Magnetic levitation high-speed rail guiding constraint control method under network attack

Abstract

The invention discloses a guide constraint control method for a maglev high-speed rail under network attacks, and belongs to the field of rail transit. The method adopts a dynamic air gap constraint and boundary layer sectional type continuous adjustment technology to perform anti-network attack control on the maglev high-speed rail guide system: establishing a dynamic mathematical model and a lateral centrifugal force model of the maglev high-speed rail guide system, and further obtaining a state-space equation and a centrifugal force suppression control rate of the maglev high-speed rail guide system; constructing a satellite navigation network attack model of the maglev high-speed rail track and driving information; converting a state-space equation of the magnetic levitation high-speed rail guiding system into a control equation of the magnetic levitation high-speed rail guiding system containing wind shear disturbance and guiding force mismatch matching interference; dynamic constraint control is adopted, a guiding controller is designed, and guiding constraint control over the magnetic levitation high-speed rail under network attacks is achieved. While the starting stability of the maglev high-speed rail is improved, mismatch of the guiding force is rapidly compensated, and stable operation of the maglev high-speed rail is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of rail transportation, and in particular to a guidance constraint control method for a maglev high-speed railway under network attacks. Background Art

[0002] Maglev high-speed rail has attracted extensive attention from researchers around the world due to its advantages such as high speed, comfort and low noise. It has now become an indispensable part of the modern transportation system. Among them, the guidance control system of the maglev high-speed rail is one of its most important subsystems, which can maintain the stability of the high-speed rail during operation. The speed of the maglev high-speed rail reaches 600km / h, and it is easily affected by sudden lateral interference such as crosswind and lateral centrifugal interference force during turning.

[0003] To ensure the safe operation of high-speed rail, satellite navigation control of maglev high-speed rail based on the extension direction of the track is essential, which can drive the high-speed rail to complete small radius turning actions under the premise of high-speed driving based on satellite navigation information. Therefore, effective real-time communication of satellite navigation information is an indispensable guarantee to ensure the passive stable operation of maglev high-speed rail under the guidance force compensation mismatch caused by the loss of navigation information when the network is congested.

[0004] It is worth noting that due to unknown changes in the external environment, such as random wind shear, the high-speed rail is prone to unstable start-up and uneven guide air gaps, which intensifies the instability during operation, causing friction between high-speed rail components and tracks, damaging facilities, and affecting stable operation. Therefore, it is particularly important to ensure that the high-speed rail starts stably and that the air gaps on both sides of the high-speed rail are strictly constrained, thereby ensuring stable operation of the high-speed rail during driving.

[0005] Due to the high nonlinearity, strong coupling and inherent instability of the guidance system, it is extremely challenging to achieve stable control. In the research on guidance control of maglev high-speed rail, traditional control methods such as PID control and state feedback control can maintain the guidance stability of high-speed rail, but as a system with extremely demanding transient performance requirements, traditional control methods cannot guarantee frictionless control between high-speed rail and track.

[0006] To this end, the present invention provides a guidance constraint control method for a maglev high-speed railway under network attacks, which can ensure the stable suspension of the high-speed railway during the starting phase, and dynamically adjust the convergence speed of the maglev high-speed railway based on the degree of horizontal displacement movement of the high-speed railway under the guidance force compensation mismatch, so as to realize the safe and stable operation of the maglev high-speed railway. Summary of the invention

[0007] The main purpose of the present invention is: in view of the shortcomings and gaps in the existing technology, the present invention provides a maglev high-speed rail guidance constraint control method under network attacks, through the maglev high-speed rail guidance constraint control method, the maglev high-speed rail guidance air gap strict starting loose operation constraint function is selected to improve the stability of the maglev high-speed rail guidance system in the starting stage; in view of the maglev high-speed rail being attacked by network during operation, especially during turning action, resulting in the loss of satellite navigation information and thus causing mismatch in high-speed rail guidance force compensation, a segmented continuous adjustment boundary layer function based on error amplitude is designed to dynamically adjust the control strength of the controller, quickly compensate for the guidance force mismatch during operation, and ensure the smooth operation of the maglev high-speed rail.

[0008] In order to achieve the above objectives, the present invention provides a method for controlling the guidance constraints of a maglev high-speed railway under a network attack, comprising the following steps:

[0009] Step 1, establishing a mathematical model of the maglev high-speed rail guidance system with random wind shear disturbance and guidance force mismatch;

[0010] Step 2, construct the state space equation of the maglev high-speed rail guidance system containing random wind shear disturbance and guidance force mismatch;

[0011] Step 3: Construct a satellite navigation network attack data model for maglev high-speed rail track and driving information;

[0012] Step 4, constructing the control equation of the maglev high-speed rail guidance system containing wind shear disturbance and guidance force mismatch matching interference;

[0013] Step 5, designing a magnetic levitation high-speed rail guidance system controller with dynamic air gap constraints;

[0014] The mathematical model of the maglev high-speed rail guidance system containing random wind shear disturbance and guidance force mismatch in step 1 is:

[0015]

[0016] Where m is the mass of the maglev high-speed rail carried by a single pair of guide coils, x is the horizontal displacement of the maglev high-speed rail, subscript i=l, r represents the left and right sides of the high-speed rail, F i is the electromagnetic attraction generated by the guide coils on the left and right sides, i i is the current flowing into the guide coils on the left and right sides, δ i is the air gap between the left and right guide coils and the track guide surface, F1 represents the lateral centrifugal interference force generated by the turning of the maglev high-speed rail, F2 represents the lateral wind shear interference force on the maglev high-speed rail, μ0 is the vacuum magnetic permeability, N is the number of turns of the guide electromagnetic coil, A is the effective area of ​​the magnetic pole of the guide coil facing the track guide surface, μ is the PWM signal of the H-bridge drive circuit, and U dc is the power supply voltage of the H-bridge driving circuit, L is the equivalent inductance of the guide coil, and R is the equivalent resistance of the guide coil.

[0017] The lateral centrifugal force model based on the maglev high-speed rail speed, track slope angle and track turning angle is:

[0018]

[0019] Among them, g is the local gravitational acceleration, θ is the track cross slope angle, v is the travel speed of the maglev high-speed rail, and r is the radius of the track flat curve.

[0020] The state space equation of the maglev high-speed rail guidance system containing random wind shear disturbance and guidance force mismatch in step 2 is:

[0021]

[0022] Among them, x1, x2, and x3 are the horizontal displacement, speed, and bias current of the high-speed rail respectively, Kc=K / m, i0 is the reference current of the maglev high-speed rail guide coil, x0 is the steady-state air gap between the maglev high-speed rail guide coil and the track guide surface, y is the output of the state space equation of the maglev high-speed rail guidance system, and the interference term F1 / m relies on satellite navigation to generate control force to maintain the stability of the high-speed rail and ensure stable steering of the high-speed rail.

[0023] Based on satellite navigation data, the centrifugal force (2) for high-speed rail stable operation steering is obtained, and the centrifugal force suppression control μ is obtained by equation (3). gud for:

[0024]

[0025] The satellite navigation network attack data model for constructing the maglev high-speed rail track and driving information in step 3 is:

[0026] 1) Satellite navigation communication parameters P based on high-speed rail track and driving information under network attack F for:

[0027]

[0028] Among them, θ F ,v F ,r F The track slope angle, high-speed rail speed, and track flat curve radius information under network attacks are shown in Figure 2. k When a cyber attack occurs, is a constant, t l The communication delay time caused by network attacks.

[0029] 2) Based on equations (2) and (4), the satellite navigation network attack data model F of the maglev high-speed rail track and driving information is obtained los for:

[0030]

[0031] Among them, mgsin(θ F (t k -t l ))-mv F 2 (t k -t l )cos(θ F (t k -t l )) / r F (t k -t l ) indicates satellite navigation communication delay caused by network attack, and 0 indicates satellite navigation communication interruption caused by network attack.

[0032] The control equation of the maglev high-speed rail guidance system containing wind shear disturbance and guidance force mismatch matching interference in step 4 is:

[0033]

[0034] in, z1=x1,z2=x2,z3=K x x1+K i x3+f1+f2,K x =4Ki0 2 / (mx0 3 ), K i =-4Ki0 / (mx0 2 ),

[0035] The design steps of the magnetic levitation high-speed railway guidance system controller with dynamic air gap constraint in step 5 are as follows:

[0036] 1) Set the horizontal displacement tracking error of the maglev high-speed rail guidance system and its velocity, acceleration, and acceleration time-varying rate as:

[0037]

[0038] Among them, z r It is the target of horizontal displacement trajectory tracking of the maglev high-speed rail guidance system.

[0039] 2) Constructing the constraint boundary of high-speed rail start-up and stable operation

[0040] ρ(0)>e st ,ρ(∞)>e op (8)

[0041] Among them, ρ(0) is the startup transient constraint boundary, ρ(∞) is the operation transient constraint boundary, and e st is the starting transient tolerance, satisfying est ≥F2T c 2 / (2m),T c The control cycle of the controller of the maglev high-speed railway guidance system with dynamic air gap constraints. op The allowable error for transient operation is, satisfying e op ≥(F1+F2)T c 2 / (2m).

[0042] 3) The constraint function of strict starting and wide loose operation of the maglev high-speed rail guidance air gap based on the sigmoid function is constructed as follows:

[0043]

[0044] Among them, α>0, β>0, l>0, l>0, Υ>0 are all adjustable parameters of the strict constraint function of the maglev high-speed rail guided air gap starting, exp is the natural exponential function, t is the time, and ρ(t) can be replaced by ρ in the mathematical description.

[0045] Then the strict startup transient constraint stage and the loose operation transient constraint stage of formula (9) must satisfy:

[0046]

[0047] The transition from startup transient to operation transient state meets the following requirements:

[0048]

[0049] Among them, e sw is the allowable error of transition from starting transient to running transient, satisfying e sw ≥F1T c 2 / (2m).

[0050] 4) Reconstruct the horizontal displacement tracking error of the maglev high-speed rail into And find its first, second, and third order derivatives as

[0051]

[0052] Among them, χ=2 / ((1+ζ / ρ)(1-ζ / ρ)ρ),

[0053] 5) Sliding mode surface of the controller of the maglev high-speed rail guidance system based on dynamic guidance air gap constraint right

[0054] The time derivative, combined with equation (7) and the sliding mode approach rate, can be obtained:

[0055]

[0056] Among them, c1>0, c2>0, are the adjustable parameters of the sliding mode surface of the controller of the maglev high-speed railway guidance system with dynamic guidance air gap constraint, is the sliding mode approach rate gain function to be designed, and tanh is the hyperbolic tangent function.

[0057] 6) Design a piecewise continuous adjustment boundary layer function based on the error amplitude:

[0058]

[0059] in, is the adjustable parameter of the boundary layer function, K s =L / (U dc K i ), e b To track the error band, the following parameters need to be met by adjusting the parameters:

[0060]

[0061] Here, abs represents absolute value.

[0062] 7) Based on equations (8) and (10), the controller of the maglev high-speed rail guidance system with dynamic guidance air gap constraint is:

[0063]

[0064] Formula (14) is the designed dynamic air gap constrained maglev high-speed rail guidance system controller, and the system composed of formula (3) and formula (14) is a closed-loop system.

[0065] In the previous formula, a dot on a letter represents the first-order derivative of the letter, two dots represent the second-order derivative of the letter, and three dots represent the third-order derivative of the letter. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Attached Figure 1 It is a schematic diagram of the maglev high-speed rail guidance system of the present invention.

[0067] Attached Figure 2 It is the simulation curve of random wind shear disturbance and lateral centrifugal interference.

[0068] Attached Figure 3 This is the simulation curve of the guide force compensation mismatch signal.

[0069] Attached Figure 4 This is the comparison curve of horizontal displacement simulation of the controller of the maglev high-speed rail guidance system with dynamic air gap constraints.

[0070] Attached Figure 5This is the simulation curve of the tracking error of the magnetic levitation high-speed rail guidance system controller with dynamic air gap constraints.

[0071] Attached Figure 6 This is the boundary layer function simulation curve under the information loss mismatch of the maglev high-speed rail guidance force compensation.

[0072] Attached Figure 7 This is the simulation curve of the boundary layer function under the time delay mismatch of the maglev high-speed rail guidance force compensation.

[0073] Attached Figure 8 This is the simulation curve of the output signal of the maglev high-speed rail guidance controller with dynamic air gap constraints.

[0074] Attached Fig. 9 This is the simulation curve of the guide coil current waveform under the guide force compensation information loss mismatch.

[0075] Attached Fig.10 This is the simulation curve of the guide coil current waveform under the guide force compensation time delay mismatch.

[0076] Among them, 1 is a high-speed rail carriage, 2 is a track, 3 is a left guide coil, 4 is a right guide coil, 5 is a left guide surface of the track, and 6 is a right guide surface of the track. DETAILED DESCRIPTION

[0077] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0078] The maglev high-speed rail guidance system is as follows Figure 1 As shown, 3 and 4 in 1 are facing 5 and 6 in 2 respectively. After the reference current i0 is passed through 3 and 4, 3 and 4 generate equal and opposite electromagnetic attraction forces on 5 and 6 respectively. At this time, the axial center line of 1 coincides with the center line of 2. When 1 is disturbed by the lateral centrifugal force during the small radius turning process, the control input μ changes accordingly, generating a bias current, so that the current i0 in 3 and 4 l ,i r Corresponding changes occur, and the electromagnetic attraction of 5 and 6 changes accordingly, generating a differential force, which suppresses the lateral centrifugal force interference caused by the random wind shear disturbance and the mismatch between the guidance force compensation during the steering process, and maintains the axial centerline of the high-speed rail near the centerline of the track.

[0079] The present invention provides a guidance constraint control method for a maglev high-speed railway under a network attack, in order to realize the starting constraint and dynamic rapid convergence of the above-mentioned maglev high-speed railway when it is subjected to random wind shear disturbance and guidance force compensation mismatch, specifically comprising the following steps:

[0080] Step 1: Establish a mathematical model of the maglev high-speed rail guidance system with random wind shear disturbance and guidance force mismatch:

[0081] The modeling process is as follows:

[0082] 1) As attached Figure 1 As shown in the figure, after the guide coils on both sides of the high-speed rail are energized, the guide electromagnetic suction force generated is:

[0083] F i (i i ,δ i )=Ki i 2 / δ i 2

[0084] As attached Figure 1 As shown in the figure, during the turning process, the maglev high-speed rail is subjected to gravity mg in the vertical direction and the lateral electromagnetic attraction F i (i i ,δ) and the lateral centrifugal force F1, F generated during the journey + The positive direction specified for modeling, during the movement, the mechanical equation of the maglev high-speed rail in the guiding direction is:

[0085]

[0086] The voltage balance equation of the guide coil is:

[0087] d(Li i ) / dt=μU dc -Ri i

[0088] In summary, the dynamic mathematical model of the maglev high-speed rail guidance system with random wind shear disturbance and guidance force compensation mismatch is:

[0089]

[0090] Where m is the mass of the maglev high-speed rail carried by a single pair of guide coils, x is the horizontal displacement of the maglev high-speed rail, subscript i=l, r represents the left and right sides of the high-speed rail, F i is the electromagnetic attraction generated by the guide coils on the left and right sides, i i is the current flowing into the guide coils on the left and right sides, δ i is the air gap between the left and right guide coils and the track guide surface, F2 represents the lateral wind shear interference force on the maglev high-speed rail, μ0 is the vacuum magnetic permeability, N is the number of turns of the guide electromagnetic coil, A is the effective area of ​​the magnetic pole of the guide coil facing the track guide surface, μ is the PWM signal of the H-bridge drive circuit, and U dc is the power supply voltage of the H-bridge driving circuit, L is the equivalent inductance of the guide coil, and R is the equivalent resistance of the guide coil.

[0091] 2) The lateral centrifugal force model based on high-speed rail speed, track slope angle and track turning angle is:

[0092]

[0093] Among them, g is the local gravitational acceleration, θ is the track cross slope angle, v is the travel speed of the maglev high-speed rail, and r is the radius of the track flat curve.

[0094] Step 2: Construct the state space equation of the maglev high-speed rail guidance system with random wind shear disturbance and guidance force mismatch:

[0095] 1) Take the horizontal displacement of the high-speed rail and the air gaps on both sides, the reference current of the guide coil and the bias current to be differentially transformed into:

[0096]

[0097] Based on the above transformation and formula (1), we get:

[0098]

[0099] x, i is the state x1~x3, x is the output y, and the state space equation of the maglev high-speed rail guidance system containing random wind shear disturbance and guidance force compensation mismatch is obtained:

[0100]

[0101] Among them, K c =K / m, i0 is the reference current of the maglev high-speed rail guide coil, x0 is the steady-state air gap between the maglev high-speed rail guide coil and the track guide surface, and the interference term F1 / m relies on satellite navigation to generate control force to maintain the stability of the high-speed rail and ensure stable steering of the high-speed rail.

[0102] 2) Based on satellite navigation data, the centrifugal force (2) for high-speed rail stable operation is obtained, and the centrifugal force suppression control law is obtained from equation (3):

[0103]

[0104] Step 3: Construct a satellite navigation network attack data model for maglev high-speed rail track and driving information:

[0105] 1) Satellite navigation communication parameters based on high-speed rail track and driving information under network attack are:

[0106]

[0107] Among them, θ F ,v F ,r F The track slope angle, high-speed rail speed, and track flat curve radius information under network attacks are shown in Figure 2. k When a cyber attack occurs, is a constant, t lThe communication delay time caused by network attacks.

[0108] 2) Based on equations (2) and (4), the satellite navigation network attack data model of the maglev high-speed rail track and driving information is obtained as follows:

[0109]

[0110] Among them, mgsin(θ F (t k -t l ))-mv F 2 (t k -t l )cos(θ F (t k -t l )) / r F (t k -t l ) indicates satellite navigation communication delay caused by network attack, and 0 indicates satellite navigation communication interruption caused by network attack.

[0111] Step 4: Construct the control equation of the maglev high-speed rail guidance system containing wind shear disturbance and guidance force mismatch interference:

[0112] The state space equation described in equation (3) is linearized near the equilibrium point (x1 = 0, x3 = 0) as follows:

[0113]

[0114] Among them, K x =4K c i0 2 / (mx0 3 ), K i =-4K c i0 / (mx0 2 ). Coordinate transformation is introduced to transform the non-matching random wind shear disturbance and the guidance force mismatch disturbance into matching disturbance:

[0115]

[0116] The control state space equation of the maglev high-speed rail guidance system containing non-matching random wind shear disturbance and guidance force compensation mismatch disturbance converted into matching disturbance is obtained as follows:

[0117]

[0118] in,

[0119] Step 5: Design a dynamic air gap constrained maglev high-speed rail guidance system controller. The design steps of the controller are:

[0120] 1) Set the horizontal displacement tracking error of the maglev high-speed rail guidance system and its velocity, acceleration, and acceleration time-varying rate as:

[0121]

[0122] Among them, z r It is the target of horizontal displacement trajectory tracking of the maglev high-speed rail guidance system.

[0123] 2) Constructing the constraint boundary of high-speed rail start-up and stable operation

[0124] ρ(0)>e st ,ρ(∞)>e op (8)

[0125] Among them, ρ(0) is the startup transient constraint boundary, ρ(∞) is the operation transient constraint boundary, and e st is the starting transient tolerance, satisfying e st ≥F2T c 2 / (2m),T c The control cycle of the controller of the maglev high-speed railway guidance system with dynamic air gap constraints. op The allowable error for transient operation is, satisfying e op ≥(F1+F2)T c 2 / (2m).

[0126] 3) The constraint function of strict starting and wide loose operation of the maglev high-speed rail guidance air gap based on the sigmoid function is constructed as follows:

[0127]

[0128] Among them, α>0, β>0, l>0, l>0, Υ>0 are all adjustable parameters of the strict constraint function of the maglev high-speed rail guide air gap startup, exp is the natural exponential function, t is the time, and in the mathematical description, ρ(t) can be replaced by ρ. Then the strict startup transient constraint stage and the loose operation transient constraint stage of formula (9) must meet:

[0129]

[0130] The transition from startup transient to operation transient state meets the following requirements:

[0131]

[0132] Among them, e sw is the allowable error of transition from starting transient to running transient, satisfying esw ≥F1T c 2 / (2m).

[0133] 4) Reconstruct the horizontal displacement tracking error of the maglev high-speed rail into And find its first, second, and third order derivatives as

[0134]

[0135] in,

[0136] 5) Sliding mode surface of the controller of the maglev high-speed rail guidance system based on dynamic guidance air gap constraint The time derivative, combined with equation (7) and the sliding mode approach rate, can be obtained:

[0137]

[0138] Among them, c1>0, c2>0, are the adjustable parameters of the sliding mode surface of the controller of the maglev high-speed railway guidance system with dynamic guidance air gap constraint, is the sliding mode approach rate gain function to be designed, and tanh is the hyperbolic tangent function.

[0139] 6) Design a piecewise continuous adjustment boundary layer function based on the error amplitude:

[0140]

[0141] in is the adjustable parameter of the boundary layer function, K s =L / (U dc K i ), e b To track the error band, the following parameters need to be met by adjusting the parameters:

[0142]

[0143] Here, abs represents absolute value.

[0144] 7) Based on equations (8) and (10), the controller of the maglev high-speed rail guidance system with dynamic guidance air gap constraint is:

[0145]

[0146] Formula (14) is the designed dynamic air gap constrained maglev high-speed rail guidance system controller, and the system composed of formula (3) and formula (14) is a closed-loop system.

[0147] The present invention is further described below using a preferred embodiment.

[0148] The parameters of the maglev high-speed rail guidance system are as follows: the equivalent inductance of the guidance coil is L = 0.1387H, the equivalent resistance of the guidance coil is R = 2.77Ω, and the effective area of ​​the guidance coil magnetic pole is A = 0.0552m 2 The number of turns of the guide coil is N = 200 turns. The parameters and specifications of the guide coils on both sides of the high-speed rail are the same. The total mass of the guide body is m = 1995 kg. The power supply voltage of the drive circuit is U dc =200V, vacuum magnetic permeability is μ0=4π×10 -7 , the steady-state air gap between the guide coil and the track guide surface is δ0=10mm, the steady-state current i0=10A, and the control target of the horizontal displacement of the high-speed rail is set to 0.

[0149] The interference encountered by the maglev high-speed rail during operation is assumed to be a linear superposition of two parts. The first part is as shown in the attached figure. Figure 2 As shown by the solid line, a sinusoidal signal with an amplitude in the range of [-0.5, 0.5] and a frequency of 1 rad / s is used to simulate the random wind shear disturbance f2 during the operation of the maglev high-speed rail, especially during the startup phase; the second part is shown in the attached figure. Figure 2 As shown by the dotted line, the track and operation data are as follows: the track curve radius R = 8000m, the high-speed rail travel speed v = 600km / h, the track cross slope angle θ = 10.02°, and the length of the transition curve is 666.67m. Figure 1 According to the force analysis shown in the figure, the lateral centrifugal interference that the high-speed railway experiences after entering the R8000 curve should be:

[0150] F1 / m=gsin(θ)-v 2 cos(θ) / R=-1.71m / s 2 ≈-1.72m / s 2

[0151] Combined with the conditions of the transition curve and the high-speed rail speed, the simulation time is set to 70s, as shown in the attached figure. Figure 2 As shown in the figure, the random wind shear disturbance and lateral centrifugal disturbance to which the high-speed railway is subjected during operation are:

[0152]

[0153] Among them, else represents other moments in the simulation time that are not involved in the random wind shear disturbance and lateral centrifugal interference.

[0154] As attached Figure 3 As shown by the solid line, under the above interference conditions, the mismatch signal of the maglev high-speed rail guidance force compensation information loss caused by the loss of satellite navigation information due to the designed network attack is:

[0155]

[0156] That is, in order to verify the effectiveness of the proposed controller, the guide force compensation mismatch, F los The case where = 0 is set in the entry transition curve, exit transition curve and R8000 curve.

[0157] As attached Figure 3 As shown by the dotted line, under the above interference conditions, the time delay mismatch signal of the maglev high-speed rail guidance force compensation under the loss of satellite navigation information caused by the designed network attack is:

[0158]

[0159] That is, the situation of compensating time delay in guiding force compensation mismatch.

[0160] According to the above simulation conditions, the system is simulated to verify the stable control ability of the maglev high-speed rail guidance control system with dynamic guidance air gap constraints under random wind shear disturbances and lateral centrifugal interferences.

[0161] Attached Figure 4 The figure shows the horizontal displacement simulation comparison curve of the maglev high-speed rail guidance system controller with dynamic air gap constraint. The dotted line is the displacement simulation curve of the maglev high-speed rail guidance force compensating for time delay mismatch, and the solid line is the displacement simulation curve of the maglev high-speed rail guidance force compensating for information loss mismatch. Figure 6 , 7 The simulation curve of the boundary layer function is based on the error amplitude piecewise continuous adjustment. Figure 6 This is the boundary layer function simulation curve under the loss of information mismatch of the guidance force compensation of the maglev high-speed rail. Figure 7 This is the boundary layer function simulation curve under the time delay mismatch of the maglev high-speed rail guidance force compensation; Figure 8 is the output signal of the maglev high-speed rail guidance controller under dynamic air gap constraint, the dotted line is the controller output signal under the guidance force compensation time delay mismatch, and the solid line is the controller output signal under the guidance force compensation information loss mismatch; Appendix Fig. 9 Figure 2 is the current waveform of the guide coil under the guidance force compensation information loss mismatch. The dotted line is the current waveform of the right guide coil, and the solid line is the current waveform of the left guide coil. Fig.10 It is the current waveform of the guide coil under the time delay mismatch of the guide force compensation. The dotted line is the current waveform of the guide coil on the right, and the solid line is the current waveform of the guide coil on the left.

[0162] Combined with Figure 4 , Attachment Figure 6 , Attachment Figure 7 , Attachment Figure 8 , Attachment Fig. 9 , Attachment Fig.10It can be seen that the proposed dynamic air gap constrained maglev high-speed rail guidance control system can quickly increase the switch gain based on the error amplitude segmented continuous adjustment switch gain function when the error fluctuates greatly due to the delay mismatch of the guidance force compensation and the information loss mismatch, and drive the guidance coil to quickly adjust the bias current to maintain the high-speed rail in a steady-state position.

[0163] Attached Figure 5 The figure shows the tracking error simulation curve of the maglev high-speed rail guidance system controller with dynamic air gap constraints, where the solid line is the tracking error simulation curve considering the mismatch between random wind shear and guidance force compensation, and the dotted line is the tracking error simulation curve without strict starting constraints. It can be seen that when disturbed by random wind shear, the proposed strict starting loose operation constraint function of the maglev high-speed rail guidance air gap can more strictly constrain the displacement of the maglev high-speed rail during the starting phase, ensuring that the starting state of the maglev high-speed rail is more stable under the condition of lateral wind shear.

[0164] The above results show that the guidance constraint control method of a maglev high-speed railway under network attack of the present invention can ensure that the system can start stably when it is disturbed by random wind shear, while quickly offsetting the lateral centrifugal force generated by the guidance force compensation mismatch during the turning process, ensuring that the maglev high-speed railway can operate reliably after a smooth start, and the system has good anti-interference ability.

Claims

1. A method for controlling the guidance constraints of a maglev high-speed railway under a network attack, characterized in that: The method comprises: S1. Establish a mathematical model of the maglev high-speed rail guidance system with random wind shear disturbance and guidance force mismatch; S2. Construct the state space equation of the maglev high-speed rail guidance system with random wind shear disturbance and guidance force mismatch; S3. Construct a satellite navigation network attack data model for maglev high-speed rail track and driving information; S4. Construct the control equation of the maglev high-speed rail guidance system with wind shear disturbance and guidance force mismatch interference; S5. Design a controller for the maglev high-speed rail guidance system with dynamic air gap constraints.

2. The method for controlling the guidance constraints of a maglev high-speed railway under a network attack according to claim 1 is characterized in that: The mathematical model of the maglev high-speed rail guidance system containing random wind shear disturbance and guidance force mismatch in S1 is specifically: Where m is the mass of the maglev high-speed rail carried by a single pair of guide coils, x is the horizontal displacement of the maglev high-speed rail, the subscript i=l, r represents the left and right sides of the train, and F i is the electromagnetic attraction generated by the guide coils on the left and right sides, i i is the current flowing into the guide coils on the left and right sides, δ i is the air gap between the left and right guide coils and the track guide surface, F1 represents the lateral centrifugal interference force generated by the turning of the maglev high-speed rail, F2 represents the lateral wind shear interference force on the maglev high-speed rail, μ0 is the vacuum magnetic permeability, N is the number of turns of the guide electromagnetic coil, A is the effective area of ​​the magnetic pole of the guide coil facing the track guide surface, μ is the PWM signal of the H-bridge drive circuit, and U dc is the power supply voltage of the H-bridge driving circuit, L is the equivalent inductance of the guide coil, and R is the equivalent resistance of the guide coil; The lateral centrifugal force model based on train speed, track slope angle and track turning angle is: Among them, g is the local gravitational acceleration, θ is the track cross slope angle, v is the travel speed of the maglev high-speed rail, and r is the radius of the track flat curve.

3. The method for controlling the guidance constraints of a maglev high-speed railway under a network attack according to claim 2 is characterized in that: The state space equation of the maglev high-speed rail guidance system containing random wind shear disturbance and guidance force mismatch in S2 is specifically: Among them, x1, x2, x3 are the horizontal displacement, speed and bias current of the train respectively, y is the output of the state space equation of the maglev high-speed rail guidance system, K c =K / m, i0 is the reference current of the maglev train guide coil, x0 is the steady-state air gap between the maglev high-speed rail guide coil and the track guide surface, and the interference term F1 / m relies on satellite navigation to generate control force to maintain the stability of the train and ensure stable steering of the train; Based on satellite navigation data, the centrifugal force (2) for stable train operation and the centrifugal force suppression control μ are obtained from equation (3). gud for:

4. The method for controlling the guidance constraints of a maglev high-speed railway under a network attack according to claim 3 is characterized in that: The specific steps of constructing the satellite navigation network attack data model of the maglev train track and driving information in S3 include: S31: Satellite navigation communication parameters P based on train track and driving information under cyber attack F for: Among them, θ F ,v F ,r F The track slope angle, train speed, and track flat curve radius information under network attack, t k is the time when the network attack occurs, θ≠0 is a constant, t l Communication delay time caused by network attacks; S32: Based on equations (2) and (4), the satellite navigation network attack data model F of the maglev train track and driving information is obtained los for: Among them, mgsin(θ F (t k -t l ))-mv F 2 (t k -t l )cos(θ F (t k -t l )) / r F (t k -t l ) indicates satellite navigation communication delay caused by network attack, and 0 indicates satellite navigation communication interruption caused by network attack.

5. The method for controlling the guidance constraints of a maglev high-speed railway under a network attack according to claim 4 is characterized in that: The control equation of the maglev high-speed rail guidance system containing wind shear disturbance and guidance force mismatch matching interference in S4 is: Among them, z1=x1,z2=x2,z3=K x x1+K i x3+F1 / m+F2 / m,K x =4Ki0 2 / (mx0 3 ), K i =-4Ki0 / (mx0 2 ), 6. The method for controlling the guidance constraints of a maglev high-speed railway under a network attack according to claim 5 is characterized in that: The design steps of the magnetic levitation high-speed railway guidance system controller with dynamic air gap constraint in S5 include: S51: Set the horizontal displacement tracking error of the maglev high-speed rail guidance system and its velocity, acceleration, and acceleration time-varying rate to: Among them, z r Tracking target for horizontal displacement trajectory of maglev high-speed rail guidance system; S52: Constructing train start and train stable operation constraint boundaries p(0)>e st ,ρ(∞)>e op (8) Among them, ρ(0) is the startup transient constraint boundary, ρ(∞) is the operation transient constraint boundary, and e st is the starting transient tolerance, satisfying e st ≥F2T c 2 / (2m), Tc is the control period of the magnetic levitation high-speed railway guidance system controller with dynamic air gap constraint, e op is the operating transient tolerance, satisfying e op ≥(F1+F2)T c 2 / (2m); S53: Construct the strict starting wide loose operation constraint function of the maglev high-speed rail guidance air gap based on the sigmoid function: Among them, α>0, β>0, l>0, l>0, Υ>0 are all adjustable parameters of the strict constraint function of the maglev high-speed rail guide air gap startup, exp is the natural exponential function, t is the time, then the strict startup transient constraint stage and the loose operation transient constraint stage of formula (9) must meet: The transition from startup transient to operation transient state meets the following requirements: Among them, e sw is the allowable error of transition from starting transient to running transient, satisfying e sw ≥F1T c 2 / (2m); S54: Reconstruct the horizontal displacement tracking error of the maglev high-speed rail as And find its first, second, and third order derivatives as Where, x = 2 / ((1+ζ / ρ)(1-ζ / ρ)ρ), S55: Sliding mode surface of the controller for the maglev high-speed rail guidance system based on dynamic guidance air gap constraints The time derivative, combined with equation (7) and the sliding mode approach rate, can be obtained: Among them, c1>0, c2>0, are the adjustable parameters of the sliding mode surface of the controller of the maglev high-speed railway guidance system with dynamic guidance air gap constraint, is the sliding mode approach rate gain function to be designed, tanh is the hyperbolic tangent function; S56: Design a piecewise continuous adjustment boundary layer function based on error amplitude: in, is the adjustable parameter of the boundary layer function, K s =L / (U dc K i ), e b To track the error band, the following parameters need to be met by adjusting the parameters: Wherein, abs represents absolute value; S57: Based on equations (8) and (10), the magnetic levitation high-speed rail guidance system controller with dynamic guidance air gap constraint is obtained as follows: Formula (14) is the designed dynamic air gap constrained maglev high-speed rail guidance system controller, and the system composed of formula (3) and formula (14) is a closed-loop system.

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