CN115009044A - Control method of vehicle axial split-phase magnetic suspension flywheel rotor system based on neural network inverse expansion structure - Google Patents

Control method of vehicle axial split-phase magnetic suspension flywheel rotor system based on neural network inverse expansion structure Download PDF

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CN115009044A
CN115009044A CN202210621243.1A CN202210621243A CN115009044A CN 115009044 A CN115009044 A CN 115009044A CN 202210621243 A CN202210621243 A CN 202210621243A CN 115009044 A CN115009044 A CN 115009044A
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朱志莹
丛冰玉
安聪
杨品海
戴必翔
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Abstract

The invention relates to a control method of an axial split-phase magnetic suspension flywheel rotor system for a vehicle based on a neural network inverse expansion structure, which comprises the following steps: step 1: constructing a flywheel rotor dynamic model, and obtaining a composite flywheel rotor system through linear amplification; step 2: constructing a dynamic neural network inverse system; and step 3: the combined pseudo linear system composite flywheel rotor system is linearized and decoupled, and then system closed-loop control is carried out; and 4, step 4: introducing the disturbance estimation value into a model of a dynamic neural network inverse system to form an extended structure, and 5: and the expansion structure replaces a dynamic neural network inverse system to finally form a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure. The invention enhances the robustness of the flywheel rotor under vehicle-mounted disturbance, simplifies the model, improves the anti-interference performance of the control system, and ensures that the rotor system is simpler to control and has more robustness and disturbance resistance.

Description

Control method of vehicle axial split-phase magnetic suspension flywheel rotor system based on neural network inverse expansion structure
Technical Field
The invention belongs to the technical field of control of magnetic suspension motors, and particularly relates to a control method of an automotive axial split-phase magnetic suspension flywheel rotor system based on a neural network inverse expansion structure.
Background
In recent years, an electric automobile is taken as a novel vehicle, a vehicle-mounted power supply is taken as power, wheels are driven by a motor to run, complex electromechanical-magnetic coupling action exists among the motor, a supporting system and the freedom degrees of a rotor in a vehicle-mounted flywheel battery, and the change of different vehicle running states such as starting, accelerating, decelerating, steering and sudden stop and the like and road conditions such as uphill, downhill, bending and uneven road surface can become complex vehicle-road-axle unmodeled dynamic factors.
Because the bending critical rotating speed of the high-speed flywheel rotor system is far higher than the rated working rotating speed, the flywheel rotor can be treated as a rigid rotor system approximately, when the flywheel rotor rotates, if the vehicle-mounted magnetic suspension rotor mainly vibrates vertically during working, the air gap between the rotor and the electromagnetic coil can be changed, the rotor is unstable, and even the suspension supporting state is lost, so that the flywheel battery cannot work normally.
At present, a great deal of research has been carried out at home and abroad aiming at the stable suspension control of a magnetic suspension flywheel rotor, and a plurality of methods are provided, so that the stable suspension control can be more mature applied to a certain extent, but the stable suspension control has defects in precision, robustness and real-time performance, for example, the most widely applied distributed PID control is adopted, the coupling effect among the degrees of freedom is ignored by the control method, and the control precision is low under the condition of high speed of the rotor; the cross feedback control algorithm mostly adopts a Taylor linearization method to linearize a system model at a balance point, so that feedback control is completed, and the defect is that the robustness of the motor air gap change is insufficient; the self-adaptive feedback control method has better control precision and robustness, but the algorithm has large calculation amount and low real-time property: the inverse system linearization decoupling algorithm has clear physical concept and is easy to implement, but is easily influenced by the change of a model and parameters, so a robust controller needs to be further designed in a control system in practical application, such as sliding mode control, H-infinity control, mu synthesis, LQR control, a neural network, fuzzy control and the like, and the algorithm is very complex.
Meanwhile, the control scheme does not fully consider the influence of the vehicle-mounted working condition, and for the vehicle-mounted flywheel battery, the dynamic characteristic of the flywheel battery is influenced by the change of the vehicle running state and the running road condition, which is 'unmodeled dynamic' outside a mechanism model, so that the reliable control performance under the vehicle-mounted working condition cannot be ensured.
In addition, the accurate model of the vehicle-mounted supporting system is difficult to construct, the complex motor operation modeling error, the nonlinear uncertainty and the environmental influence make the accurate suspension rotor control difficult to realize, the disturbance resistance capability to the flywheel battery under the vehicle-mounted condition is important, for the traditional flywheel rotor, the mechanical bearing is used as the supporting structure, when the vehicle decelerates and accelerates, the inertia force directly acts on the mechanical bearing, and at the moment, the high-speed flywheel rotor collides with the mechanical bearing, so that the service life of the supporting system is greatly shortened. When the magnetic suspension bearing is used, the bearing can be realized in a friction-free state under a vacuum environment due to no mechanical contact, and the magnetic suspension bearing is an ideal bearing of a flywheel, but the electromagnetic bearing needs to realize rotor suspension support by controlling winding current, and the self-disturbance-rejection capability of a suspension support system is more important due to the fact that the stress of a rotor is changed due to the complex changes of the vehicle running condition and the road condition.
Therefore, the influence mechanism of the driving state of the electric automobile, such as starting acceleration, cruising at a constant speed, braking deceleration, and the change of the driving road conditions, such as turning, ascending, descending and uneven road surfaces, on the flywheel battery supporting system needs to be researched, and the gyro effect suppression and robust control method under the vehicle-mounted complex disturbance of the flywheel rotor needs to be researched, so that the stable operation of the flywheel battery magnetic suspension rotor under the vehicle-mounted working condition is realized.
Disclosure of Invention
In order to solve the problems, the invention provides a control method of an axial split-phase magnetic suspension flywheel rotor system for a vehicle based on a neural network inverse expansion structure, starting from the angle of flywheel rotor dynamics, the control of a complex system of an axial split-phase magnetic suspension flywheel motor can be converted into the control of five second-order linear subsystems by using the neural network inverse system, then closed-loop control is performed by using an active disturbance rejection controller, a disturbance value in a state observer is led out, stable suspension control of a magnetic suspension flywheel rotor under a vehicle-mounted condition is further realized after the neural network inverse system expansion structure is constructed, and the existing robustness and anti-interference performance can be solved.
In order to achieve the purpose, the invention is realized by the following technical scheme:
the invention relates to a control method of an axial split-phase magnetic suspension flywheel rotor system for a vehicle based on a neural network inverse expansion structure, which comprises the following steps:
step 1: considering the interference of the vehicle running state and the running road condition, forming a vehicle-mounted flywheel battery rotor dynamics analysis result, constructing a flywheel rotor dynamics model, and performing linear amplification through a bipolar power amplifier to obtain a composite flywheel rotor system;
step 2: using a static neural network and an integrator S -1 Constructing a dynamic neural network inverse system;
and 3, step 3: the dynamic neural network inverse system constructed in the step 2 is arranged in front of the composite flywheel rotor system, a pseudo-linear system is combined to carry out linearization and decoupling on the composite flywheel rotor system obtained in the step 1, and the decoupled pseudo-linear system utilizes an active disturbance rejection controller to carry out system closed-loop control;
and 4, step 4: introducing a disturbance estimation value generated by an extended state observer in an active disturbance rejection controller into a model of a neural network inverse system to form an extended structure of the neural network inverse system and increase adaptability and anti-interference capability to the disturbance change of a composite flywheel rotor system;
and 5: and finally, a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure is formed by replacing the dynamic neural network inverse system in the last step with the neural network inverse expansion structure, increasing the number of input nodes of the neural network and utilizing the disturbance estimation signal of the controlled flywheel rotor system.
The specific process of the step 1 is as follows:
step 1-1: because the bending critical rotating speed of the high-speed flywheel rotor system is far higher than the rated working rotating speed, the flywheel rotor system can be approximately treated as a rigid rotor system, a three-dimensional coordinate system is established by taking the mass center G of the rigid rotor as an original point, the external damping and gravity influence of the system are ignored, and according to a Lagrange's equation method in the multi-rigid system dynamics theory, the power equation of the axial split-phase magnetic suspension flywheel rotor system can be obtained:
Figure BDA0003676838830000031
wherein: m is the mass of the flywheel rotor, x, y and z are the translational displacement of the rotor in the directions of x, y and z axes under the coordinate of mass center, alpha and beta are the rotation angles of the rotor around the x axis and the y axis without considering the bending deformation of the rotor, alpha is a positive value,
Figure BDA0003676838830000032
respectively, the second derivative thereof, f x And p x Is the electromagnetic force and moment in the x-direction at the center of mass, f y And p y Is the electromagnetic force and moment in the y-direction at the center of mass, f z Is the electromagnetic force in the z direction at the centroid, Δ f and Δ p are the external disturbance force and disturbance moment, f ax And f bx Electromagnetic force in the x-axis direction under the coordinate system of the motor A phase and the motor B phase, respectively, f ay And f by Electromagnetic force in the y-axis direction under the coordinate system of the phase A and the phase B of the motor respectively;
step 1-2: the power equation of the axial split-phase magnetic suspension flywheel rotor system is expressed in a matrix form:
Figure BDA0003676838830000041
namely:
Figure BDA0003676838830000042
wherein: rotor mass matrix of
Figure BDA0003676838830000043
Coordinate vector of flywheel rotor centroid
Figure BDA0003676838830000044
Gyro matrix
Figure BDA0003676838830000045
Rotor moment arm coefficient matrix
Figure BDA0003676838830000046
Magnetic bearing electromagnetic force
Figure BDA0003676838830000047
Step 1-3: a bipolar power amplifier for driving a control signal to generate an actual control signal is connected in series in front of the magnetic suspension flywheel rotor system to form a composite flywheel rotor system.
The specific process of constructing the dynamic neural network inverse system in the step 2 is as follows:
step 2-1: using a static neural network and 10 integrators S -1 Constructing a neural network inverse system, approximating nonlinear mapping with a static neural network, and using an integrator to reflect the dynamic characteristics of the inverse system to convert the input of the flywheel rotor system into
Figure BDA0003676838830000048
As the desired output of the neural network, the output quantity y of the flywheel rotor system is set to [ y ═ y [ [ y ] 1 ,y 2 ,y 3 ,y 4 ,y 5 ] T ＝[x a ,y a ,z,x b ,y b ] T When the method is used as the input of a neural network, when a sample is selected, firstly, a proper excitation current signal, namely a plurality of groups of different random square waves, is selected to excite a controlled object, and the controlled object is controlledThe image output displacement signal is filtered by a high-order digital filter to remove high-frequency noise in the sampling data, so that a high-precision original data sample { u }is obtained 1 ,u 2 ,u 3 ,u 4 ,u 5 ,y 1 ,y 2 ,y 3 ,y 4 ,y 5 And sampling the measurable internal state x, observing a system internal state design state observer which is difficult to directly measure, and accurately calculating the first and second derivatives of y by adopting a high-order numerical differentiation method, namely a five-point derivation method, wherein the five-point derivation formula is as follows:
Figure BDA0003676838830000051
Figure BDA0003676838830000052
step 2-2: normalizing the input and output { u, y } signals, fully normalizing the data with large span to-1, and finally forming an input sample set and an expected output sample set of a training neural network by the normalized data
Figure BDA0003676838830000053
Directly storing sampling data into a To Workspace module in a simulation system, setting the simulation time of the system To be 30 seconds and the sampling interval time To be 0.01 second, acquiring 3000 groups of data, adopting a neural network as an identification model of an inverse system according To the data sample, wherein an input node is 15, an output node is 4, the number of nodes of a hidden layer is determined by experiments, further selecting 2500 groups of data from a training sample for training, and performing off-line learning on a composite controlled object by using another 500 groups of data for detection and verification so as To determine each weight coefficient of a static neural network layer and finally reach the precision requirement, and after the static neural network is finished, 10 integrators S are used -1 Before being connected in series to the static neural network, x is obtained after an integral link because the input is the derivative of displacement and angle a ,y a ,z,x b ,y b The first and second derivatives and the original value of the dynamic neural network are input into the static neural network to finally form a dynamic neural network structure.
The specific process of the step 3 is as follows:
step 3-1: and (3) placing the dynamic neural network inverse system constructed in the step (2) in front of the composite flywheel rotor system to form a pseudo linear system which is equivalent to five second-order linear integral subsystems, namely linearizing and decoupling the pseudo linear system into five mutually independent integral linear subsystems.
Step 3-2: converting a rotor displacement signal detected by a displacement sensor to the position of the mass center of the rotor, and assuming that radial translational displacements of the rotor detected by a phase displacement sensor A of the motor are respectively x a And y a The radial translational displacement of the rotor detected by the phase displacement sensor B of the motor is x respectively b And y b Then, the translational displacement at the rotor centroid O and the rotation angles of the rotor around the x-axis and the y-axis are respectively:
Figure BDA0003676838830000054
obtaining translation and rotation signals (x, y, Z, alpha and beta) at the position of the mass center of the rotor, wherein the displacement in the Z direction does not pass through a sensor, so that conversion is not needed;
step 3-3: when using a second-order linear active disturbance rejection controller, the model of the controlled object is considered as:
Figure BDA0003676838830000055
wherein f (t) is generalized disturbance d generated by interference of two aspects of the driving state of the vehicle and the road condition under driving, which can be met by the flywheel rotor system under the vehicle-mounted condition, and in order to estimate the generalized disturbance, the generalized disturbance is regarded as a new state variable, and z is made to be 1 ＝y,
Figure BDA0003676838830000061
z 3 ＝f,
Figure BDA0003676838830000062
y represents only the output quantity, and then the set value (x) at the center of mass of the rotor is set * ,y * ,z * ,α * ,β * ) Inputting the signals into an active disturbance rejection controller, arranging a transition process for the input signals through a tracking differentiator, and respectively corresponding to given signals (x) * ,y * ,z * ,α * ,β * ) Processing is carried out and the value of the processed input signal itself is recorded as
Figure BDA0003676838830000063
The derivative thereof is recorded as
Figure BDA0003676838830000064
Waiting for transmission to the next step;
step 3-4: inputting actual displacement and rotation signals (x, y, z, alpha, beta) generated by the feedback of the pseudo linear composite system after the generalized disturbance is added in the step 3-3 and a control quantity u into a second-order extended state observer, observing and estimating each stage state of the control model and the sum of the internal disturbance and the external disturbance acting on the model and the unmodeled dynamic state of the system, and obtaining an actual signal estimated value z 1 And a disturbance estimate z 3 And estimating z for the actual signal 1 Is subjected to differential processing to obtain z 2 ；
Step 3-5: subjecting the product obtained in step 3-3
Figure BDA0003676838830000065
Respectively with z obtained in step 3-4 1 、z 2 Calculating by a linear feedback controller to obtain a primary control quantity u after difference processing 0 And then a disturbance estimated value z obtained by using a second-order extended state observer 3 At the preliminary control amount u 0 The final control quantity u is obtained by the compensation.
The step 4 specifically comprises the following steps:
step 4-1: actual disturbance estimate z generated in the auto-disturbance rejection controller 3 The state variable is used as a new state variable of a neural network inverse system under the vehicle-mounted condition, and when a vehicle is started and accelerated, the acceleration is setThe degree is kept unchanged and is consistent with the acceleration transmitted to the magnetic suspension flywheel battery, at the moment, the flywheel rotor is static in an initial state, the center of mass of a rotating shaft of the flywheel rotor is delayed on the shaft in the advancing direction, when disturbance with the suddenly increased acceleration value is set, the relative offset of the rotor is changed to cause the change of electromagnetic force, and at the moment, the active disturbance rejection controller estimates the displacement and angle operation states of the flywheel rotor under different working conditions;
step 4-2: the method comprises the steps that a pseudo linear system closed loop simulation model based on an active disturbance rejection controller is established, a second-order linear system is formed by a neural network inverse system and a flywheel rotor system, and the decoupled flywheel rotor system can be replaced by the second-order pseudo linear system, so that the influence of interference in the neural network inverse system and an integral link module of simulink software in the rotor system can be favorably ignored, and then the pseudo linear system closed loop simulation model based on the active disturbance rejection controller is formed;
step 4-3: simulating different running conditions of a vehicle by using different types of disturbance signals according to the influence of unmodeled dynamics on the system, introducing various disturbance signals into the pseudo linear system closed-loop simulation model formed in the step 4-2, adjusting parameters in the active disturbance rejection controller, and obtaining a better control effect through closed-loop simulation after parameter adjustment is finished;
step 4-4: after simulation, the disturbance estimated value z 3 The values are led out and stored in a To Workspace module, and the signals are normalized To finally form an input sample set and an expected output sample set of a training neural network
Figure BDA0003676838830000071
Since 3000 groups of data are acquired when the neural network inverse system is constructed, z here 3 Similarly, adjusting the sampling time, setting the time to be 30 seconds, and setting the sampling time interval to be 0.01 second to obtain 3000 groups of data for data processing;
and 4-5: the disturbance estimation value is participated in the construction of the neural network inverse system, when a neural network fitting function is utilized, the neural network inverse system expansion structure is fitted according to the corresponding relation between the input value and the output value, unmodeled dynamics is considered on the original basis in the expansion structure after the disturbance estimation value is introduced, the problem of disturbance encountered by the magnetic suspension flywheel battery rotor during working is solved, and the subsequent control is more accurate.
The step 5 specifically comprises the following steps: replacing the neural network inverse system with the expanded structure of the neural network inverse system obtained in the step 4, and converting the reference values (x) of the displacement and rotation signals * ,y * ,z * ,α * ,β * ) And the five active disturbance rejection controllers of actual values (x, y, z, alpha and beta) are combined to form a complete closed-loop control system containing the active disturbance rejection controllers, a neural network inverse system expansion structure, a PWM amplifier and an axial phase-splitting magnetic suspension flywheel rotor system, a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure is constructed, and finally stable suspension control of the axial phase-splitting magnetic suspension flywheel rotor system for vehicles under different working conditions is achieved on the basis of realizing decoupling.
The invention has the beneficial effects that:
1. according to the method, on the basis of a method of utilizing a neural network inverse system, a model of an axial split-phase magnetic suspension rotor estimates the disturbance by utilizing the algorithm of an extended state observer in an active disturbance rejection controller under the vehicle-mounted condition, and the disturbance is introduced into the neural network to form an inverse system expansion structure, so that the robustness of a flywheel rotor under the vehicle-mounted disturbance is enhanced;
2. the invention utilizes the neural network inverse method to perform high-performance decoupling aiming at the high coupling and gyro effect of the axial split-phase magnetic suspension flywheel rotor system, thereby further simplifying the model;
3. the invention uses the active disturbance rejection controller to carry out closed-loop control on the axial split-phase magnetic suspension flywheel rotor system, thereby further improving the anti-disturbance performance of the control system.
The invention converts the motion system control of the axial split-phase magnetic suspension flywheel rotor into the control of a rotor position second-order linear subsystem by utilizing the algorithm of the neural network inverse system, then estimates the internal and external disturbance of a position model in real time by utilizing an active disturbance rejection controller, introduces the disturbance into the neural network to form an extended structure of the neural network inverse system, enhances the adaptability of the neural network inverse system, namely enables the neural network inverse system to approach the unmodeled dynamic state, and enables the rotor system to be simpler to control and have more robustness and disturbance resistance.
Drawings
FIG. 1 is a schematic diagram of a rotor coordinate system of an axial split-phase magnetic suspension flywheel motor in an embodiment.
Fig. 2 is a schematic structural diagram of a composite controlled object in the embodiment.
FIG. 3 is a schematic diagram of an inverse system of the RBF neural network in the embodiment.
FIG. 4 is a schematic diagram of the structure of the dynamic neural network system in the embodiment.
FIG. 5 is a schematic diagram of the structure of the pseudo-linear system in the embodiment.
Fig. 6 is a schematic structural diagram of a second-order active disturbance rejection controller in the embodiment.
FIG. 7 is a schematic diagram of sampling of disturbance estimation values of a pseudo-linear system in the x-axis direction of an example rotor in the embodiment.
FIG. 8 is an expanded structural diagram of an example rotor x-axis direction neural network inverse system in the embodiment.
FIG. 9 is a schematic block diagram of active disturbance rejection control of a magnetic suspension flywheel rotor based on a neural network inverse expansion structure.
Detailed Description
In the following description, for purposes of explanation, numerous implementation details are set forth in order to provide a thorough understanding of the embodiments of the invention. It should be understood, however, that these implementation details are not to be interpreted as limiting the invention. That is, in some embodiments of the invention, such implementation details are not necessary.
As shown in fig. 9, the present invention is a control method of a vehicle axial split-phase magnetic suspension flywheel rotor system based on a neural network inverse expansion structure, the control method includes the following steps:
step 1: considering the interference of the vehicle running state and the running road condition, forming a vehicle-mounted flywheel battery rotor dynamics analysis result, constructing a flywheel rotor dynamics model, and performing linear amplification through a bipolar power amplifier to obtain a composite flywheel rotor system;
step 2: using a static neural network and an integrator S -1 Constructing a dynamic neural network inverse system;
and step 3: the dynamic neural network inverse system constructed in the step 2 is arranged in front of the composite flywheel rotor system, a pseudo-linear system is combined to carry out linearization and decoupling on the composite flywheel rotor system obtained in the step 1, and the decoupled pseudo-linear system utilizes an active disturbance rejection controller to carry out system closed-loop control;
and 4, step 4: introducing a disturbance estimation value generated by an extended state observer in the active disturbance rejection controller into the model of the dynamic neural network inverse system in the step 2 to form an extended structure of the neural network inverse system and increase adaptability and anti-interference capability to the interference change of the composite flywheel rotor system;
and 5: and (4) replacing the dynamic neural network inverse system in the step (4) with the neural network inverse system expansion structure in the step (4), increasing the number of input nodes of the neural network, and utilizing the interference estimation signal of the controlled flywheel rotor system to finally form a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure.
The control method of the present invention will be specifically described below with reference to examples.
The control method of the invention comprises the following steps:
and S1, constructing a dynamic model in simulink based on a power equation of the axial split-phase magnetic suspension flywheel rotor system, and linearly amplifying through a bipolar power amplifier to obtain a mathematical model of the composite controlled object.
In step S11, an axial split-phase magnetic levitation flywheel rotor motion coordinate system is constructed, as shown in fig. 1, where: establishing a three-dimensional coordinate system with the center of mass O of the rigid rotor as an origin, f ax And f bx The suspension force f in the radial x direction and the radial y direction of the rotor of the A phase axial split phase magnetic suspension flywheel motor are respectively z Is the axial suspension force applied to the mass center in the z direction, l is the distance between the stator centers of the motor phases A and B, l is the axial suspension force a And l b Respectively the distances from the centers of the A phase stator and the B phase stator to a mass center point O, l sa And l sa The distances from the A phase shift sensor and the B phase shift sensor to the centroid O, l s The distance between the centers of the phase shift sensors of the motor A phase and the B phase shift sensor.
Suppose that the radial translation displacements of the rotor detected by the phase displacement sensor A of the motor are x respectively a And y a The radial translational displacement of the rotor detected by the phase displacement sensor B of the motor is x respectively b And y b Then, the translational displacement at the rotor centroid O and the rotation angles of the rotor around the x-axis and the y-axis are respectively:
Figure BDA0003676838830000091
in step S12, a dynamic model of the magnetic levitation rotor without considering the gyroscopic effect is constructed. According to Newton mechanics, a dynamic model of the magnetic suspension flywheel rotor can be obtained as follows:
Figure BDA0003676838830000092
wherein: m is the mass of the flywheel rotor; x, y and z are translational displacement of the rotor in the directions of x, y and z axes under the coordinate of the mass center, alpha and beta are rotation angles of the rotor around the x axis and the y axis without considering the bending deformation of the rotor, alpha is a positive value,
Figure BDA0003676838830000101
respectively, its second derivative; f. of x And p x Is the electromagnetic force and moment in the x-direction at the centroid; f. of y And p y Is the electromagnetic force and moment in the y-direction at the centroid; f. of z Is the electromagnetic force in the z direction at the centroid; Δ f and Δ p are external disturbance force and disturbance moment; f. of ax And f bx Electromagnetic force in the x-axis direction under the coordinate system of the motor A phase and the motor B phase, respectively, f ay And f by The electromagnetic force in the y-axis direction under the coordinate system of the phase A and the phase B of the motor is respectively.
The motion equation of the rotor of the magnetic suspension flywheel system is expressed in a matrix form:
Figure BDA0003676838830000102
namely:
Figure BDA0003676838830000103
wherein: rotor mass matrix of
Figure BDA0003676838830000104
Coordinate vector of flywheel rotor centroid
Figure BDA0003676838830000105
Gyro matrix
Figure BDA0003676838830000106
Rotor moment arm coefficient matrix
Figure BDA0003676838830000107
Magnetic bearing electromagnetic force
Figure BDA0003676838830000108
Suspension force f of A phase and B phase of motor in formula 2 ax 、f bx 、f ay And f by Available current stiffness k at equilibrium position i And displacement stiffness k r Represents:
Figure BDA0003676838830000109
wherein: x is the number of a 、y a 、x b And y b Respectively the translational displacement of the rotor under the coordinate systems of the phase A and the phase B of the motor; z is the axial displacement of the motor; i.e. i ax 、i ay 、i bx And i by Respectively controlling currents of the suspension windings under the A-phase and B-phase coordinate systems of the motor; i.e. i z Control current for the motor axial suspension winding;
in step S13, the bipolar power amplifier for generating the actual control signal from the driving control signal is connected in series with the magnetic suspension flywheel rotor systemBefore, as shown in FIG. 2, the signal (x) output by the module at this time a 、y a 、x b And y b ) The radial displacement signal of the rotor detected by a sensor at an electromagnetic bearing is required to be used in a control system by converting into displacement signals (x, y, alpha and beta) at a centroid, the axial displacement z of the motor does not need to be subjected to coordinate transformation, and a coordinate transformation process is constructed:
Figure BDA0003676838830000111
step S2, adopting static neural network and integrator S -1 And constructing a dynamic neural network inverse system of the composite control object.
Step S21: the utility model discloses in adopt RBF neural network to carry out the inverse system mapping, as shown in fig. 3, adopt static neural network and 10 integrators S in the picture -1 Constructing a neural network inverse system, approximating nonlinear mapping with a static neural network, and using an integrator to reflect the dynamic characteristics of the inverse system to convert the input of the flywheel rotor system into
Figure BDA0003676838830000112
As the desired output of the neural network, the output quantity y of the flywheel rotor system is set to [ y ═ y [ [ y ] 1 ,y 2 ,y 3 ,y 4 ,y 5 ] T ＝[x a ,y a ,z,x b ,y b ] T When the method is used as the input of a neural network, when a sample is selected, firstly, a proper excitation current signal (a plurality of groups of different random square waves) is selected to excite a controlled object, the controlled object outputs a displacement signal and high-frequency noise in sampling data is filtered by a high-order digital filter, so that a high-precision original data sample { u } of the original data sample is obtained 1 ,u 2 ,u 3 ,u 4 ,u 5 ,y 1 ,y 2 ,y 3 ,y 4 ,y 5 And sampling the measurable internal state x, observing a system internal state design state observer difficult to directly measure, and calculating the first order of y by adopting a high-order numerical differentiation method (a five-point derivation method)And second derivative, the five-point derivation formula is as follows:
Figure BDA0003676838830000113
Figure BDA0003676838830000114
in step S21, normalization processing is carried out on the input and output { u, y } signals, the data with large span is fully normalized to-1, and the normalized data can finally form an input sample set and an expected output sample set of a training neural network
Figure BDA0003676838830000115
Directly storing sampling data into a To Workspace module in a simulation system, setting the simulation time of the system To be 30 seconds and the sampling interval time To be 0.01 second, acquiring 3000 groups of data, adopting an RBF neural network as an identification model of an inverse system according To the data sample, and adopting an RBF neural network structure, wherein as shown in figure 3, an input node is set To be 15, an output node is set To be 4, the number of nodes of a hidden layer is determined by experiments, 2500 groups of data are further selected from the training sample To be trained, the other 500 groups of data are used for detection and verification, and a composite controlled object is subjected To offline learning, so that each weight coefficient of a static neural network layer is determined, the precision requirement is finally met, and 10 integrators S are used after the static neural network is finished -1 Before being connected in series to a static neural network, x is obtained after an integral link because the input is the derivative of displacement and angle a ,y a ,z,x b ,y b The first and second derivatives and the original values of (A) are inputted into the static neural network, and finally the dynamic neural network structure is formed as shown in FIG. 4.
And step S3, placing the constructed dynamic neural network inverse system in front of the composite flywheel rotor system, combining into a pseudo linear system, linearizing and decoupling the composite flywheel rotor system obtained in the step 1, and performing system closed-loop control on the decoupled pseudo linear system by using an active disturbance rejection controller.
Step S31, the constructed dynamic neural network inverse system is arranged in front of the composite flywheel rotor system to form a pseudo linear system, which is equivalent to five second-order linear integral subsystems as shown in FIG. 5, namely, the dynamic neural network inverse system is linearized and decoupled into five mutually independent integral linear subsystems;
step S32, converting the rotor displacement signal detected by the displacement sensor to the rotor mass center, assuming that the rotor radial translation displacements detected by the motor A phase displacement sensor are x respectively a And y a The radial translational displacement of the rotor detected by the phase displacement sensor B of the motor is x respectively b And y b Then, the translational displacement at the rotor centroid O and the rotation angles of the rotor around the x-axis and the y-axis are respectively:
Figure BDA0003676838830000121
obtaining translation and rotation signals (x, y, Z, alpha and beta) at the center of mass of the rotor, wherein the displacement in the Z direction does not pass through a sensor, so that conversion is not needed;
when the second-order linear active disturbance rejection controller is used in step S33, the model of the controlled object is considered as:
Figure BDA0003676838830000122
wherein f (t) is generalized disturbance d generated by interference of two aspects of the driving state of the vehicle and the road condition under driving, which can be met by the flywheel rotor system under the vehicle-mounted condition, and in order to estimate the generalized disturbance, the generalized disturbance is regarded as a new state variable, and z is made to be 1 ＝y,
Figure BDA0003676838830000123
z 3 ＝f,
Figure BDA0003676838830000124
y represents only the output quantity, and then the given value (x) set at the center of mass of the rotor * ,y * ,z * ,α * ,β * ) Inputting the signals into an active disturbance rejection controller, arranging a transition process for the input signals through a tracking differentiator, and respectively corresponding to given signals (x) * ,y * ,z * ,α * ,β * ) For processing, e.g. for a given rotor translational displacement signal x * Performing smooth noise reduction processing, and recording the value of the processed input signal as
Figure BDA0003676838830000131
The derivative thereof is recorded as
Figure BDA0003676838830000132
Waiting for transmission to the next step;
step S34, the observer adopts a second-order extended state observer, as shown in fig. 6, and inputs actual displacement and rotation signals (x, y, z, α, β) generated by the feedback of the pseudo linear composite system after the generalized disturbance and the control quantity u into a second-order extended state observer LESO, and performs observation and estimation on each stage state of the control model and the sum of the internal and external disturbances acting on the model and the unmodeled dynamics of the system to obtain an actual signal estimation value z 1 And a disturbance estimate z 3 And estimating z for the actual signal 1 Is subjected to differential processing to obtain z 2 ；
Step S35, the result of step S33
Figure BDA0003676838830000133
Respectively with z obtained in step S34 1 、z 2 Calculating by a linear feedback controller to obtain a preliminary control quantity u after difference processing 0 And then using the disturbance estimated value z obtained by the observer 3 At the preliminary control amount u 0 The final control quantity u is obtained by the compensation.
And step S4, introducing a disturbance estimation value generated by an extended state observer in the active disturbance rejection controller into the model of the dynamic neural network inverse system in the step 2, and forming an expansion structure of the neural network inverse system to increase adaptability and anti-interference capability to the disturbance change of the composite flywheel rotor system.
Actual generated in the active disturbance rejection controller in step S41Disturbance estimate z 3 The method is used as a new state variable of a neural network inverse system under the vehicle-mounted condition, for example, when a vehicle is started and accelerated, if the acceleration is kept unchanged and is consistent with the acceleration transmitted to a magnetic suspension flywheel battery, the flywheel rotor is static in an initial state, the center of mass of a rotating shaft of the flywheel rotor can generate a hysteresis phenomenon on the shaft in the advancing direction, when disturbance with an suddenly increased acceleration value is set, the relative offset of the rotor can be changed to cause the change of electromagnetic force, and then a state observer in an active disturbance rejection controller estimates the disturbance;
a pseudo linear system closed-loop simulation model based on the active disturbance rejection controller is established in the step S42, as shown in fig. 7, a decoupled flywheel rotor system is replaced by a second-order pseudo linear system in the figure, for example, the rotor x-axis direction pseudo linear system performs closed-loop control, so that the influence of interference in a neural network inverse system and an integral link module of simulink software in the rotor system can be ignored, and then the pseudo linear system closed-loop simulation model based on the active disturbance rejection controller is formed to lay a cushion for a later sampling disturbance estimation value;
in step S43, on the basis, the influence of unmodeled dynamics on the system is simulated by using 10 different types of disturbance signals to simulate different operating conditions of the vehicle, such as start-up acceleration, cruise at a constant speed, brake deceleration, climbing, turning, up-down vibration, lateral direction, longitudinal direction, yaw, and pitch, and the various different disturbance signals are introduced into the closed-loop pseudo linear system formed in the previous step to adjust parameters in the active disturbance rejection controller. The corresponding second order system state equation is
Figure BDA0003676838830000141
Wherein z is 1 、z 2 Respectively, y and an estimate of the rate of change thereof, z 3 Is an estimate of the system generalized disturbance, beta 1 、β 2 、β 3 Is a controller adjustable parameter, B is an object parameter, u represents a control rate, B is a system input gain,
Figure BDA0003676838830000142
when ESO is inCan realize z 3 F, the control system will be converted to two integral series links, the desired equation in the form of the transfer function:
Figure BDA0003676838830000143
the parameters to be adjusted are the controller parameters B, k p ，k d And observer parameter beta 1 ，β 2 ，β 3 。
In the actual control process, the medium-low frequency coefficient (beta) 2 And beta 3 ) Is significantly larger than the high frequency coefficient beta 1 Therefore, the formula is simplified to obtain the disturbance estimation value and the laplace variation formula of the system:
Figure BDA0003676838830000144
wherein
Figure BDA0003676838830000145
The higher the k value, the higher the ESO observation speed, let beta 1 ＝3ω 0 ，
Figure BDA0003676838830000146
k d ＝2ω c ，
Figure BDA0003676838830000147
ω 0 ＝4ω c 。ω c For controller bandwidth, ω 0 Is the observer bandwidth. The six parameters are adjusted and converted into three parameters which are respectively the controller bandwidth omega c The control gain B of the controller and the dynamic adjustment coefficient K. Omega c The dynamic characteristics of the system become better as K becomes larger when B is constant, and ω is c And when K is unchanged, the dynamic characteristic of the system becomes worse along with the increase of B, the three influence each other, the K value is increased, the B value is reduced, and omega is adjusted c Then, observing a simulation diagram of the closed-loop control system, controlling the simulation diagram to have a higher dynamic characteristic and obtaining a better control effect to prove that the parameter adjustment is finished;
in step S44, the disturbance estimation value z is simulated and then 3 The value of (a) is led out and stored into a 'To Workspace' module, such as a pseudo-line in the x-axis direction of a rotorSampling the disturbance estimation value of the sexual system, normalizing the signal, and finally forming an input sample set and an expected output sample set of a training neural network
Figure BDA0003676838830000148
Since 3000 groups of data are acquired when the neural network inverse system is constructed, z here 3 Similarly, adjusting the sampling time, setting the time to be 30 seconds, and setting the sampling time interval to be 0.01 second to obtain 3000 groups of data for data processing;
in step S45, the disturbance estimation value participates in the structure of the neural network inverse system, and when a neural network fitting function is utilized, an extended structure of the neural network inverse system is fitted according to a corresponding relationship between an input value and an output value, as shown in fig. 8, for example, the extended structure of the neural network inverse system in the x-axis direction of the rotor, and the extended structure after the disturbance estimation value is introduced considers unmodeled dynamics on the original basis, so that the problem of disturbance encountered by the magnetic suspension flywheel battery rotor during operation is solved, and the subsequent control is more accurate.
S5, replacing the dynamic neural network inverse system in the step 4 with the neural network inverse system expansion structure in the step 4, and finally forming a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure by increasing the number of input nodes of the neural network and utilizing the disturbance estimation signal of the controlled flywheel rotor system. The method specifically comprises the following steps: replacing the neural network inverse system with the expanded structure of the neural network inverse system obtained in the previous step, and converting the reference values (x) of the displacement and rotation signals * ,y * ,z * ,α * ,β * ) And the five active disturbance rejection controllers of actual values (x, y, z, alpha and beta) are combined to form a complete closed-loop control system containing the active disturbance rejection controllers, a neural network inverse system expansion structure, a PWM amplifier and an axial phase-splitting magnetic suspension flywheel rotor system, and a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure is constructed, as shown in figure 9, and finally stable suspension control of the axial phase-splitting magnetic suspension flywheel rotor system for vehicles under different working conditions is achieved on the basis of realizing decoupling.
The control method of the invention firstly constructs a magnetic suspension rotor dynamic switching model based on the axial split-phase magnetic suspension flywheel motor rotor dynamic equation, then utilizes a method of forming a dynamic neural network by utilizing a static neural network and an integrator, can realize nonlinear dynamic decoupling between suspension forces and adopts an active disturbance rejection controller to carry out closed-loop control, and the invention interferes the running state (starting acceleration, braking deceleration, turning and climbing) of the vehicle and the running road condition (longitudinal vibration, transverse vibration and pitching vibration of the vehicle caused by uneven road surface) of the vehicle which can be met when the rotor applied to an electric vehicle works on the basis of the two aspects of the invention, and a relatively accurate value of the disturbance estimated by an extended state observer in the active disturbance rejection controller is put into the structure of a neural network inverse system to form an extended structure of the inverse system, so that the neural network has stronger adaptability to the change of a flywheel rotor system after modeling non-dynamic state, the strong robust control of the axial split-phase magnetic suspension flywheel rotor for the electric automobile under different working conditions can be further realized.
The above description is only an embodiment of the present invention, and is not intended to limit the present invention. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (6)

1. The control method of the vehicle axial split-phase magnetic suspension flywheel rotor system based on the neural network inverse expansion structure is characterized by comprising the following steps of: the control method comprises the following steps:
step 1: considering the interference of the vehicle running state and the running road condition, forming a vehicle-mounted flywheel battery rotor dynamics analysis result, constructing a flywheel rotor dynamics model, and performing linear amplification through a bipolar power amplifier to obtain a composite flywheel rotor system;
step 2: using a static neural network and an integrator S -1 Constructing a dynamic neural network inverse system;
and step 3: the dynamic neural network inverse system constructed in the step 2 is arranged in front of the composite flywheel rotor system, a pseudo-linear system is combined to carry out linearization and decoupling on the composite flywheel rotor system obtained in the step 1, and the decoupled pseudo-linear system utilizes an active disturbance rejection controller to carry out system closed-loop control;
and 4, step 4: introducing a disturbance estimation value generated by an extended state observer in the active disturbance rejection controller into the model of the dynamic neural network inverse system in the step 2 to form an extended structure of the neural network inverse system and increase adaptability and anti-interference capability to the interference change of the composite flywheel rotor system;
and 5: and (4) replacing the dynamic neural network inverse system in the step (4) with the neural network inverse system expansion structure in the step (4), increasing the number of input nodes of the neural network, and utilizing the interference estimation signal of the controlled flywheel rotor system to finally form a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure.
2. The control method of the vehicle axial split-phase magnetic suspension flywheel rotor system based on the neural network inverse expansion structure is characterized by comprising the following steps of: the specific process of constructing the dynamic neural network inverse system in the step 2 is as follows:
step 2-1: using a static neural network and 10 integrators S -1 Constructing a neural network inverse system, and converting the input of the flywheel rotor system into
Figure FDA0003676838820000011
As the desired output of the neural network, the output quantity y of the flywheel rotor system is set to [ y ═ y [ [ y ] 1 ,y 2 ,y 3 ,y 4 ,y 5 ] T ＝[x a ,y a ,z,x b ,y b ] T When the method is used as the input of a neural network, when a sample is selected, firstly, a proper excitation current signal is selected to excite a controlled object, the controlled object outputs a displacement signal and filters high-frequency noise in sampling data through a high-order digital filter, so that a high-precision original data sample { u } is obtained 1 ,u 2 ,u 3 ,u 4 ,u 5 ,y 1 ,y 2 ,y 3 ,y 4 ,y 5 And sampling the measurable internal state x, observing a system internal state design state observer which is difficult to directly measure, and calculating first and second derivatives of y by adopting a five-point derivation method, wherein the five-point derivation formula is as follows:
Figure FDA0003676838820000012
Figure FDA0003676838820000021
step 2-2: normalizing the input and output { u, y } signals to finally form an input sample set and an expected output sample set of the training neural network
Figure FDA0003676838820000022
Step 2-3: directly storing the sampling input sample set and the expected output sample set in the step 2-3 into a To Workspace module in a simulation system, setting the simulation time of the system To obtain training data, and adopting a neural network as an identification model of an inverse system according To the data sample;
step 2-4: further selecting data from the training data samples respectively for training, detecting and checking, and performing off-line learning on the composite controlled object, thereby determining each weight coefficient of the static neural network layer, finally reaching the precision requirement, and completing the static neural network by 10 integrators S -1 Before being connected in series to the static neural network, x is obtained after an integral link because the input is the derivative of displacement and angle a ,y a ,z,x b ,y b The first and second derivatives and the original value of the dynamic neural network are input into the static neural network to finally form a dynamic neural network structure.
3. The control method of the vehicle axial split-phase magnetic suspension flywheel rotor system based on the neural network inverse expansion structure is characterized by comprising the following steps of: the specific process of the step 3 is as follows:
step 3-1: the dynamic neural network inverse system constructed in the step 2 is arranged in front of the composite flywheel rotor system to form a pseudo-linear system;
step 3-2: converting a rotor displacement signal detected by a displacement sensor to the position of the mass center of the rotor, and setting the radial translational displacement of the rotor detected by a motor A phase displacement sensor as x a And y a The radial translational displacement of the rotor detected by the phase displacement sensor B of the motor is x respectively b And y b Then, the translational displacement at the rotor centroid O and the rotation angles of the rotor around the x-axis and the y-axis are respectively:
Figure FDA0003676838820000023
obtaining translation and rotation signals (x, y, Z, alpha and beta) at the position of the mass center of the rotor, wherein the displacement in the Z direction does not pass through a sensor, so that conversion is not needed;
step 3-3: when using a second-order linear active disturbance rejection controller, the model of the controlled object is considered as:
Figure FDA0003676838820000024
wherein f (t) is generalized disturbance d generated by interference of two aspects of the driving state of the vehicle and the road condition under driving, which can be met by the flywheel rotor system under the vehicle-mounted condition, and in order to estimate the generalized disturbance, the generalized disturbance is regarded as a new state variable, and z is made to be 1 ＝y,
Figure FDA0003676838820000031
z 3 ＝f,
Figure FDA0003676838820000032
y represents only the output quantity, and then the given value (x) set at the center of mass of the rotor * ,y * ,z * ,α * ,β * ) Is inputted intoIn an active disturbance rejection controller, transitions are arranged for the input signal via a tracking differentiator, respectively for a given signal (x) * ,y * ,z * ,α * ,β * ) Processing is carried out and the value of the processed input signal itself is recorded as
Figure FDA0003676838820000033
The derivative thereof is recorded as
Figure FDA0003676838820000034
Waiting for transmission to the next step;
step 3-4: inputting actual displacement and rotation signals (x, y, z, alpha, beta) generated by the pseudo linear composite system feedback after the generalized disturbance is added in the step 3-3 and a control quantity u into a second-order extended state observer, observing and estimating each stage state of the control model and the sum of the internal disturbance and the external disturbance acting on the model and the unmodeled dynamic state of the system, and obtaining an actual signal estimation value z 1 And a disturbance estimate z 3 And estimating z for the actual signal 1 Is subjected to differential processing to obtain z 2 ；
Step 3-5: subjecting the product obtained in step 3-3
Figure FDA0003676838820000035
Respectively with z obtained in step 3-4 1 、z 2 Calculating by a linear feedback controller to obtain a preliminary control quantity u after difference processing 0 And then a disturbance estimated value z obtained by using a second-order extended state observer 3 At the preliminary control amount u 0 The final control quantity u is obtained by the compensation.
4. The control method of the vehicle axial split-phase magnetic suspension flywheel rotor system based on the neural network inverse expansion structure is characterized by comprising the following steps of: the step 4 specifically comprises the following steps:
step 4-1: actual disturbance estimate z generated in the active disturbance rejection controller 3 When the vehicle is started, the state variable is used as a new state variable of a neural network inverse system under the vehicle-mounted conditionDuring acceleration, the set acceleration is kept unchanged and is consistent with the acceleration transmitted to the magnetic suspension flywheel battery, at the moment, the flywheel rotor is static in an initial state, the center of mass of a rotating shaft of the flywheel rotor is delayed on the shaft in the advancing direction, when disturbance with the suddenly increased acceleration value is set, the relative offset of the rotor is changed to cause the change of electromagnetic force, and at the moment, the active disturbance rejection controller estimates the displacement and angle running states of the flywheel rotor under different working conditions;
step 4-2: establishing a pseudo-linear system closed-loop simulation model based on an active disturbance rejection controller, wherein the pseudo-linear system replaces a flywheel rotor system to obtain a second-order closed-loop active disturbance rejection control system;
step 4-3: simulating different running conditions of a vehicle by using different types of disturbance signals according to the influence of unmodeled dynamics on the system, introducing various disturbance signals into the pseudo linear system closed-loop simulation model formed in the step 4-2, adjusting parameters in the active disturbance rejection controller, and obtaining a better control effect through closed-loop simulation after parameter adjustment is finished;
step 4-4: after simulation, the disturbance estimated value z 3 The values are led out and stored in a To Workspace module, and the signals are normalized To finally form an input sample set and an expected output sample set of a training neural network
Figure FDA0003676838820000041
And 4-5: and (3) participating the disturbance estimation value in the construction of the neural network inverse system, and fitting the neural network inverse system expansion structure according to the corresponding relation between the input value and the output value when a neural network fitting function is utilized.
5. The control method of the vehicle axial split-phase magnetic suspension flywheel rotor system based on the neural network inverse expansion structure as claimed in claim 4, wherein: the step 5 specifically comprises the following steps: replacing the neural network inverse system with the expanded structure of the neural network inverse system obtained in the step 4, and converting the reference values (x) of the displacement and rotation signals * ,y * ,z * ,α * ,β * ) And the five active disturbance rejection controllers of actual values (x, y, z, alpha and beta) are combined to form a complete closed-loop control system containing the active disturbance rejection controllers, a neural network inverse system expansion structure, a PWM amplifier and an axial split-phase magnetic suspension flywheel rotor system switching model, a complete magnetic suspension flywheel rotor active disturbance rejection control system based on the neural network inverse expansion structure is constructed, and finally stable suspension control of the axial split-phase magnetic suspension flywheel rotor system for vehicles under different working conditions is achieved on the basis of decoupling.
6. The control method of the vehicle axial split-phase magnetic suspension flywheel rotor system based on the neural network inverse expansion structure is characterized by comprising the following steps of: the specific process of the step 1 comprises the following steps:
step 1-1: designing a power equation of an axial split-phase magnetic suspension flywheel rotor system:
Figure FDA0003676838820000042
wherein: m is the mass of the flywheel rotor, x, y and z are the translational displacement of the rotor in the directions of x, y and z axes under the coordinate of mass center, alpha and beta are the rotation angles of the rotor around the x axis and the y axis without considering the bending deformation of the rotor, alpha is a positive value,
Figure FDA0003676838820000043
respectively, the second derivative thereof, f x And p x Is the electromagnetic force and moment in the x-direction at the center of mass, f y And p y Is the electromagnetic force and moment in the y-direction at the center of mass, f z Is the electromagnetic force in the z direction at the centroid, Δ f and Δ p are the external disturbance force and disturbance moment, f ax And f bx Electromagnetic force in the x-axis direction under the coordinate system of the motor A phase and the motor B phase, respectively, f ay And f by Electromagnetic force in the y-axis direction under the coordinate system of the phase A and the phase B of the motor respectively;
step 1-2: expressing the power equation of the axial split-phase magnetic suspension flywheel rotor system in the step 1-1 in a matrix form:
Figure FDA0003676838820000051
namely:
Figure FDA0003676838820000052
wherein: rotor mass matrix of
Figure FDA0003676838820000053
Coordinate vector of flywheel rotor centroid
Figure FDA0003676838820000054
Gyro matrix
Figure FDA0003676838820000055
Rotor moment arm coefficient matrix
Figure FDA0003676838820000056
Magnetic bearing electromagnetic force
Figure FDA0003676838820000057
Step 1-3: a bipolar power amplifier for driving the control signal to generate an actual control signal is connected in series in front of the magnetic suspension flywheel rotor to form a composite flywheel rotor system.
CN202210621243.1A 2022-06-02 2022-06-02 Control method of vehicle axial split-phase magnetic suspension flywheel rotor system based on neural network inverse expansion structure Pending CN115009044A (en)

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