CN113051834A - Model reference-based cabin suspension system RBF neural network adaptive decoupling control method - Google Patents

Model reference-based cabin suspension system RBF neural network adaptive decoupling control method Download PDF

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CN113051834A
CN113051834A CN202110392579.0A CN202110392579A CN113051834A CN 113051834 A CN113051834 A CN 113051834A CN 202110392579 A CN202110392579 A CN 202110392579A CN 113051834 A CN113051834 A CN 113051834A
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褚晓广
周洁
蔡彬
马骢
李文玉
王伟超
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Qufu Normal University
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Abstract

The invention discloses a model reference-based adaptive decoupling control method for an RBF neural network of a suspension system of an engine room, which comprises the steps of constructing suspension models at two ends of the engine room, wherein the suspension models comprise axial and pitching two-degree-of-freedom motion, combining model reference adaptive control with the RBF neural network, designing an RBF neural network adaptive controller based on model deviation by means of the strict linear non-coupling characteristic of the reference model and the infinite approximation capability of the RBF neural network, and enabling the suspension system model to completely approximate to the reference model, thereby realizing complete decoupling. The invention greatly improves the suspension tracking, interference suppression and two-end suspension synchronization performance of the engine room, is beneficial to yaw wind under the suspension of the wind power engine room, and has stronger guiding significance for multi-point suspension control of heavier suspended matters.

Description

Model reference-based cabin suspension system RBF neural network adaptive decoupling control method
Technical Field
The invention relates to a model reference-based adaptive decoupling control method for a Radial Basis Function (RBF) neural network of a nacelle suspension system, in particular to a yaw wind alignment method applied to a horizontal axis wind power generation system after a nacelle is stably suspended, solving the problem that the nacelle is easy to pitch due to the difference of windward areas of a blade side and a tail wing side, and belonging to the field of wind power generation magnetic suspension.
Background
A horizontal axis wind power generation system is a popular type of a wind power system, a traditional wind power yaw device adopts a mechanical coupling type yaw structure, and the problems of high friction power consumption, poor wind alignment precision, high failure rate and the like exist. Because the suspension working condition of the nacelle is bad, the wind speed and the wind direction are time-varying, the quality of the blade side and the empennage side of the nacelle is not completely the same, so that the nacelle is very easy to pitch, the operation safety of the wind turbine generator is seriously influenced, how to improve the axial suspension stability of the nacelle, effectively inhibit the pitching of the nacelle and improve the synchronization performance of the suspension system is the key to the suspension stability of the wind turbine generator, although the patent 202010552436 adopts a synchronization control method to reduce the synchronization error at the two ends of the nacelle so that the wind turbine generator has certain anti-interference capability, but does not completely solve the problem of the coupling of the blade side and the empennage side of the nacelle, for the decoupling control of the suspension system, the traditional distributed PID plus cross coupling control and linearization decoupling method requires that a controlled system must adopt an accurate mathematical model for description, the suspension stability and yaw wind accuracy of the wind power cabin are severely limited.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a model reference-based adaptive decoupling control method for an RBF neural network of a nacelle suspension system, which converts coupling suspension systems at two ends of a nacelle into single-ended suspension independent control, constructs a single-ended suspension linear decoupling model, infinitely approaches the single-ended suspension linear decoupling model of the nacelle single-ended suspension system by virtue of the infinite approximation capability of the RBF neural network, realizes decoupling and interference suppression of the suspension systems at two ends of the nacelle and provides a suspension current reference for a suspension converter; the single-ended suspension linear decoupling model adopts a three-order linear non-coupling stable system model; the single-ended suspension independent control is realized by introducing an RBF neural network on the basis of model reference adaptive control and designing an RBF neural network adaptive controller and a linear tracking controller based on model reference; the RBF neural network self-adaptive controller based on model reference adopts 5 hidden layer neuron structures, designs a self-adaptive law of RBF neural network weight based on model deviation, a first derivative of the model deviation and a second derivative of the model deviation of a suspension system at two ends of an engine room and a linear decoupling model, and performs optimization adjustment of the network weight on line; the effective reference input of the linear tracking controller is composed of a suspension air gap reference sum and an output of the RBF neural network self-adaptive controller, the suspension air gap feedback is easy, a suspension air gap tracking error, an error first derivative and a tracking error second derivative are generated to serve as state feedback control inputs, the suspension tracking control of the engine room is completed, and the suspension decoupling at two ends and the suspension synchronous control at two ends are realized. The method comprises the following steps:
step 1, constructing an equation of motion with two degrees of freedom of axial direction and pitching
Figure BDA0003017334830000011
Where ω is the pitch angular velocity,
Figure BDA0003017334830000012
to a pitch angle, FA、FBRespectively, independent suspension suction on two sides, J is the pitching moment of inertia of the cabin, m is the mass of the wind power cabin, g is the gravity acceleration, delta is the axial suspension air gap, fdFor axial disturbances of the nacelle, TsThe overturning moment of the engine room, and r is the rotating radius of the engine room.
Step 2, constructing a suspension force equation at two ends of the engine room
Figure BDA0003017334830000021
In the formula, mu0For vacuum permeability, N is the number of turns of the suspension windings on both sides, S is the area of the magnetic pole, and deltaA、iAIs the blade side suspension air gap, suspension current, deltaB、iBThe tail side suspension air gap and suspension current.
Step 3, converting the suspension dynamic models at two ends of the fan engine room
Firstly, converting a two-degree-of-freedom motion equation of the formula (1) into a front-rear-side air gap motion equation by adopting coordinate transformation
Figure BDA0003017334830000022
Second step, based on (delta)0，i0) Converting the formula (3) into a linear dynamic model at two ends of the engine room:
Figure BDA0003017334830000023
in the formula, delta0Is the air gap between the levitation winding and the nacelle at the balance point, i0To balance the levitation current flowing through the levitation winding at the point,
Figure BDA0003017334830000024
Δ f is the higher order term after linearization.
Thirdly, the derivation is carried out on the formula (4) to obtain
Figure BDA0003017334830000025
And fourthly, because the inner ring suspension current is controlled by the suspension converter, for the convenience of research, the suspension winding coil is modeled, namely the suspension winding coil is replaced by a resistor and an inductor which are connected in series. According to the law of electromagnetic induction and kirchhoff law of circuits, the voltage equation of the suspension winding of the unilateral cabin is u (t) ═ ri (t) + d ψ (t)/dt, and the air-gap magnetic field ψ can be shownShown as psi-Li-N phimTherefore, the dynamic model of the levitation current transformer can be expressed as:
Figure BDA0003017334830000026
in the formula, R and L are respectively equivalent resistance and equivalent inductance in the suspension converter.
And fifthly, assuming that parameters such as resistance, inductance and the like in the suspension converter do not change in the process of suspending the nacelle, the method can be represented by formula (6)
Figure BDA0003017334830000028
Comprises the following steps:
Figure BDA0003017334830000027
sixthly, when the suspension cabin is in a balanced state, the acceleration is zero, namely
Figure BDA0003017334830000031
Then, it can be obtained from equation (4):
Figure BDA0003017334830000032
seventh, in combination with formulas (7) and (8), formula (5) can be converted to:
Figure BDA0003017334830000033
step eight, the cross coupling term, the axial disturbance term and the pitching disturbance term in the formula are summarized as system uncertainty terms respectively
Figure BDA0003017334830000034
Figure BDA0003017334830000035
Equation (9) can be simplified to the following form:
Figure BDA0003017334830000036
step 4, selecting single-ended suspension linear decoupling model
Firstly, constructing a linear system model as an expected model of a suspension system at two ends of a cabin, wherein the expected model is represented as follows:
Figure BDA0003017334830000037
in the second step, as can be seen from equation (11), the expected model is a completely linear and uncoupled model, and its differential equation can be described as:
Figure BDA0003017334830000038
in the formula, Am，BmIs an expected constant; r is a reference air gap input, and the expected model state variable is consistent with the model state variable of the suspension system, namely Xm＝X。
Thirdly, in order to ensure good tracking performance, ξ is equal to 0.8, omeganIf 70, the coefficient matrix in equation (12) is:
Figure BDA0003017334830000039
at the same time, the dominant pole s of the desired model can be obtained060, and a pole s1＝-70+2.48×10-8i，s2＝-70-2.48×10-8i, it is clear that the three poles of the desired model are all distributed in the left half-plane and there is no overshoot, proving that the linear system taken is asymptotically stable.
Step 5, designing a RBF neural network self-adaptive controller and a linear tracking controller based on model reference
First, take side A as an example when designing a controller, set state variables
Figure BDA0003017334830000041
u is the control input, then the state space equation for single-ended suspension independent control can be written as:
Figure BDA0003017334830000042
in the formula, K is a parameter matrix of the linear controller and can be obtained by an ideal model by referring to the adaptive decoupling matching condition of the RBF neural network.
And step two, as can be seen from the selection of the single-ended suspension linear decoupling model in the step 4, the differential equation of the expected model of the single-ended suspension system of the cabin is as follows:
Figure BDA0003017334830000043
thirdly, an adaptive controller of the RBF neural network based on model reference is adopted to enable the model of the single-ended suspension system of the engine room to approach an expected model, the RBF neural network outputs real-time adjustment reference air gap and feedback air gap, and the RBF neural network approaches the composite uncertain disturbance term of the suspension system to phi*Existence of an ideal neural network weight vector θ*To make
Φ*＝θ*Th(x)+ε (16)
In the formula, h (x) is a radial basis function vector, epsilon is a neural network approximation error, and the condition that | epsilon | is less than or equal to epsilon |0。
Fourthly, combining formula (16), and converting the state space description of the single-side suspension system model into:
Figure BDA0003017334830000044
the fifth step is to get
Figure BDA0003017334830000045
The control target needs to design a control law:
u＝K(Xref-X+Φ*) (18)
where K is the linear controller feedback gain.
Sixth, formula (18) is substituted for formula (17) to obtain:
Figure BDA0003017334830000046
seventh, compare equation (19) with the expected reference dynamic equation (15), and for the controller to exist as equation (18), the ideal control gain must satisfy the matching condition
A-BK＝Am
BKXref＝Bmr (20)
And eighthly, assuming that the matching conditions are satisfied, a closed-loop system which is the same as the reference model can be obtained by using the equation (20), so that the fixed gain controller equation (20) ensures the global consistent progressive tracking performance for any bounded reference input signal. The value of the parameter matrix K of the linear tracking controller in this chapter can be obtained by the formula (20), wherein BK is A-Am. Wherein A, B are defined by formula (14), AmDefined by equation (15), then:
Figure BDA0003017334830000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003017334830000052
the ninth step, the linear tracking controller parameter matrix K obtained from equation (21) is:
Figure BDA0003017334830000053
defining the difference value between the expected output air gap and the output air gap of the two-point suspension system as a state tracking error, wherein the state tracking error is E (t) Xm(t) -x (t), the state tracking error e (t) being input to the RBF neural network adaptive controller, and the control target being t → ∞ time, the state tracking error e (t) → 0. Order to
Figure BDA0003017334830000054
As a weight theta of the neural network*Then the output of the RBF neural network is:
Figure BDA0003017334830000055
in the eleventh step, the suspension system control law can be written as:
Figure BDA0003017334830000056
the tenth step, in combination with formula (15), formula (17), formula (20) and formula (24), may yield e (t) ═ XmClosed loop dynamics of (t) -x (t):
Figure BDA0003017334830000057
the thirteenth step, get
Figure BDA0003017334830000058
Then
Figure BDA0003017334830000059
And fourteenth, constructing a Lyapunov function of the closed-loop system as follows:
Figure BDA00030173348300000510
wherein, alpha is a normal number,
Figure BDA00030173348300000511
the matrix P being positive definiteMatrix and satisfy Am TP+PAm＝-Q。
In the fifteenth step, the derivation of equation (27) can be:
Figure BDA0003017334830000061
sixthly, adaptively obtaining the weight
Figure BDA0003017334830000062
A seventeenth step, in which formula (31) is combined, formula (30) is converted to:
Figure BDA0003017334830000063
due to the fact that
Figure BDA0003017334830000064
The RBF neural network can be designed to have an approximation error epsilon small enough to ensure that
Figure BDA0003017334830000065
The model reference-based adaptive decoupling control method for the RBF neural network of the engine room suspension system comprises the following five working steps, wherein the coordinate transformation equation in the step 3 is as follows:
Figure BDA0003017334830000066
in the formula, deltaABlade-side suspension air gap, δBIs a tail wing side suspension air gap, and r is the radius of a suspension cabin.
The conversion method is to solve the second derivative of the coordinate conversion equation (20) as
Figure BDA0003017334830000067
The invention has the beneficial effects that:
1) the design of the controller does not depend on an accurate mathematical model of a suspension system, and the suspension system model is completely close to the reference model by means of the strict linear coupling-free characteristic of the reference model and the infinite approaching capability of the RBF neural network, so that complete decoupling is realized, pitching moment is effectively inhibited, and synchronous errors at two ends of the cabin are greatly reduced.
2) The provided linear tracking controller takes the decoupled suspension system as reference to complete suspension tracking control, and greatly improves the suspension stability of the wind power engine room.
Drawings
FIG. 1 is a schematic diagram of a horizontal axis wind yaw system nacelle suspension structure of the model reference-based nacelle suspension system RBF neural network adaptive decoupling control method.
FIG. 2 is a horizontal axis wind yaw system nacelle suspension control structure diagram of the model reference-based nacelle suspension system RBF neural network adaptive decoupling control method.
FIG. 3 is an experimental diagram of the tracking of the variable air gap of the cabin air gap under the control and PID control of the model reference-based RBF neural network adaptive decoupling control method of the cabin suspension system.
FIG. 4 is an experimental diagram of axial disturbance force applied by the nacelle under PID control.
FIG. 5 is an experimental graph of axial disturbance force applied to a cabin under the control of the model reference-based cabin suspension system RBF neural network adaptive decoupling control method.
Fig. 6 is an experimental diagram of the pitching interference force applied by the nacelle under the PID control.
FIG. 7 is an experimental graph of a cabin applied pitching interference force under the control of a model reference-based cabin suspension system RBF neural network adaptive decoupling control method.
In the figure: 1-a fan blade, 2-a fan cabin, 3-a yaw stator, 4-a front side winding, 5-a rear side winding, 6-a front side air gap sensor, 7-a rear side air gap sensor, 8-a tower, 9, 10-a linear decoupling model, 11-a blade side RBF neural network self-adaptive controller, 12-a blade side neural network weight self-adaptive law, 13, 16-li Kati equation, 14-a tail side RBFNMN controller, 15-a tail side neural network weight self-adaptive law, 17-a blade side linear tracking controller, 18-a tail side linear tracking controller, 19-a blade side current tracking controller, 20-a blade side suspension converter, 21-a tail side current tracking controller, 22-a tail side suspension converter, 23-model suspension at both ends of the nacelle.
Detailed Description
The model reference-based cabin suspension system RBF neural network self-adaptive decoupling control method comprises the steps of converting coupled suspension systems at two ends of a cabin into single-ended suspension independent control, constructing single-ended suspension linear decoupling models (9 and 10), infinitely approaching the cabin single-ended suspension system to the single-ended suspension linear decoupling model by means of the infinite approaching capacity of the RBF neural network, achieving decoupling and interference suppression of the cabin two-end suspension systems, and providing suspension current reference for suspension converters (19, 20, 21 and 22); the single-ended suspension linear decoupling models (9 and 10) adopt a three-order linear non-coupling stable system model; the single-ended suspension independent control (9, 11, 12, 13, 17 or 10, 14, 15, 16, 18) is realized by introducing an RBF neural network on the basis of model reference adaptive control and designing an RBF neural network adaptive controller and a linear tracking controller based on model reference; the model reference-based RBF neural network adaptive controller (11, 12, 13, 14, 15, 16) adopts 5 hidden layer neuron structures, designs an adaptive law of RBF neural network weights based on model deviation, a model deviation first derivative and a model deviation second derivative of a suspension system at two ends of an engine room and a linear decoupling model, and performs optimization adjustment of the network weights on line; effective reference input of the linear tracking controllers (17 and 18) is composed of suspension air gap reference and RBF neural network self-adaptive controller output, suspension air gap feedback is easy, suspension air gap tracking error, error first derivative and tracking error second derivative are generated to serve as state feedback control input, suspension tracking control of the engine room is completed, and suspension decoupling at two ends and synchronous control at two ends are achieved. Comprises the following steps.
Step 1, constructing an equation of motion with two degrees of freedom of axial direction and pitching
Figure BDA0003017334830000071
Where ω is the pitch angular velocity,
Figure BDA0003017334830000081
to a pitch angle, FA、FBRespectively, independent suspension suction on two sides, J is the pitching moment of inertia of the cabin, m is the mass of the wind power cabin, g is the gravity acceleration, delta is the axial suspension air gap, fdFor axial disturbances of the nacelle, TsThe overturning moment of the engine room, and r is the rotating radius of the engine room.
Step 2, constructing a suspension force equation at two ends of the engine room
Figure BDA0003017334830000082
In the formula, mu0For vacuum permeability, N is the number of turns of the suspension windings on both sides, S is the area of the magnetic pole, and deltaA、iAIs the blade side suspension air gap, suspension current, deltaB、iBThe tail side suspension air gap and suspension current.
Step 3, converting the suspension dynamic models at two ends of the fan engine room
Firstly, converting a two-degree-of-freedom motion equation of the formula (1) into a front-rear-side air gap motion equation by adopting coordinate transformation
Figure BDA0003017334830000083
Second step, based on (delta)0，i0) Converting the formula (3) into a linear dynamic model at two ends of the engine room:
Figure BDA0003017334830000084
in the formula, delta0Is the air gap between the levitation winding and the nacelle at the balance point, i0To balance the levitation current flowing through the levitation winding at the point,
Figure BDA0003017334830000085
Δ f is the higher order term after linearization.
Thirdly, the derivation is carried out on the formula (4) to obtain
Figure BDA0003017334830000086
And fourthly, because the inner ring suspension current is controlled by the suspension converter, for the convenience of research, the suspension winding coil is modeled, namely the suspension winding coil is replaced by a resistor and an inductor which are connected in series. According to the law of electromagnetic induction and kirchhoff law of circuits, the voltage equation of the levitation winding of the single-sided cabin is u (t) ═ ri (t) + d ψ (t)/dt, and the air-gap magnetic field ψ is represented by Li ═ N Φ ψmTherefore, the dynamic model of the levitation current transformer can be expressed as:
Figure BDA0003017334830000087
in the formula, R and L are respectively equivalent resistance and equivalent inductance in the suspension converter,
and fifthly, assuming that parameters such as resistance and inductance in the levitation current transformer do not change in the process of suspending the nacelle, the value represented by formula (6) is:
Figure BDA0003017334830000091
sixthly, when the suspension cabin is in a balanced state, the acceleration is zero, namely
Figure BDA0003017334830000092
Then can be free(4) Obtaining:
Figure BDA0003017334830000093
seventh, in combination with formulas (7) and (8), formula (5) can be converted to:
Figure BDA0003017334830000094
step eight, the cross coupling term, the axial disturbance term and the pitching disturbance term in the formula are summarized as system uncertainty terms respectively
Figure BDA0003017334830000095
Figure BDA0003017334830000096
Equation (9) can be simplified to the following form:
Figure BDA0003017334830000097
step 4, selecting single-ended suspension linear decoupling model
Firstly, constructing a linear system model as an expected model of a suspension system at two ends of a cabin, wherein the expected model is represented as follows:
Figure BDA0003017334830000098
in the second step, as can be seen from equation (11), the expected model is a completely linear and uncoupled model, and its differential equation can be described as:
Figure BDA0003017334830000099
in the formula, Am，BmIs an expected constant; r is a reference air gap input, and the expected model state variable is consistent with the model state variable of the suspension system, namely Xm＝X。
Thirdly, in order to ensure good tracking performance, ξ is equal to 0.8, omeganIf 70, the coefficient matrix in equation (12) is:
Figure BDA0003017334830000101
at the same time, the dominant pole s of the desired model can be obtained060, and a pole s1＝-70+2.48×10-8i，s2＝-70-2.48×10-8i, it is clear that the three poles of the desired model are all distributed in the left half-plane and there is no overshoot, proving that the linear system taken is asymptotically stable.
Step 5, designing a RBF neural network self-adaptive controller and a linear tracking controller based on model reference
First, take side A as an example when designing a controller, set state variables
Figure BDA0003017334830000102
u is the control input, then the state space equation for single-ended suspension independent control can be written as:
Figure BDA0003017334830000103
in the formula, K is a parameter matrix of the linear controller and can be obtained by an ideal model by referring to the adaptive decoupling matching condition of the RBF neural network.
And step two, as can be seen from the selection of the single-ended suspension linear decoupling model in the step 4, the differential equation of the expected model of the single-ended suspension system of the cabin is as follows:
Figure BDA0003017334830000104
thirdly, adopting model reference-based RBF neural network self-adaptationThe controller is used for enabling the model of the single-ended suspension system of the engine room to approach an expected model, enabling the RBF neural network to output real-time regulation reference air gaps and feedback air gaps, and enabling the RBF neural network to approach the composite uncertain disturbance term of the suspension system to phi*Existence of an ideal neural network weight vector θ*To make
Φ*＝θ*Th(x)+ε (16)
In the formula, h (x) is a radial basis function vector, epsilon is a neural network approximation error, and the condition that | epsilon | is less than or equal to epsilon |0。
Fourthly, combining formula (16), and converting the state space description of the single-side suspension system model into:
Figure BDA0003017334830000105
the fifth step is to get
Figure BDA0003017334830000106
The control target needs to design a control law:
u＝K(Xref-X+Φ*) (18)
where K is the linear controller feedback gain.
Sixth, formula (18) is substituted for formula (17) to obtain:
Figure BDA0003017334830000107
seventh, compare equation (19) with the expected reference dynamic equation (15), and for the controller to exist as equation (18), the ideal control gain must satisfy the matching condition
Figure BDA0003017334830000108
Eighth, assuming these matching conditions are true, a closed loop system identical to the reference model is obtained using equation (20), thus, for any bounded reference input signal, fixed gain controller equation (20) ensures full coverageLocal consistent progressive tracking performance. The value of the parameter matrix K of the linear tracking controller in this chapter can be obtained by the formula (20), wherein BK is A-Am. Wherein A, B are defined by formula (14), AmDefined by equation (15), then:
Figure BDA0003017334830000111
in the formula (I), the compound is shown in the specification,
Figure BDA0003017334830000112
the ninth step, the linear tracking controller parameter matrix K obtained from equation (21) is:
Figure BDA0003017334830000113
defining the difference value between the expected output air gap and the output air gap of the two-point suspension system as a state tracking error, wherein the state tracking error is E (t) Xm(t) -x (t), the state tracking error e (t) being input to the RBF neural network adaptive controller, and the control target being t → ∞ time, the state tracking error e (t) → 0. Order to
Figure BDA0003017334830000114
As a weight theta of the neural network*Then the output of the RBF neural network is:
Figure BDA0003017334830000115
in the eleventh step, the suspension system control law can be written as:
Figure BDA0003017334830000116
the tenth step, in combination with formula (15), formula (17), formula (20) and formula (24), may yield e (t) ═ XmClosed loop dynamics of (t) -x (t):
Figure BDA0003017334830000117
the thirteenth step, get
Figure BDA0003017334830000118
Then
Figure BDA0003017334830000119
And fourteenth, constructing a Lyapunov function of the closed-loop system as follows:
Figure BDA00030173348300001110
wherein, alpha is a normal number,
Figure BDA00030173348300001111
the matrix P is a symmetric positive definite matrix and satisfies Am TP+PAm＝-Q。
In the fifteenth step, the derivation of equation (27) can be:
Figure BDA0003017334830000121
sixthly, adaptively obtaining the weight
Figure BDA0003017334830000122
A seventeenth step, in which formula (31) is combined, formula (30) is converted to:
Figure BDA0003017334830000123
due to the fact that
Figure BDA0003017334830000124
The RBF neural network can be designed to have an approximation error epsilon small enough to ensure that
Figure BDA0003017334830000125
The model reference-based adaptive decoupling control method for the RBF neural network of the engine room suspension system comprises the following five working steps, wherein the coordinate transformation equation in the step 3 is as follows:
Figure BDA0003017334830000126
in the formula, deltaABlade-side suspension air gap, δBIs a tail wing side suspension air gap, and r is the radius of a suspension cabin.
The conversion method is to solve the second derivative of the coordinate conversion equation (20) as
Figure BDA0003017334830000127
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The suspension parameters of the wind power magnetic suspension yaw system cabin are shown in table 1, the suspension weight of the cabin is 484kg, the total number of turns of the suspension windings is 930 turns, the number of turns of the front side winding and the rear side winding is 465 turns, the rotating radius of the cabin is 360mm, the power of each of the two suspension converters is 1kW, the suspension air gap sensor adopts an eddy current displacement sensor, the precision is 0.27v/mm, the following 3 examples are respectively carried out, namely an air gap variable tracking experiment, an axial interference force application experiment and an anti-pitching moment experiment are respectively carried out, and the effective effects of the invention are explained.
TABLE 1 wind power magnetic suspension yaw system cabin suspension system parameters
Figure BDA0003017334830000131
Example a variable air gap tracking experiment, as shown in fig. 3, the chamber starts to float when t is 0s, the initial levitation reference height is set to 13mm, the levitation height reference value is switched to 15mm when t is 4s, the levitation height reference value is switched back to the initial levitation reference value when t is 15s, and the variable air gap tracking performance comparison table is shown in table 2. When t is more than or equal to 0s and less than 4s, the engine room is in a suspension starting stage, the suspension starting time and the steady state fluctuation value of the engine room are mainly considered, the starting time controlled by the method is 0.2s, the steady state fluctuation value is 0.0099mm, and the fluctuation is smaller than that of the steady state suspension height of a PID controller; the suspension switching time and the overshoot of the engine room are mainly considered in the suspension height switching stage of the engine room with t being more than or equal to 4s and less than 15s, the reference switching stable time controlled by the method is 0.2s, and the overshoot is avoided. Therefore, the control of the invention not only obviously improves the dynamic performance of the suspension system, but also greatly reduces the overshoot and the steady-state error, and achieves good decoupling control effect on the suspension systems at two ends of the engine room.
TABLE 2 variable air gap tracking Performance
Figure BDA0003017334830000132
Example two-axial disturbance force application experiments, as shown in fig. 4 and 5, an initial levitation height reference value of a nacelle is set to 13mm, 1000N of axial downward force disturbance is applied to one side of a levitation system when t is 4s to simulate axial disturbance of external wind to the nacelle, the axial downward force disturbance is cancelled when t is 15s, the maximum drop value and the drop rise time of the disturbed nacelle and the maximum rise value and the regression stability time of the disturbed nacelle are observed, and the axial disturbance resistance performance of the one-side nacelle is shown in table 3. It can be seen that when the suspension cabin is disturbed on one side at t-4 s and t-15 s, the maximum drop value controlled by the method is 0.0194mm, the suspension cabin can return to the initial suspension height after 0.1s, the maximum drop value is smaller and the drop return time is shorter than that controlled by a PID (proportion integration differentiation), the response speed of a suspension system is effectively improved, and the suspension cabin has better axial disturbance resistance.
TABLE 3 comparison of axial disturbance force application Performance
Figure BDA0003017334830000133
Example three anti-pitching moment experiments, as shown in fig. 6 and 7, analyze the synchronization performance of the suspension control on two sides of the nacelle; setting the initial suspension height reference value of the cabin to be 13mm, applying 1000N pitching moment disturbance to one side of the suspension system when t is 4s to simulate external crosswind interference, canceling the pitching moment disturbance when t is 15s, and observing the maximum falling value and falling rise time of the cabin after disturbance and the maximum rise value and return stabilization time after disturbance cancellation. The single-sided nacelle pitch disturbance resistance performance vs. ratio is shown in table 4. It can be seen that when the suspension cabin is disturbed on one side at t 4s and t 15s, the traditional controller is directly out of control, and the inclination of the suspension cabin cannot stably return to the initial suspension height at the moment, but the maximum drop of the suspension cabin is controlled to be 0.044mm, so that the suspension cabin can return to the initial suspension height after 0.2s, therefore, the drop value is smaller and the drop return time is shorter when the suspension system is controlled, the response speed of the suspension system is effectively improved, the suspension cabin has better disturbance resistance, and the difference of air gaps on two sides of the suspension cabin can be quickly stabilized.
TABLE 4 comparison table of single-sided interference performance
Figure BDA0003017334830000141

Claims (3)

1. Model reference-based adaptive decoupling control method for RBF neural network of engine room suspension system, which is characterized by comprising the following steps: the coupling suspension systems at the two ends of the engine room are converted into single-ended suspension independent control, a single-ended suspension linear decoupling model is constructed, the infinite approximation capability of the RBF neural network is used for carrying out infinite approximation on the single-ended suspension system of the engine room to the single-ended suspension linear decoupling model, decoupling and interference suppression of the suspension systems at the two ends of the engine room are realized, and meanwhile, a suspension current reference is provided for the suspension converter; the single-ended suspension linear decoupling model adopts a three-order linear non-coupling stable system model; the single-ended suspension independent control is realized by introducing an RBF neural network on the basis of model reference adaptive control and designing an RBF neural network adaptive controller and a linear tracking controller based on model reference; the RBF neural network self-adaptive controller based on model reference adopts 5 hidden layer neuron structures, designs a self-adaptive law of RBF neural network weight based on model deviation, a first derivative of the model deviation and a second derivative of the model deviation of a suspension system at two ends of an engine room and a linear decoupling model, and performs optimization adjustment of the network weight on line; the effective reference input of the linear tracking controller is composed of suspension air gap reference and output of the RBF neural network self-adaptive controller, suspension air gap feedback is easy, suspension air gap tracking errors, first-order error derivatives and second-order tracking error derivatives are generated to serve as state feedback control input, suspension tracking control of the engine room is completed, and suspension decoupling at two ends and synchronous control at two ends are achieved.
2. The model reference-based adaptive decoupling control method for the RBF neural network of the nacelle suspension system based on the model reference of claim 1, comprising the following steps:
step 1, constructing an equation of motion with two degrees of freedom of axial direction and pitching
Figure FDA0003017334820000011
Where ω is the pitch angular velocity,
Figure FDA0003017334820000012
to a pitch angle, FA、FBRespectively, independent suspension suction on two sides, J is the pitching moment of inertia of the cabin, m is the mass of the wind power cabin, g is the gravity acceleration, delta is the axial suspension air gap, fdFor axial disturbances of the nacelle, TsThe moment of overturning the engine room, and r is the rotating radius of the engine room;
step 2, constructing a suspension force equation at two ends of the engine room
Figure FDA0003017334820000013
In the formula, mu0For vacuum permeability, N is the number of turns of the suspension windings on both sides, S is the area of the magnetic pole, and deltaA、iAIs the blade side suspension air gap, suspension current, deltaB、iBThe tail wing side suspension air gap and suspension current are adopted;
step 3, converting the suspension dynamic models at two ends of the fan engine room
Firstly, converting a two-degree-of-freedom motion equation of the formula (1) into a front-rear-side air gap motion equation by adopting coordinate transformation
Figure FDA0003017334820000014
Second step, based on (delta)0，i0) Converting the formula (3) into a linear dynamic model at two ends of the engine room:
Figure FDA0003017334820000021
in the formula, delta0Is the air gap between the levitation winding and the nacelle at the balance point, i0To balance the levitation current flowing through the levitation winding at the point,
Figure FDA0003017334820000022
Δ f is a linearized higher order term;
thirdly, the derivation is carried out on the formula (4) to obtain
Figure FDA0003017334820000023
Fourthly, because the inner ring suspension current is controlled by the suspension converter, for research convenience, the suspension winding coil is modeled, namely the suspension winding coil is replaced by a resistor and an inductor which are connected in series, and the suspension of the single-side engine room can be known according to the electromagnetic induction law and the kirchhoff law of the circuitThe winding voltage equation is u (t) ═ ri (t) + d ψ (t)/dt, and the air-gap magnetic field ψ can be expressed as ψ ═ Li ═ N Φ (t)/dtmTherefore, the dynamic model of the levitation current transformer can be expressed as:
Figure FDA0003017334820000024
in the formula, R and L are respectively equivalent resistance and equivalent inductance in the suspension converter;
and fifthly, assuming that parameters such as resistance, inductance and the like in the suspension converter do not change in the process of suspending the nacelle, the method can be represented by formula (6)
Figure FDA0003017334820000029
Comprises the following steps:
Figure FDA0003017334820000025
sixthly, when the suspension cabin is in a balanced state, the acceleration is zero, namely
Figure FDA0003017334820000026
Then, it can be obtained from equation (4):
Figure FDA0003017334820000027
seventh, in combination with formulas (7) and (8), formula (5) can be converted to:
Figure FDA0003017334820000028
step eight, the cross coupling term, the axial disturbance term and the pitching disturbance term in the formula are summarized as system uncertainty terms respectively
Figure FDA0003017334820000031
Figure FDA0003017334820000032
Equation (9) can be simplified to the following form:
Figure FDA0003017334820000033
step 4, selecting single-ended suspension linear decoupling model
Firstly, constructing a linear system model as an expected model of a suspension system at two ends of a cabin, wherein the expected model is represented as follows:
Figure FDA0003017334820000034
in the second step, as can be seen from equation (11), the expected model is a completely linear and uncoupled model, and its differential equation can be described as:
Figure FDA0003017334820000035
in the formula, Am，BmFor the desired constant, r is the reference air gap input, the desired model state variable is consistent with the model state variable of the suspension system, i.e., Xm＝X；
Thirdly, in order to ensure good tracking performance, ξ is equal to 0.8, omeganIf 70, the coefficient matrix in equation (12) is:
Figure FDA0003017334820000036
at the same time, the dominant pole s of the desired model can be obtained060, and a pole s1＝-70+2.48×10-8i，s2＝-70-2.48×10-8i, it is clear that the three poles of the desired model are all distributed in the left half-plane and are free of overshoot, proving the linear system takenThe system is asymptotically stable;
step 5, designing a RBF neural network self-adaptive controller and a linear tracking controller based on model reference
First, take side A as an example when designing a controller, set state variables
Figure FDA0003017334820000037
u is the control input, then the state space equation for single-ended suspension independent control can be written as:
Figure FDA0003017334820000038
in the formula, K is a parameter matrix of the linear controller and can be obtained by an ideal model by referring to RBF neural network adaptive decoupling matching conditions;
and step two, as can be seen from the selection of the single-ended suspension linear decoupling model in the step 4, the differential equation of the expected model of the single-ended suspension system of the cabin is as follows:
Figure FDA0003017334820000039
thirdly, an adaptive controller of the RBF neural network based on model reference is adopted to enable the model of the single-ended suspension system of the engine room to approach an expected model, the RBF neural network outputs real-time adjustment reference air gap and feedback air gap, and the RBF neural network approaches the composite uncertain disturbance term of the suspension system to phi*Existence of an ideal neural network weight vector θ*To make
Φ*＝θ*Th(x)+ε (16)
In the formula, h (x) is a radial basis function vector, epsilon is a neural network approximation error, and the condition that | epsilon | is less than or equal to epsilon |0；
Fourthly, combining formula (16), and converting the state space description of the single-side suspension system model into:
Figure FDA0003017334820000041
the fifth step is to get
Figure FDA0003017334820000042
The control target needs to design a control law:
u＝K(Xref-X+Φ*) (18)
in the formula, K is the feedback gain of the linear controller;
sixth, formula (18) is substituted for formula (17) to obtain:
Figure FDA0003017334820000043
seventh, compare equation (19) with the expected reference dynamic equation (15), and for the controller to exist as equation (18), the ideal control gain must satisfy the matching condition
Figure FDA0003017334820000044
And an eighth step of assuming that the matching conditions are satisfied, obtaining a closed-loop system which is the same as the reference model by using the formula (20), so that the fixed gain controller formula (20) ensures the global consistent progressive tracking performance for any bounded reference input signal, and the formula (20) can obtain the value of a parameter matrix K of the linear tracking controller in the current chapter, wherein BK is A-AmWherein A and B are defined by formula (14), AmDefined by equation (15), then:
Figure FDA0003017334820000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003017334820000046
the ninth step, the linear tracking controller parameter matrix K obtained from equation (21) is:
Figure FDA0003017334820000047
defining the difference value between the expected output air gap and the output air gap of the two-point suspension system as a state tracking error, wherein the state tracking error is E (t) Xm(t) -x (t), the state tracking error e (t) being input to the adaptive controller for RBF neural network, the control target being such that when t → ∞ is reached, the state tracking error e (t) → 0, and the control unit commands
Figure FDA0003017334820000048
As a weight theta of the neural network*Then the output of the RBF neural network is:
Figure FDA0003017334820000049
in the eleventh step, the suspension system control law can be written as:
Figure FDA00030173348200000410
the tenth step, in combination with formula (15), formula (17), formula (20) and formula (24), may yield e (t) ═ XmClosed loop dynamics of (t) -x (t):
Figure FDA0003017334820000051
the thirteenth step, get
Figure FDA0003017334820000052
Then
Figure FDA0003017334820000053
And fourteenth, constructing a Lyapunov function of the closed-loop system as follows:
Figure FDA0003017334820000054
wherein, alpha is a normal number,
Figure FDA0003017334820000055
the matrix P is a symmetric positive definite matrix and satisfies Am TP+PAm＝-Q；
In the fifteenth step, the derivation of equation (27) can be:
Figure FDA0003017334820000056
sixthly, adaptively obtaining the weight
Figure FDA0003017334820000057
A seventeenth step, in which formula (31) is combined, formula (30) is converted to:
Figure FDA0003017334820000058
due to the fact that
Figure FDA0003017334820000059
The RBF neural network can be designed to have an approximation error epsilon small enough to ensure that
Figure FDA00030173348200000510
3. The model reference-based adaptive decoupling control method for the RBF neural network of the nacelle suspension system according to claim 2, wherein the model reference-based adaptive decoupling control method comprises the following steps: the coordinate transformation equation in the step 3 is
Figure FDA00030173348200000511
In the formula, deltaABlade-side suspension air gap, δBIs a tail wing side suspension air gap, and r is the radius of a suspension cabin;
the conversion method is to solve the second derivative of the coordinate conversion equation (20) as
Figure FDA00030173348200000512
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116360274A (en) * 2023-05-12 2023-06-30 曲阜师范大学 Obstacle Lyapunov function-based full-state constraint wind turbine cabin suspension control method
CN116880165A (en) * 2023-05-30 2023-10-13 济宁医学院 Model reference self-adaptive finite time control method of non-contact suspension grabbing system

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116360274A (en) * 2023-05-12 2023-06-30 曲阜师范大学 Obstacle Lyapunov function-based full-state constraint wind turbine cabin suspension control method
CN116360274B (en) * 2023-05-12 2024-01-02 曲阜师范大学 Obstacle Lyapunov function-based full-state constraint wind turbine cabin suspension control method
CN116880165A (en) * 2023-05-30 2023-10-13 济宁医学院 Model reference self-adaptive finite time control method of non-contact suspension grabbing system
CN116880165B (en) * 2023-05-30 2024-01-30 济宁医学院 Model reference self-adaptive finite time control method of non-contact suspension grabbing system

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