the step 3 and the fault observer established in the step 4, and embedding the control algorithm into a wind turbine controller;
the sensor monitors the vibration condition of the tower body in real time and transmits information to the controller, the output value of the controller is obtained through a software real-time calculation control algorithm in the controller, the output value of the controller is given to the actuator positioned at the top of the tower in real time to serve as an input signal, and the actuator exerts a control action on the top of the tower by receiving the input signal given by the controller, so that the vibration of the tower body is suppressed.
2. The PDE-model-based control method for suppressing vibration of a tower body of a wind turbine generator according to claim 1, wherein the initial parameters in step 1 comprise: the height of the flexible tower, the concentrated mass at the top of the flexible tower, the mass density of the flexible tower, the elastic modulus of the flexible tower body, the uneven moment of the flexible tower body, the uneven cross-sectional area of the flexible tower body, and the vibration attenuation coefficient of the flexible tower body.
3. The PDE-model-based control method for suppressing tower vibration of a wind turbine generator as claimed in claim 1, wherein in step 2, the sensors comprise a laser displacement sensor, an inclinometer and a shear force sensor which are arranged at the top boundary of the flexible tower; the laser displacement sensor is used for acquiring data information of deflection of the tower top, the inclinometer is used for acquiring data information of primary partial derivative of deflection of the tower top to space variation, and the shearing force sensor is used for acquiring data information of tertiary partial derivative of deflection of the tower top to space variation.
4. The control method for suppressing tower body vibration of a wind driven generator according to claim 1, wherein a partial differential equation model of a wind driven generator system is established based on the kinetic potential energy conversion and virtual work theorem of structural mechanics according to the original parameters of the tower body of the flexible tower obtained in step 1 and the data information obtained by the sensor arranged at the tower top of the flexible tower in step 2, and specifically comprises:
when the flexible tower body is subjected to a distributed load psi (tau, xi), analyzing the inherent vibration generated by the tower body under the action of the distributed load; one end of the bottom end of the tower body is fixed, and virtual displacement omega (tau, xi) generated by vibration is defined to respectively obtain the kinetic potential energy and the external force of the tower body to do work;
according to the virtual work principle, the work of the external force on the virtual displacement is equal to the work of the internal force on the virtual displacement, and the following results are obtained:
E k (ξ)+E p (ξ)＝δW(ξ)
wherein E is k (xi) is the kinetic energy of the tower, E p (xi) is the potential energy of the tower body, and delta W (xi) is the sum of virtual work done on the tower body, including the towerVirtual work done by body damping, virtual work done by distributed loads of the tower body, virtual work done by suppressing vibration of the tower body by control action and virtual work produced by a controller due to potential faults;
applying a Hamilton principle, considering the whole tower body to obtain a four-order non-homogeneous partial differential equation of the dynamic characteristic of the tower body, and obtaining a PDE model of the wind driven generator system, wherein the four-order non-homogeneous partial differential equation comprises the following specific components:
wherein in the formula
Is a partial derivative symbol; tau is the space position of each tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; rho is the mass density of the tower body, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the tower body, m 2 ；
Is the transverse vibration of the tower body, m;
is the tower top deflection distance, m; mu is the damping coefficient of tower vibration, NS/m 2 (ii) a Δ (ξ) is the controller failure; ψ (τ, ξ) is the unknown distributed load borne by the tower body; u (ξ) is the control force given at the top of the column, N.
5. The control method for suppressing tower body vibration of a wind driven generator based on the PDE model according to claim 4, wherein a sum of virtual work and tower top kinetic potential energy generated at the tower top due to control force distributed at the tower top and potential failure of a controller is equal to 0, and boundary conditions are obtained as follows:
wherein, in the formula
Is a partial derivative symbol; tau is the space position of each tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; rho is the mass density of the tower body, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the column body, m 2 ；
Is the transverse vibration of the tower body, m;
is the tower top deflection distance, m; mu is the vibration attenuation coefficient of the tower body, NS/m 2 (ii) a Δ (ξ) is the controller failure; psi (τ, ξ) is the unknown distributed load borne by the tower body; u ([ xi ]) is the given control force at the top of the column, N.
6. The control method for suppressing the tower body vibration of the wind driven generator based on the PDE model according to claim 1, wherein a fault observer for observing potential faults of the controller is constructed based on the Lyapunov stability analysis theory according to the original parameters of the tower body of the flexible tower obtained in the step 1 and data information obtained by the sensor arranged at the tower top of the flexible tower in the step 2;
wherein, the fault observer observes and compensates the potential fault of the controller, and the observation and compensation are expressed as follows:
φ (ξ) is obtained from the following differential equation:
wherein d is the sign of the full derivative;
is a partial derivative symbol;
an optional parameter that is positive; tau is the space position of each tower body, m; xi is time, s; i is the height of the tower body, m; q is the concentrated mass at the top of the column, kg; rho is the mass density of the tower body, kg/m 3 (ii) a Kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；Θ ξ (τ) is the cross-sectional area of the tower body, m 2 ；
Is the transverse vibration of the tower body, m;
is the deflection distance at the top of the tower, m;
a fault observed for the fault observer;
observing errors for a fault observer; u ([ xi ]) is the given control force at the top of the column, N.
7. The control method for suppressing tower body vibration of a wind driven generator based on the PDE model according to claim 1, wherein a control algorithm is derived according to the PDE model established in step 3 and the fault observer established in step 4, and the design control algorithm is as follows:
wherein, theta, epsilon, chi and zeta > 0 are positive optional parameters;
in the formula
Is a partial derivative symbol; i is the height of the column, m; q is the concentrated mass at the top of the column, kg; kappa is the modulus of elasticity of the tower body, N/m 2 (ii) a Gamma (tau) is the moment of inertia of the tower section, m 4 ；
Is the transverse vibration of the tower body, m;
is the overhead deflection, m;
a fault observed for the fault observer; u ([ xi ]) is the given control force at the top of the column, N.
8. The PDE-model-based control method for suppressing tower vibration of a wind turbine generator as claimed in claim 1, wherein in step 5, actuators used for different types of wind turbine generator systems comprise: and the hydraulic self-balancing gearbox, the pendulum damper, the liquid damper, the magnetorheological damper and the hydraulic variable pitch mechanism are arranged at the top of the tower.
9. The PDE-model-based control method for suppressing vibration of a tower of a wind turbine generator as defined in claim 8, wherein when the actuator is a liquid damper, the liquid damper adjusts damping of the tower by adjusting the size of holes in the water tank to reduce vibration of the tower;
when the actuator is a pendulum damper, the pendulum damper generates the swing opposite to the vibration direction in the tower body through a hydraulic mechanism so as to reduce the vibration of the tower body;
when the actuator is a hydraulic pitch-variable mechanism, the hydraulic pitch-variable mechanism reduces the influence of impact load by adjusting the angle of the blade.
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