CN111806246A - Suspension system control method for magnetic suspension train - Google Patents

Suspension system control method for magnetic suspension train Download PDF

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CN111806246A
CN111806246A CN202010561052.1A CN202010561052A CN111806246A CN 111806246 A CN111806246 A CN 111806246A CN 202010561052 A CN202010561052 A CN 202010561052A CN 111806246 A CN111806246 A CN 111806246A
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suspension
sliding mode
controller
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levitation
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孙友刚
徐俊起
陈琛
林国斌
荣立军
吉文
倪菲
高定刚
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Tongji University
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B60VEHICLES IN GENERAL
    • B60LPROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L13/00Electric propulsion for monorail vehicles, suspension vehicles or rack railways; Magnetic suspension or levitation for vehicles
    • B60L13/04Magnetic suspension or levitation for vehicles
    • B60L13/06Means to sense or control vehicle position or attitude with respect to railway

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Abstract

The invention relates to a control method of a suspension system for a magnetic suspension train, which specifically comprises the following steps: constructing a second-order sliding mode surface based on a suspension control dynamics model of a maglev train, and introducing a nonlinear bounded function which is related to a positioning error signal and is approximated by an online real-time training neural network to obtain a final sliding mode variable structure control law model which is used for constructing a maglev controller of a suspension system; inputting set physical parameters of a suspension system in a magnetic suspension controller; the magnetic suspension controller acquires gap data between the track and the train body in real time and outputs a control signal; and peripheral hardware of the suspension system receives the control signal and then drives the suspension electromagnet to move to the target position within a limited time. Compared with the prior art, the method can realize random approximation of uncertain working model parameters in practice, improve the adaptability of the controller to various environments, and finally improve the stability of the control of the suspension system.

Description

Suspension system control method for magnetic suspension train
Technical Field
The invention relates to the field of magnetic suspension trains, in particular to a suspension system control method for a magnetic suspension train.
Background
Maglev trains are a modern mode of transportation with contactless electromagnetic levitation, guidance and drive systems. It relies on electromagnetic attraction or electrical repulsion to suspend the train in the air to achieve no mechanical contact between the train and the track and is driven by a linear motor. Magnetic levitation trains are ideal vehicles due to their high speed, low energy consumption, comfortable ride and low noise. At present, magnetic Suspension trains are generally divided into two categories according to different Suspension principles and modes adopted by magnetic Suspension vehicles, wherein one category is electric Suspension (EDS type for short); one type is Electromagnetic Suspension (EMS) type for short. The EDS type magnetic levitation system suspends the vehicle above the track by using electromagnetic repulsion force, while the EMS type magnetic levitation system lifts the vehicle by using attraction force generated by an electromagnet located below the track to ensure that the vehicle does not contact the track. The EDS type magnetic levitation system can stably suspend without applying control, and the EMS type magnetic levitation system can ensure the stable suspension of the system by applying active control. At present, the commercial operation is an EMS type magnetic suspension train.
For EMS magnetic levitation trains, the levitation system is the key and core of the magnetic levitation train. However, suspension systems have strong non-linearity and open-loop instability. Furthermore, the system parameters have uncertainties and the system is subject to external disturbances during operation. Therefore, the design of a high-performance levitation controller poses a high challenge.
The most urgent problems currently faced by the levitation systems of EMS type maglev trains are model uncertainty and extraneous disturbances, such as uncertainty of passenger weight, disturbances of wind, etc. Currently, most maglev vehicle levitation controllers are linear PID controllers. When parameters are changed or external interference is large, under the action of the current linear controller, the control performance of the system is reduced, and the stability of the system is reduced or even loses stability.
Disclosure of Invention
The present invention is directed to overcoming the above-mentioned deficiencies of the prior art and providing a method for controlling a levitation system for a magnetic levitation vehicle.
The purpose of the invention can be realized by the following technical scheme:
a suspension system control method for a magnetic suspension train is characterized by comprising the following steps:
s1, constructing a second-order sliding mode surface based on a suspension control dynamics model of the maglev train, and introducing a nonlinear bounded function which is related to a positioning error signal and is approximated by an online real-time training neural network to obtain a final sliding mode variable structure control law model for constructing a maglev controller of a suspension system;
s2, inputting set physical parameters of the suspension system in the magnetic suspension controller;
s3, the magnetic suspension controller acquires gap data between the track and the train body in real time and outputs a control signal;
and S4, after receiving the control signal, the peripheral hardware of the suspension system drives the suspension electromagnet to move to the target position within a limited time and keeps within the position error limit range.
Further, in step S1, the expression of the final sliding mode variable structure control law model is:
Figure BDA0002546297260000021
Figure BDA0002546297260000022
Figure BDA0002546297260000023
wherein sgn (·) is a sign function, s is a dynamic sliding mode surface, e is a system error, c1、c2Eta and mu are control gain parameters,
Figure BDA0002546297260000024
and
Figure BDA0002546297260000025
neural network approximations of unknown nonlinear bounded functions f (-) and g (-) respectively, x being the network input, j being the jth hidden layer node, W*,L*Is the ideal network weight, h, of f (-) and g (-) inf(x) And hg(x) A Koski equation of a neural network, wherein r is an ideal tracking instruction;
according to the minimum parameter learning method, the self-adaptive rate of f (-) and g (-) is defined as a single parameter
Figure BDA0002546297260000026
And
Figure BDA0002546297260000027
Figure BDA0002546297260000028
Figure BDA0002546297260000029
wherein the parameter gamma1212∈R+
Further, the method for constructing the final sliding mode variable structure control law model in step S1 includes:
s11, establishing an affine nonlinear mathematical model;
s12, carrying out sliding mode control law design on the sliding mode controller according to the affine nonlinear mathematical model to obtain a sliding mode variable structure control law model and two nonlinear bounded functions f (·) and g (·);
s13, approximating nonlinear bounded functions f (cndot.) and g (cndot.) in the sliding mode variable structure control law model through RBF neural network online learning to obtain the final sliding mode variable structure control law model.
Further, in step S11, the expression of the affine nonlinear mathematical model is as follows:
Figure BDA0002546297260000031
wherein,
Figure BDA0002546297260000032
Figure BDA0002546297260000033
in the formula, z1Denotes the air gap spacing, z2Representing the speed of change of the air gap distance, z3Represents the air gap acceleration, m is the vehicle body mass, mu0Is a vacuum permeability, NmNumber of coil windings, AmIs the cross-sectional area of the magnet, RmRepresenting the electromagnet winding resistance.
Further, in step S12, the expression of the sliding mode variable structure control law model is:
Figure BDA0002546297260000034
in the formula uSMC(x, t) is the control output, η, μ ∈ R+Respectively representing a constant arrival coefficient and an exponential arrival coefficient, r being an ideal trace instruction, c1,c2∈R+Is the positive position control gain, e represents the system error and s represents the dynamic sliding mode surface.
Furthermore, the suspension system comprises a gap sensor, a chopper, a magnetic suspension controller and an electromagnet, wherein the gap sensor is connected with the magnetic suspension controller through the chopper, the electromagnet is connected with the magnetic suspension controller through peripheral hardware, and the gap sensor is installed on the electromagnet.
Furthermore, the gap sensor is connected with the chopper through the gap processing plate, the control plate and the interface conversion plate.
Further, the magnetic suspension controller comprises computer hardware and algorithm software, and is used for executing the operation of the neural network approximation algorithm, acquiring the input set physical parameters of the suspension system, acquiring the gap data between the track and the vehicle body in real time and outputting a control signal.
Compared with the prior art, the invention has the following advantages:
according to the method, the magnetic suspension controller of the suspension system is reestablished, a second-order sliding mode surface is constructed based on the suspension control dynamics model of the magnetic suspension train, and a nonlinear bounded function which is related to the positioning error signal and is approximated by an online real-time training neural network is introduced to obtain a final sliding mode variable structure control law model, so that any approximation to uncertain working model parameters in practice can be realized, the adaptability of the controller to various environments is improved, and the control stability of the suspension system is finally improved.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic diagram of a maglev train levitation control dynamics model.
Fig. 3 is a schematic diagram of a closed-loop control system of a magnetic levitation controller.
Fig. 4 is a schematic structural diagram of the suspension system.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, the present embodiment provides a suspension system control method for a magnetic levitation train, which specifically includes the following steps:
s1, constructing a second-order sliding mode surface based on a suspension control dynamics model of the maglev train, and introducing a nonlinear bounded function which is related to a positioning error signal and is approximated by an online real-time training neural network to obtain a final sliding mode variable structure control law model for constructing a maglev controller of a suspension system;
step S2, inputting the set physical parameters of the suspension system in the magnetic suspension controller;
step S3, the magnetic suspension controller acquires the gap data between the track and the train body in real time and outputs a control signal;
and step S4, after receiving the control signal, the peripheral hardware of the suspension system drives the suspension electromagnet to move to the target position within a limited time, and the position is kept within the position error limit range, so that a stable and reliable suspension control effect is achieved.
In step S1, the method for constructing the final sliding mode variable structure control law model includes:
step S11, establishing an affine nonlinear mathematical model;
s12, carrying out sliding mode control law design on the sliding mode controller according to the affine nonlinear mathematical model to obtain a sliding mode variable structure control law model and two nonlinear bounded functions f (·) and g (·);
and step S13, performing online learning to approximate nonlinear bounded functions f (-) and g (-) in the sliding mode variable structure control law model through an RBF (radial basis function) neural network to obtain the final sliding mode variable structure control law model.
The specific development of the steps is as follows:
as shown in fig. 2, the suspension control dynamics model of a magnetic levitation train is a set of electromagnetic and mechanical equations established using newton's law and maxwell's equations:
Figure BDA0002546297260000051
in the above formula, the state quantity x1(t)=xm(t) is the gap, state quantity
Figure BDA0002546297260000052
The speed of change of the gap distance, the state quantity x3(t)=im(t) is the control input current, NmNumber of coil windings, AmIs the sectional area of the magnet, m is the vehicle body mass, g is the gravity constant, um(t) is a control voltage, fdTo a degree of interference, mu0For vacuum permeability, RmRepresenting the electromagnet winding resistance.
And step S11, establishing an affine nonlinear mathematical model.
In order to obtain an affine nonlinear mathematical model of the suspension system, according to the principle of nonlinear coordinate transformation, the nonlinear transformation coordinates are selected as follows:
η=[z1z2z3]T∈Ωη,Ωη∈R3
wherein,
Figure BDA0002546297260000053
in the formula, z1Denotes the air gap spacing, z2Representing the speed of change of the air gap distance, z3Represents the air gap spacing acceleration; x is the number of1、x2、x3I.e. the state quantity x1(t)、x2(t)、x3(t)。
The derivation is performed on the above formula to obtain:
Figure BDA0002546297260000054
for simplicity of presentation, k and L are defined as follows:
Figure BDA0002546297260000055
according to maxwell's equations and Biot-Savar's theory,
Figure BDA0002546297260000056
it can also be expressed as:
Figure BDA0002546297260000061
thus, an affine nonlinear mathematical model is obtained:
Figure BDA0002546297260000062
therein, two non-linear bounded functions are defined:
Figure BDA0002546297260000063
and step S12, carrying out synovial membrane control law design according to the affine nonlinear mathematical model.
The state variable of the magnetic levitation system is selected to be z1=x1=xm(t),
Figure BDA0002546297260000064
Defining the system error as e and the error change rate as
Figure BDA0002546297260000065
Wherein e ═ z1-r, r is the desired position.
The slip form surface is designed as follows:
Figure BDA0002546297260000066
wherein, c1,c2∈R+Is a positive position control gain, having e ═ z1-r=x1-r。
Derivation of the above equation yields:
Figure BDA0002546297260000067
wherein f (x) and g (x) are two nonlinear bounded functions f (x) and g (x) in the affine nonlinear mathematical model.
Thus, a sliding mode variable structure control law model is obtained as follows:
Figure BDA0002546297260000068
wherein u isSMC(x, t) is the controller output, η, μ ∈ R+Respectively representing a constant arrival coefficient and an exponential arrival coefficient, r being an ideal trace instruction.
Verifying a sliding mode variable structure control law model:
the lyapunov equation is defined as:
Figure BDA0002546297260000069
the equation is positive and semi-positive, and two sides are derived at the same time to obtain:
Figure BDA00025462972600000610
therefore, based on lyapunov theory, the control system is globally stable.
The sliding mode variable structure controls the law model, but f (-) and g (-) are uncertain and even unknown, so that the approximation of f (-) and g (-) needs to be learned online through an RBF neural network.
And S13, correcting the sliding mode variable structure control law model through RBF neural network online learning approximation f (-) and g (-) to obtain the final sliding mode variable structure control law model.
A schematic of the closed loop control system is shown in fig. 3.
The input and output of the RBF neural network are:
Figure BDA0002546297260000071
f(x)=W*Thf(x)+f,g(x)=L*Thg(x)+g
where x is the network input, j is the jth hidden layer node, and h ═ hj]TIs the output of the Gaussian equation, W, L are approximate network approximation weights, W*,L*Is f (-), g (-) the ideal network weight,f,grespectively being network approximation errorf|≤Mf,|g|≤MgC is the neural network node center vector, b is the Gaussian basis function width.
When x ═ x1x2x3]TDetermined, the output of the RBF neural network is:
Figure BDA0002546297260000072
wherein h isf(x) And hg(x) For the Koski equation for RBF neural networks,
Figure BDA0002546297260000073
and
Figure BDA0002546297260000074
are the estimated network weights of f (x) and g (x).
Neural network minimum parameter learning methods are used for f (-) and g (-) respectively. Make phi ═ W2Phi is a positive real number,
Figure BDA0002546297260000075
is an on-line estimate of phi, learning error
Figure BDA0002546297260000076
Make it
Figure BDA0002546297260000077
Figure BDA0002546297260000078
Is a positive real number and is,
Figure BDA0002546297260000079
is that
Figure BDA00025462972600000710
On-line estimation of (1), learning error of
Figure BDA00025462972600000711
Therefore, the final sliding mode variable structure control law model is expressed as follows:
Figure BDA00025462972600000712
wherein sgn (·) is a symbolic equation, s is a dynamic sliding mode surface, um(x, t) is the control output.
According to the least parameter learning method, the adaptation law of f (-) and g (-) is defined as a single parameter
Figure BDA00025462972600000713
And
Figure BDA00025462972600000714
Figure BDA00025462972600000715
Figure BDA00025462972600000716
wherein, γ1212∈R+
Verifying the final sliding mode variable structure control law model:
according to step S13, the equation can be obtained:
Figure BDA0002546297260000081
the lyapunov equation is defined as:
Figure BDA0002546297260000082
it can be known that: v is more than or equal to 0
Figure BDA0002546297260000083
Wherein,
Figure BDA00025462972600000813
the method comprises the following steps of (1) preparing,
Figure BDA0002546297260000084
in the same way, the method for preparing the composite material,
Figure BDA0002546297260000085
Figure BDA0002546297260000086
because of RBF neural network approximation errorfFor very small real numbers, the rewrite is as follows:
Figure BDA0002546297260000087
the comprehensive self-adaptive rate is as follows:
Figure BDA0002546297260000088
wherein,
Figure BDA0002546297260000089
the following can be obtained:
Figure BDA00025462972600000810
wherein,
Figure BDA00025462972600000811
solution inequality
Figure BDA00025462972600000812
The following can be obtained:
Figure BDA0002546297260000091
Figure BDA0002546297260000092
it can be seen that the system is ultimately uniformly bounded. Thus, the system is demonstrated for both bounciness and convergence.
The embodiment is realized by the cooperation of software and hardware of the suspension system.
As shown in fig. 4, the levitation system includes a gap sensor, a chopper, a magnetic levitation controller, and a levitation electromagnet. The gap sensor is connected with the magnetic suspension controller through a chopper, the suspension electromagnet is connected with the magnetic suspension controller through peripheral hardware, and the gap sensor is installed on the suspension electromagnet. Further, the gap sensor is connected with the chopper through the gap processing plate, the control plate and the interface conversion plate.
The magnetic suspension controller comprises computer hardware and algorithm software. And the algorithm software for programming the magnetic suspension controller is stored in computer hardware. When the magnetic suspension controller works, the magnetic suspension controller is responsible for executing the operation of a neural network approximation algorithm, acquiring the input set physical parameters of the suspension system, acquiring the clearance data between the track and the vehicle body in real time, calculating and controlling the output control signal.
The working principle of the embodiment is as follows:
the gap sensor continuously measures and collects air gap distance data at a high speed in real time, and transmits the air gap distance data to computer equipment bearing the magnetic suspension controller through a communication line after the air gap distance data is modulated by analog-to-digital conversion and filtering. And the computer equipment bearing the magnetic suspension controller outputs the control quantity obtained by the magnetic suspension controller to peripheral hardware to drive the suspension electromagnet to work so as to suspend the train. And the error between the air gap distance and the target position is calculated by the magnetic suspension controller to obtain a control output quantity. With the real-time uninterrupted work of the gap sensor, the computer equipment and the peripheral hardware of the suspension electromagnet, the train can move to a target position within a limited time and keep within the position error limit range, and a stable and reliable suspension control effect is achieved.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (8)

1. A suspension system control method for a magnetic suspension train is characterized by comprising the following steps:
s1, constructing a second-order sliding mode surface based on a suspension control dynamics model of the maglev train, and introducing a nonlinear bounded function which is related to a positioning error signal and is approximated by an online real-time training neural network to obtain a final sliding mode variable structure control law model for constructing a maglev controller of a suspension system;
s2, inputting set physical parameters of the suspension system in the magnetic suspension controller;
s3, the magnetic suspension controller acquires gap data between the track and the train body in real time and outputs a control signal;
and S4, after receiving the control signal, the peripheral hardware of the suspension system drives the suspension electromagnet to move to the target position within a limited time and keeps within the position error limit range.
2. The levitation system control method for magnetic levitation trains as recited in claim 1, wherein in step S1, the expression of the final sliding mode variable structure control law model is:
Figure FDA0002546297250000011
Figure FDA0002546297250000012
Figure FDA0002546297250000013
wherein sgn (·) is a sign function, s is a dynamic sliding mode surface, e is a system error, c1、c2Eta and mu are control gain parameters,
Figure FDA0002546297250000014
and
Figure FDA0002546297250000015
neural network approximations of unknown nonlinear bounded functions f (-) and g (-) respectively, x being the network input, j being the jth hidden layer node, W*,L*Is the ideal network weight, h, of f (-) and g (-) inf(x) And hg(x) A Koski equation of a neural network, wherein r is an ideal tracking instruction;
according to the minimum parameter learning method, the self-adaptive rate of f (-) and g (-) is defined as a single parameter
Figure FDA0002546297250000016
And
Figure FDA0002546297250000017
Figure FDA0002546297250000018
Figure FDA0002546297250000019
wherein the parameter gamma1212∈R+
3. The levitation system control method for magnetic levitation trains as recited in claim 1, wherein the final sliding mode variable structure control law model construction method in step S1 comprises:
s11, establishing an affine nonlinear mathematical model;
s12, carrying out sliding mode control law design on the sliding mode controller according to the affine nonlinear mathematical model to obtain a sliding mode variable structure control law model and two nonlinear bounded functions f (·) and g (·);
s13, approximating nonlinear bounded functions f (cndot.) and g (cndot.) in the sliding mode variable structure control law model through RBF neural network online learning to obtain the final sliding mode variable structure control law model.
4. A levitation system control method for magnetic levitation trains as recited in claim 3, wherein in said step S11, the expression of affine non-linear mathematical model is:
Figure FDA0002546297250000021
wherein,
Figure FDA0002546297250000022
Figure FDA0002546297250000023
in the formula, z1Denotes the air gap spacing, z2Representing the speed of change of the air gap distance, z3Represents the air gap acceleration, m is the vehicle body mass, mu0Is a vacuum permeability, NmNumber of coil windings, AmIs the cross-sectional area of the magnet, RmRepresenting the electromagnet winding resistance.
5. The method as claimed in claim 4, wherein in step S12, the expression of the sliding mode variable structure control law model is:
Figure FDA0002546297250000024
in the formula uSMC(x, t) is the control output, η, μ ∈ R+Respectively representing a constant arrival coefficient and an exponential arrival coefficient, r being an ideal trace instruction, c1,c2∈R+Is the positive position control gain, e represents the system error and s represents the dynamic sliding mode surface.
6. The method as claimed in claim 1, wherein the levitation system comprises a gap sensor, a chopper, a magnetic levitation controller and an electromagnet, the gap sensor is connected to the magnetic levitation controller through the chopper, the electromagnet is connected to the magnetic levitation controller through peripheral hardware, and the gap sensor is mounted on the electromagnet.
7. A levitation system control method as recited in claim 6, wherein the gap sensor is connected to the chopper through a gap processing board, a control board and an interface conversion board.
8. The levitation system control method as recited in claim 1, wherein the levitation controller comprises computer hardware and algorithm software for performing neural network approximation algorithm operation, obtaining input set levitation system physical parameters, and obtaining gap data between the track and the car body in real time and outputting control signals.
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CN113263921B (en) * 2021-05-28 2022-07-15 同济大学 Dynamic suspension control method of magnetic-levitation train combined with vibration identification
CN114002953A (en) * 2021-10-09 2022-02-01 福州大学 Adaptive notch sliding mode differentiator method for maglev train signal processing
CN114002953B (en) * 2021-10-09 2023-12-08 福州大学 Self-adaptive notch sliding mode differentiator method for magnetic levitation train signal processing
CN116774588A (en) * 2023-07-25 2023-09-19 石家庄铁道大学 EMS type magnetic suspension train suspension frame double cross coupling self-adaptive backstepping control method
CN116774588B (en) * 2023-07-25 2024-01-23 石家庄铁道大学 EMS type magnetic suspension train suspension frame double cross coupling self-adaptive backstepping control method
CN118393967A (en) * 2024-06-24 2024-07-26 华东交通大学 Control method, device, medium and product for operation process of heavy-duty train

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