Maglev High-Speed Railway Guidance Constraint Control Method under Cyber Attacks

Abstract

A method for guiding and restraining control of maglev high-speed trains under cyber attacks belongs to the field of rail transit. This method uses dynamic air gap constraint and boundary layer segmented continuous adjustment technology to perform anti-cyber attack control on the maglev high-speed train guiding system: establish a dynamic mathematical model and a lateral centrifugal force model of the maglev high-speed train guiding system, and then obtain the state space equation and centrifugal force suppression control rate of the maglev high-speed train guiding system; construct a satellite navigation cyber attack model for the maglev high-speed train track and train operation information; transform the state space equation of the maglev high-speed train guiding system into a control equation of the maglev high-speed train guiding system with wind shear disturbance and guiding force mismatch matching interference; adopt dynamic constraint control to design a guiding controller to achieve guiding and restraining control of the maglev high-speed train under cyber attacks. The present invention improves the starting stability of the maglev high-speed train while quickly compensating for the guiding force mismatch and ensuring the smooth operation of the maglev high-speed train.

Description

Technical Field

[0001] The present invention relates to the field of rail transit, and particularly to a guide constraint control method for maglev high-speed trains under cyber attacks. Background Art

[0002] Maglev high-speed trains have attracted extensive attention from researchers around the world due to their advantages such as high running speed, comfort, and low noise, and have now become an indispensable part of the modern transportation system. Among them, the maglev high-speed train guide control system is one of its most important subsystems, which can keep the maglev high-speed train stable during driving. The maglev high-speed train can reach a speed of 600 km / h and is easily affected by sudden lateral disturbances such as crosswinds and lateral centrifugal interference forces during the steering process.

[0003] To ensure the safe operation of maglev high-speed trains, satellite navigation control of maglev high-speed trains based on the track extension direction is essential, which can drive the high-speed train to complete small-radius steering actions based on satellite navigation information under the premise of high-speed driving. Therefore, effective real-time communication of satellite navigation information is an essential guarantee to ensure the passive stable operation of maglev high-speed trains when the navigation information is lost due to network congestion and the guide force compensation is mismatched.

[0004] It should be noted that due to unknown changes in the external environment, such as random wind shear, it is easy to cause unstable starting of maglev high-speed trains and uneven guide air gaps, resulting in an increase in unstable conditions during operation, causing friction between maglev high-speed train components and the track, damaging facilities, and affecting stable operation. Therefore, it is particularly important to ensure the stable suspension start of maglev high-speed trains and strictly constrain the air gaps on both sides of maglev high-speed trains, so as to ensure the stable operation of maglev high-speed trains during driving.

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

[0006] Therefore, a guide constraint control method for maglev high-speed trains under cyber attacks according to the present invention can ensure the stable suspension of maglev high-speed trains during the starting stage, and at the same time dynamically adjust the convergence speed of maglev high-speed trains based on the degree of horizontal displacement movement of maglev high-speed trains under the mismatch of guide force compensation, so as to achieve the safe and stable operation of maglev high-speed trains. Summary of the Invention

[0007] The main objective of the present invention is: aiming at the deficiencies and gaps in the existing technologies, the present invention provides a guidance constraint control method for maglev high-speed trains under network attacks. Through the guidance constraint control method for maglev high-speed trains, a strict starting and loose running constraint function for the maglev high-speed train guidance air gap is selected to improve the stability of the maglev high-speed train guidance system in the starting stage; aiming at the situation that the maglev high-speed train is under network attacks during operation, especially during turning maneuvers, resulting in the loss of satellite navigation information and thus the mismatch of the guidance force compensation, a boundary layer function based on error amplitude segmented continuous adjustment is designed to dynamically adjust the control intensity of the controller, quickly compensate for the mismatch of the guidance force during operation, and ensure the smooth operation of the maglev high-speed train.

[0008] To achieve the above objectives, a guidance constraint control method for maglev high-speed trains under network attacks according to the present invention includes the following steps:

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

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

[0011] Step 3, construct a satellite navigation network attack data model of the maglev high-speed train track and train operation information;

[0012] Step 4, construct a control equation of the maglev high-speed train guidance system with random wind shear disturbance and guidance force mismatch matching interference;

[0013] Step 5, design a controller for the maglev high-speed train guidance system with dynamic air gap constraint;

[0014] The mathematical model of the maglev high-speed train guidance system with random wind shear disturbance and guidance force mismatch in Step 1 is as follows:

[0015]

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

[0017] The lateral centrifugal interference force model based on the traveling speed of the maglev high - speed train, the track cross - slope angle, and the track steering angle is

[0018]

[0019] where g is the local acceleration due to gravity, θ is the track cross - slope angle, v is the traveling speed of the maglev high - speed train, and r is the radius of the horizontal curve of the track.

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

[0021]

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

[0023] Based on satellite navigation data, the lateral centrifugal interference force of the maglev high - speed train for stable operation is obtained from equations (2) and (3), and the lateral centrifugal interference force suppression control μ gud is:

[0024]

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

[0026] 1) The satellite navigation communication parameter P based on the maglev high - speed train track and train operation information under network attack F is:

[0027]

[0028] where θ F , v F , r F are the track cross - slope angle, the traveling speed of the maglev high - speed train, and the radius of the horizontal curve of the track information respectively under network attack, t k is the occurrence time of the network attack, is a constant, and t l is the communication delay time caused by the network attack.

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

[0030]

[0031] Among them, \(mg\sin(\theta F (t k -t l )) - mv F 2 (t k -t l )\cos(\theta F (t k -t l )) / r F (t k -t l ) is the time delay of satellite navigation communication caused by cyber attacks, and \(0\) is the interruption of satellite navigation communication caused by cyber attacks.

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

[0033]

[0034] Among them, 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]

[0036] The design steps of the controller of the maglev high - speed rail guiding system with dynamic air - gap constraint in step 5 are:

[0037] 1) Set the horizontal displacement tracking error of the maglev high - speed rail guiding system and its speed, acceleration, and acceleration time - varying rate as:

[0038]

[0039] Among them, z r is the horizontal displacement trajectory tracking target of the maglev high - speed rail guiding system.

[0040] 2) Construct the constraint boundaries for the start - up and stable operation of the maglev high - speed rail

[0041] ρ(0) > e st , ρ(∞) > e op (8)

[0042] where ρ(0) is the starting transient constraint boundary, ρ(∞) is the running transient constraint boundary, and e st is the starting transient allowable error, satisfying e st ≥F2T c 2 / (2m), and T c is the control period of the maglev high-speed rail guiding system controller with dynamic air-gap constraint. e op is the running transient allowable error, satisfying e op ≥(F1 + F2)T c 2 / (2m).

[0043] 3) Construct the strict starting and loose running constraint function of the maglev high-speed rail guiding air-gap based on the sigmoid function as:

[0044]

[0045] where α > 0, β > 0, l > 0, Υ > 0 are all adjustable parameters of the strict starting and loose running constraint function of the maglev high-speed rail guiding air-gap, exp is the natural exponential function, t is the time, and in mathematical description, ρ(t) can be replaced by ρ.

[0046] Then the strict starting transient constraint stage and the loose running transient constraint stage of Equation (9) need to satisfy:

[0047]

[0048] The starting transient to running transient transition stage satisfies:

[0049]

[0050] where e sw is the allowable error from starting transient to running transient, satisfying e sw ≥F1T c 2 / (2m).

[0051] 4) Reconstruct the horizontal displacement tracking error of the maglev high-speed rail as and obtain its first, second, and third derivatives as

[0052]

[0053] where χ = 2 / ((1 + ζ / ρ)(1 - ζ / ρ)ρ),

[0054] 5) The sliding mode surface of the maglev high-speed rail guiding system controller based on the dynamic guiding air-gap constraint For

[0055] The derivative with respect to time, combining Equation (7) with the sliding mode reaching law, gives:

[0056]

[0057] where \(c_1 > 0\), \(c_2 > 0\) are adjustable parameters of the sliding mode surface of the maglev high-speed train guiding system controller for the dynamic guiding air gap constraint, is the gain function of the sliding mode reaching law to be designed, and tanh is the hyperbolic tangent function.

[0058] 6) Design a piecewise continuous adjustment boundary layer function based on the error amplitude as

[0059]

[0060] where, is the adjustable parameter of the boundary layer function, \(K\) s = \(L / (U\) dc \(K\) i ), \(e\) b is the tracking error band. By adjusting the parameters, it is required to satisfy:

[0061]

[0062] where abs represents the absolute value.

[0063] 7) Based on Equations (11) and (12), the controller of the maglev high-speed train guiding system with dynamic guiding air gap constraint is:

[0064]

[0065] Equation (14) is the designed controller of the maglev high-speed train guiding system with dynamic air gap constraint. Then, the system composed of Equations (3) and (14) is a closed-loop system.

[0066] In the previous formulas, a dot above a letter represents the first derivative of that letter, two dots represent the second derivative, and three dots represent the third derivative. Description of the Drawings

[0067] Att Figure 1 is a schematic diagram of the maglev high-speed train guiding system of the present invention.

[0068] Att Figure 2 is the simulation curve of random wind shear disturbance and lateral turning centrifugal interference.

[0069] Att Figure 3 is the simulation curve of the guiding force compensation mismatch signal.

[0070] Att Figure 4Horizontal displacement simulation comparison curve of the controller for the maglev high-speed rail guiding system with dynamic air gap constraint.

[0071] Appendix Figure 5 Tracking error simulation curve of the controller for the maglev high-speed rail guiding system with dynamic air gap constraint.

[0072] Appendix Figure 6 Boundary layer function simulation curve under the mismatch of guiding force compensation information loss for the maglev high-speed rail.

[0073] Appendix Figure 7 Boundary layer function simulation curve under the mismatch of guiding force compensation time delay for the maglev high-speed rail.

[0074] Appendix Figure 8 Output signal simulation curve of the maglev high-speed rail guiding controller with dynamic air gap constraint.

[0075] Appendix Figure 9 Guiding coil current waveform simulation curve under the mismatch of guiding force compensation information loss.

[0076] Appendix Figure 10 Guiding coil current waveform simulation curve under the mismatch of guiding force compensation time delay.

[0077] Among them, 1 is the high-speed rail carriage, 2 is the track, 3 is the left guiding coil, 4 is the right guiding coil, 5 is the left guiding surface of the track, and 6 is the right guiding surface of the track. Specific implementation mode

[0078] The present invention will be further described in detail below with reference to the accompanying drawings.

[0079] The maglev high-speed rail guiding system is as shown in Appendix Figure 1 As shown, 3 and 4 in 1 are respectively opposite to 5 and 6 in 2. After passing the reference current i0 into 3 and 4, 3 and 4 respectively generate equal and opposite electromagnetic suction forces on 5 and 6. 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 currents i l , i r change accordingly, and the electromagnetic suction forces on 5 and 6 change accordingly, generating a differential force to suppress the lateral centrifugal force interference generated by the random wind shear disturbance and the guiding force compensation mismatch during the turning process, and maintaining the high-speed rail axial center line near the track center line.

[0080] A maglev high-speed rail guiding constraint control method under network attacks according to the present invention. In order to achieve the starting constraint and dynamic fast convergence of the above-mentioned maglev high-speed rail when being disturbed by random wind shear and having a guiding force compensation mismatch, the method specifically includes the following steps:

[0081] Step 1, establish a mathematical model of the maglev high-speed train guidance system with random wind shear disturbance and guidance force mismatch:

[0082] The modeling process is as follows:

[0083] 1) As shown in the appendix Figure 1 , after the guidance coils on both sides of the maglev high-speed train are energized, the guidance electromagnetic suction force is:

[0084] F i (i i , δ i ) = Ki i 2 / δ i 2

[0085] As shown in the appendix Figure 1 , during the turning process of the maglev high-speed train, it is vertically affected by gravity mg, and laterally by the guidance electromagnetic suction force F i (i i , δ) and the lateral centrifugal force F1 generated during the traveling process. F + is the positive direction specified for modeling. During the traveling process, the mechanical equation in the guidance direction of the maglev high-speed train is:

[0086]

[0087] The voltage balance equation of the guidance coil is:

[0088] d(Li i ) / dt = μU dc -Ri i

[0089] In summary, the dynamic mathematical model of the maglev high-speed train guidance system with random wind shear disturbance and guidance force compensation mismatch is:

[0090]

[0091] Among them, m is the mass of the maglev high-speed train carried by a single pair of guidance coils, x is the horizontal displacement of the maglev high-speed train, the subscript i = l, r represents the left and right sides of the high-speed train, F i is the electromagnetic suction force generated by the left and right guidance coils, i i is the current passed through the left and right guidance coils, δ i is the air gap between the left and right guidance coils and the track guidance surface, F2 represents the random wind shear disturbance received by the maglev high-speed train, μ0 is the vacuum permeability, N is the number of turns of the guidance electromagnetic coil, A is the effective area of the magnetic pole of the guidance coil facing the track guidance surface, μ is the PWM signal of the H-bridge drive circuit, U dc is the power supply voltage of the H-bridge drive circuit, L is the equivalent inductance of the guidance coil, and R is the equivalent resistance of the guidance coil.

[0092] 2) The lateral centrifugal interference force model based on the traveling speed of the maglev high-speed train, the track cross slope angle, and the track steering angle is

[0093]

[0094] where g is the local acceleration due to gravity, θ is the track cross slope angle, v is the traveling speed of the maglev high-speed train, and r is the radius of the horizontal curve of the track.

[0095] Step 2, construct the state space equation of the maglev high-speed train guidance system with random wind shear disturbance and guidance force mismatch:

[0096] 1) Take the horizontal displacement of the maglev high-speed train and the air gaps on both sides, and the differential transformation of the reference current and the bias current of the guidance coil as:

[0097]

[0098] Based on the above transformation and Equation (1), we get:

[0099]

[0100] Respectively take as the states x1 to x3, and take x as the output y, then the state space equation of the maglev high-speed train guidance system with random wind shear disturbance and guidance force compensation mismatch is:

[0101]

[0102] where K c = K / m, i0 is the reference current of the maglev high-speed train guidance coil, x0 is the steady-state air gap between the maglev high-speed train guidance coil and the track guidance surface, and the interference term F1 / m depends on satellite navigation to generate control force to maintain the stability of the maglev high-speed train and ensure the stable turning of the maglev high-speed train.

[0103] 2) Based on satellite navigation data, obtain the lateral centrifugal interference force (2) for the stable operation of the maglev high-speed train, and the lateral centrifugal force suppression control law μ gud is:

[0104]

[0105] Step 3, construct the satellite navigation network attack data model for the maglev high-speed train track and train operation information:

[0106] 1) The satellite navigation communication parameters based on the maglev high-speed train track and train operation information under network attack are:

[0107]

[0108] where θ F , vF , r F The information of the track cross slope angle, the traveling speed of the maglev high - speed train, and the radius of the track horizontal curve under different network attacks, t k is the occurrence time of the network attack, is a constant, t l is the communication delay time caused by the network attack.

[0109] 2) Based on Equations (2) and (4), the satellite navigation network attack data model F of the maglev high - speed train track and train operation information is obtained los as follows:

[0110]

[0111] where, 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 ) is the satellite navigation communication time delay caused by the network attack, and 0 is the satellite navigation communication interruption caused by the network attack.

[0112] Step 4, construct the control equation of the maglev high - speed train guidance system with random wind shear disturbance and guiding force mismatch matching interference:

[0113] Linearize the state - space equation described in Equation (3) near the equilibrium point (x1 = 0, x3 = 0) as:

[0114]

[0115] where, K x = 4K c i0 2 / (mx0 3 ), K i = - 4K c i0 / (mx0 2 ). Introduce a coordinate transformation to convert the non - matching random wind shear disturbance and guiding force mismatch interference into matching interference:

[0116]

[0117] The control state - space equation of the maglev high - speed train guidance system with the non - matching random wind shear disturbance and guiding force compensation mismatch interference converted into matching interference is obtained as:

[0118]

[0119] Among them,

[0120]

[0121] Step 5: Design a controller for the maglev high-speed rail guiding system with dynamic air-gap constraints. The design steps of the controller are as follows:

[0122] 1) Set the horizontal displacement tracking error of the maglev high-speed rail guiding system and its velocity, acceleration, and acceleration time-variation rate as:

[0123]

[0124] Among them, z r is the horizontal displacement trajectory tracking target of the maglev high-speed rail guiding system.

[0125] 2) Construct the starting and stable operation constraint boundaries of the maglev high-speed rail

[0126] ρ(0) > e st , ρ(∞) > e op (8)

[0127] Among them, ρ(0) is the starting transient constraint boundary, ρ(∞) is the running transient constraint boundary, and e st is the starting transient allowable error, satisfying e st ≥F2T c 2 / (2m), T c is the control period of the controller for the maglev high-speed rail guiding system with dynamic air-gap constraints. e op is the running transient allowable error, satisfying e op ≥(F1 + F2)T c 2 / (2m).

[0128] 3) Construct a sigmoid function-based strict starting and loose running constraint function for the maglev high-speed rail guiding air-gap as:

[0129]

[0130] Among them, α > 0, β > 0, l > 0, Υ > 0 are all adjustable parameters of the strict starting and loose running constraint function for the maglev high-speed rail guiding air-gap. exp is the natural exponential function, and t is time. In mathematical descriptions, ρ(t) can be replaced by ρ. Then, the strict starting transient constraint stage and the loose running transient constraint stage of Equation (9) need to satisfy:

[0131]

[0132] The transition stage from starting transient to running transient satisfies:

[0133]

[0134] where e sw is the allowable error for the transition from starting transient to running transient, and satisfies e sw ≥F1T c 2 / (2m).

[0135] 4) Reconstruct the horizontal displacement tracking error of the maglev high - speed train as and obtain its first, second, and third - order derivatives as

[0136]

[0137] where χ = 2 / ((1 + ζ / ρ)(1 - ζ / ρ)ρ),

[0138] 5) Based on the derivative of the sliding mode surface of the maglev high - speed train guiding system with dynamic guiding air - gap constraint with respect to time, combining Equation (7) and the sliding mode reaching law, we can obtain:

[0139]

[0140] where c1>0, c2>0 are adjustable parameters of the sliding mode surface of the maglev high - speed train guiding system with dynamic guiding air - gap constraint, is the gain function of the sliding mode reaching law to be designed, and tanh is the hyperbolic tangent function.

[0141] 6) Design a piece - wise continuous adjustment boundary - layer function based on the error amplitude as

[0142]

[0143] where is the adjustable parameter of the boundary - layer function, K s =L / (U dc K i ), e b is the tracking error band, and through the adjustment of parameters, it needs to satisfy:

[0144]

[0145] where abs represents the absolute value.

[0146] 7) Based on Equations (11) and (12), the controller of the maglev high - speed train guiding system with dynamic guiding air - gap constraint is:

[0147]

[0148] Equation (14) is the designed controller of the maglev high-speed rail guidance system with dynamic air-gap constraint. The system composed of Equations (3) and (14) is a closed-loop system.

[0149] The following uses a preferred embodiment to further illustrate the present invention.

[0150] The parameters of the maglev high-speed rail guidance system are as follows: the equivalent inductance value of the guidance coil is L = 0.1387 H, the equivalent resistance value of the guidance coil is R = 2.77 Ω, the effective area of the magnetic pole of the guidance coil is A = 0.0552 m 2 , the number of turns of the guidance coil is N = 200 turns. The parameter specifications of the guidance coils on both sides of the high-speed rail are the same. The total mass of the guide body is m = 1995 kg, and the power supply voltage of the drive circuit is U dc = 200 V, the vacuum permeability is μ0 = 4π × 10 -7 , the steady-state air gap between the guidance coil and the track guidance surface is δ0 = 10 mm, the steady-state current i0 = 10 A, and the control target of the horizontal displacement of the high-speed rail is set to 0.

[0151] Set the interference suffered during the operation of the maglev high-speed rail as the linear superposition of two parts. The first part is as shown by the solid line in the appendix Figure 2 . A sine 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 suffered during the operation of the maglev high-speed rail, especially during the starting stage; the second part is as shown by the dashed line in the appendix Figure 2 . The track and operation data with a track curve radius R = 8000 m, a high-speed rail traveling speed v = 600 km / h, a track cross slope angle θ = 10.02°, and a transition curve length of 666.67 m are used. According to the force analysis shown in the appendix Figure 1 , the lateral centrifugal interference suffered by the maglev high-speed rail after entering the R8000 curve should be:

[0152] F1 / m = gsin(θ) - v 2 cos(θ) / R = -1.71 m / s 2 ≈ -1.72 m / s 2

[0153] Combined with conditions such as the transition curve and the high-speed rail traveling speed, set the simulation time to 70 s. As shown in the appendix Figure 2 , the random wind shear disturbance and lateral centrifugal interference suffered during the operation of the maglev high-speed rail are:

[0154]

[0155] Among them, else represents other moments not involved in the random wind shear disturbance and lateral centrifugal interference during the simulation time.

[0156] As shown in the Figure 3 solid line, under the above interference conditions, the mismatch signal of the magnetic levitation high-speed rail guiding force compensation information loss caused by the designed cyber attack resulting in the loss of satellite navigation information is:

[0157]

[0158] That is, in order to verify the effectiveness of the proposed controller, in the guiding force compensation mismatch, the case of F los = 0 is set in the transition curve at the entrance of the curve, the transition curve at the exit of the curve, and the R8000 curve.

[0159] As shown in the Figure 3 dashed line, under the above interference conditions, the mismatch signal of the magnetic levitation high-speed rail guiding force compensation time delay caused by the designed cyber attack resulting in the loss of satellite navigation information is:

[0160]

[0161] That is, the case of the compensation time delay in the guiding force compensation mismatch.

[0162] According to the above simulation conditions, the system is simulated to verify the stable control ability of the magnetic levitation high-speed rail guiding control system with dynamic guiding air gap constraint under random wind shear disturbance and lateral centrifugal interference.

[0163] As shown in the Figure 4 figure is the simulation comparison curve of the horizontal displacement of the controller of the magnetic levitation high-speed rail guiding system with dynamic air gap constraint. The dashed line is the displacement simulation curve of the magnetic levitation high-speed rail guiding force compensation time delay mismatch, and the solid line is the displacement simulation curve of the magnetic levitation high-speed rail guiding force compensation information loss mismatch; as shown in the Figure 6 、 7 figure is the simulation curve of the piecewise continuous adjustment boundary layer function based on the error amplitude, as shown in the Figure 6 figure is the boundary layer function simulation curve under the magnetic levitation high-speed rail guiding force compensation information loss mismatch, as shown in the Figure 7 figure is the boundary layer function simulation curve under the magnetic levitation high-speed rail guiding force compensation time delay mismatch; as shown in the Figure 8 figure is the output signal of the magnetic levitation high-speed rail guiding controller with dynamic air gap constraint. The dashed line is the output signal of the controller under the magnetic levitation high-speed rail guiding force compensation time delay mismatch, and the solid line is the output signal of the controller under the magnetic levitation high-speed rail guiding force compensation information loss mismatch; as shown in the Figure 9 figure is the guiding coil current waveform under the magnetic levitation high-speed rail guiding force compensation information loss mismatch. The dashed line is the current waveform of the right guiding coil, and the solid line is the current waveform of the left guiding coil; as shown in the Figure 10For the guide coil current waveform under the time delay mismatch of the guiding force compensation, the dashed line is the current waveform of the right guide coil, and the solid line is the current waveform of the left guide coil.

[0164] Combined with the attached Figure 4 , attached Figure 6 , attached Figure 7 , attached Figure 8 , attached Figure 9 , attached Figure 10 It can be seen that when the error fluctuates greatly due to the time delay mismatch of the guiding force compensation and the information loss mismatch, the proposed dynamic air-gap constrained maglev high-speed rail guiding control system can quickly increase the switching gain based on the error amplitude segmented continuous adjustment of the switching gain function, drive the guide coil to quickly adjust the bias current, and maintain the maglev high-speed rail at the steady-state position.

[0165] Attached Figure 5 The figure shows the simulation curve of the tracking error of the controller of the dynamic air-gap constrained maglev high-speed rail guiding system. Among them, the solid line is the simulation curve of the tracking error considering random wind shear and guiding force compensation mismatch, and the dashed line is the simulation curve of the tracking error without strict starting constraints. It can be seen that when affected by random wind shear disturbances, the proposed maglev high-speed rail guiding air-gap strict starting and loose running constraint function can more strictly constrain the displacement of the maglev high-speed rail in the starting stage, ensuring that the starting state of the maglev high-speed rail is more stable under the condition of lateral wind shear.

[0166] The above results show that a maglev high-speed rail guiding constraint control method under network attacks according to the present invention can quickly offset the lateral centrifugal force generated due to the guiding force compensation mismatch during the steering process while ensuring stable starting when the system is disturbed by random wind shear, ensuring that the maglev high-speed rail can operate reliably after smooth starting, and the system has good anti-interference ability.

Claims

1. A guiding constraint control method for maglev high-speed trains under cyber attacks, characterized in that, The method includes: S1. Establish a mathematical model of the maglev high-speed rail guiding system with random wind shear disturbance and guiding force mismatch as: Among them, m is the mass of the maglev high-speed train borne by a single pair of guiding coils, x is the horizontal displacement of the maglev high-speed train, the subscript i = l, r represents the left and right sides of the maglev high-speed train, F i is the electromagnetic suction force generated by the guiding coils on the left and right sides, i i is the current passed through the guiding coils on the left and right sides, δ i is the air gap between the guiding coils on the left and right sides and the track guiding surface, F1 represents the lateral centrifugal interference force generated by the turning of the maglev high-speed train, F2 represents the random wind shear disturbance received by the maglev high-speed train, μ0 is the vacuum permeability, N is the number of turns of the guiding electromagnetic coil, A is the effective area of the magnetic pole of the guiding coil facing the track guiding surface, μ is the PWM signal of the H-bridge drive circuit, U dc is the power supply voltage of the H-bridge drive circuit, L is the equivalent inductance of the guiding coil, and R is the equivalent resistance of the guiding coil; The lateral centrifugal interference force model based on the traveling speed of the maglev high-speed rail, the cross slope angle of the track, and the turning angle of the track is where g is the local acceleration of gravity, θ is the cross slope angle of the track, v is the traveling speed of the maglev high-speed rail, and r is the radius of the horizontal curve of the track; S2. Construct the state space equation of the maglev high-speed rail guiding system with random wind shear disturbance and guiding force mismatch; S3. Construct a satellite navigation network attack data model for the maglev high-speed rail track and train operation information. The specific steps include: S31: Satellite navigation communication parameter P based on maglev high-speed rail track and train operation information under cyber attack F is as follows: Among them, θ F , v F , r F are the information of the cross slope angle of the track, the traveling speed of the maglev high-speed train, and the radius of the horizontal curve of the track under network attacks respectively, and t k is the occurrence time of the network attack, is a constant, and t l is the communication delay time caused by the network attack; S32: Based on Equations (2) and (3), obtain the satellite navigation network attack data model F of the maglev high-speed rail track and train operation information los as follows: where, 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 ) is the time delay of satellite navigation communication caused by a cyber attack, and 0 is the interruption of satellite navigation communication caused by a cyber attack; S4. Construct the control equation of the maglev high-speed rail guiding system with random wind shear disturbance and guiding force mismatch matching interference; S5. Design a controller for the maglev high-speed rail guiding system with dynamic air gap constraint.

2. The maglev high-speed rail guiding constraint control method under network attacks according to claim 1, wherein, The state space equation of the maglev high-speed rail guiding system with random wind shear disturbance and guiding force mismatch in S2 is specifically: Among them, x1, x2, and x3 are the horizontal displacement, speed, and bias current of the maglev high-speed train respectively, y is the output of the state-space equation of the maglev high-speed train guidance system, K c = K / m, i0 is the reference current of the maglev high-speed train guidance coil, x0 is the steady-state air gap between the maglev high-speed train guidance coil and the track guidance surface, and the interference term F1 / m relies on satellite navigation to generate control force to maintain the stability of the maglev high-speed train and ensure the stable turning of the maglev high-speed train; Based on satellite navigation data, the lateral centrifugal interference force for the stable operation of the maglev high-speed train is obtained. From equations (2) and (5), the lateral centrifugal interference force suppression control μ is as follows: gud is:

3. The maglev high-speed rail guiding constraint control method under network attacks according to claim 2, wherein, The control equation of the maglev high-speed rail guiding system with random wind shear disturbance and guiding force mismatch matching interference in S4 is: where 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 ), 4. The maglev high-speed rail guiding constraint control method under network attacks according to claim 3, wherein, The design steps of the controller for the maglev high-speed rail guiding system with dynamic air gap constraint in S5 include: S51: Set the horizontal displacement tracking error of the maglev high-speed rail guiding system and its speed, acceleration, and acceleration time rate of change as: where z r is the tracking target of the horizontal displacement trajectory of the maglev high-speed rail guiding system; S52: Construct the constraint boundaries for the start-up and stable operation of the maglev high-speed rail. ρ(0) > e st , ρ(∞) > e op (8) Among them, ρ(0) is the starting transient constraint boundary, ρ(∞) is the operating transient constraint boundary, and e st is the starting transient allowable error, satisfying e st ≥F2T c 2 / (2m), where T c is the control period of the controller of the maglev high-speed rail guiding system with dynamic air-gap constraint, and e op is the operating transient allowable error, satisfying e op ≥(F1 + F2)T c 2 / (2m); S53: Construct a sigmoid function-based strict start-up and loose operation constraint function for the maglev high-speed rail guiding air gap as: where α > 0, β > 0, l > 0, Υ > 0 are all adjustable parameters of the strictly starting and loosely operating constraint function for the guide air gap of the maglev high-speed train, exp is the natural exponential function, and t is the time. Then, the strictly starting transient constraint stage and the loosely operating transient constraint stage of Equation (9) need to satisfy: The transition stage from the start-up transient to the operation transient satisfies: where, e sw is the allowable error for the transition from the starting transient state to the running transient state, and satisfies e sw ≥F1T c 2 / (2m); S54: Reconstruct the horizontal displacement tracking error of the maglev high-speed train into and obtain its first, second, and third-order derivatives as where χ = 2 / ((1 + ζ / ρ)(1 - ζ / ρ)ρ), S55: Sliding mode surface of the controller of the maglev high-speed train guidance system based on dynamic guiding air-gap constraint The derivative with respect to time, combined with Equation (7) and the sliding mode reaching law, can be obtained as follows: where \(c_1>0\), \(c_2>0\) are adjustable parameters of the sliding mode surface of the maglev high-speed rail guidance system controller for dynamic guidance air-gap constraint, is the sliding mode reaching rate gain function to be designed, and tanh is the hyperbolic tangent function; S56: Design a piecewise continuous adjustment boundary layer function based on the error amplitude as Among them, is an adjustable parameter of the boundary layer function, K s = L / (U dc K i ), e b is the tracking error band. Through the adjustment of parameters, it is necessary to satisfy: where abs represents the absolute value; S57: Based on equations (11) and (12), the controller for the maglev high-speed rail guiding system with dynamic guiding air gap constraint is: Equation (14) is the designed controller for the maglev high-speed rail guiding system with dynamic air gap constraint. The system composed of equations (5) and (14) is a closed-loop system.

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