High-speed train anti-skid control method with input time delay compensation and actuator fault tolerance

Abstract

The application discloses a high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance, and specifically relates to the following steps: establishing a train adhesion dynamics model with input time delay and actuator fault for a train to achieve an anti-skid control target; processing the train model by using linearization technology to obtain a train cruise running stage approximate model, and further performing cruise stage controller design to obtain a corresponding time delay stable upper limit; taking the obtained time delay stable upper limit as the input time delay of the whole train running process, and compensating through a predictor to design an anti-skid control strategy of the whole train running process. The application can still achieve the anti-skid control target of the train when the input time delay and the actuator fault occur, and has important practical significance for guaranteeing the driving safety of the train.

Description

Technical Field

[0001] This invention belongs to the field of train operation control, and particularly relates to a high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance. Background Technology

[0002] The safe and reliable operation of trains is crucial to the safety of passengers' lives and property, making research on anti-skid control of significant theoretical and practical value. Train operation safety depends on the adhesion between the wheels and rails. Wheel slippage affects the wheel-rail adhesion state, thereby disrupting the train's mechanical balance and endangering operational safety. Therefore, by adjusting the train's traction / braking force to maintain effective adhesion between the wheels and rails, adverse conditions such as wheel slippage can be prevented.

[0003] Wheel-rail adhesion is a key factor in ensuring train wheel anti-skid, and research on wheel-rail adhesion control has yielded a series of representative results. However, given the increasing complexity and intelligence of train railway systems, and considering the complexity of the real-world train operating environment, further research is urgently needed. On one hand, current research typically uses onboard sensors to collect train speed and other status information to design controllers. However, limitations in train communication networks lead to delays in the transmission of train status information, resulting in a mismatch between the collected data used by the controller and the real-time train status information. This causes input time delay, which affects system performance, and existing anti-skid controls that do not consider input time delay cannot handle its adverse effects. On the other hand, actuator failures in train control systems can affect the system structure and jeopardize the entire train system's control strategy. Especially with today's increasingly high train speeds, high-speed trains pose even more serious hazards when failures occur. Therefore, train operation control under fault conditions has become a research hotspot in the field of rail transit. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance.

[0005] The present invention provides a high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance, comprising the following steps:

[0006] Step 1: Based on the wheel-rail adhesion mechanism and dynamic laws, establish a train adhesion dynamic model with input time delay and actuator failure, and refine it into a traction / braking model.

[0007] Step 2: For the train cruise operation phase, linearization technology is used to process the train model to obtain an approximate model for the train cruise operation phase.

[0008] Step 3: Based on the desired speed and desired creep rate of the selected cruise operation phase, calculate the deviation of the train's operating state to obtain the error dynamic model of the train's cruise operation phase.

[0009] Step 4: Analyze the error dynamic model for the train cruise operation phase to obtain the coupling relationship between the expected speed and the expected creep rate during the train cruise operation phase, and further obtain the method for calculating the expected creep rate during the cruise phase.

[0010] Step 5: Design a virtual controller, and based on this, matrix-encode the error dynamic model of the train cruise operation phase.

[0011] Step 6: Design the Lyapunov functional, and combine it with the dynamic error model of the train cruise operation phase to analyze and derive the system stability conditions during the train cruise operation phase.

[0012] Step 7: Using Matlab / Simulink software, calculate the controller parameters and corresponding upper bounds of time delay stability to ensure stable operation of the train during the cruise phase.

[0013] Step 8: Obtain the train cruise phase controller through the virtual controller, wherein: the obtained upper bound of the time delay stability is used as the input time delay and compensated by the predictor.

[0014] Step 9: Use the obtained upper bound of the time delay stability as the input time delay for the entire train operation process.

[0015] Step 10: Using the optimal creep rate as the expected creep rate for the train traction acceleration phase, design the controller for the train traction phase based on the backstepping method, where the input time delay is compensated by a predictor.

[0016] Step 11: Design the desired creep speed during the train braking phase. With creep speed tracking as the control objective, design the controller for the train braking operation phase. Similarly, the input time delay is compensated by the predictor.

[0017] Step 12: The developed train anti-skid control algorithm with time delay compensation and actuator fault tolerance is simulated and verified on a computer. By setting the simulation environment and designing the controller parameters, the purpose of train anti-skid control is achieved.

[0018] Step 13: Load the designed control algorithms for each stage of train operation into the ATO onboard equipment to achieve anti-skid operation control of the train in the event of input time delay and actuator failure.

[0019] Furthermore, step 1 includes the following steps:

[0020] Step 1.1: For wheel-rail creep, calculate the wheel-rail adhesion force based on the wheel-rail adhesion mechanism:

[0021] f a =μ(λ(t))mg (1)

[0022] Where: m represents the mass of the train; g is the acceleration due to gravity; μ(λ(t)) represents the adhesion coefficient, which is a function of the creep rate λ(t):

[0023]

[0024] Where λ(t)>0 corresponds to train traction operation, and λ(t)<0 corresponds to train braking operation; different values ​​of coefficients a, b, and c represent different track surfaces; and the creep rate is defined as:

[0025]

[0026] Where v(t) represents the vehicle speed; v w (t) is the tangential velocity of the wheel circumference, that is:

[0027] v ω (t)=ω(t)r (4)

[0028] In the formula, ω(t) and r are the wheel angular velocity and radius, respectively.

[0029] Step 1.2: Establish a train adhesion dynamics model based on the laws of dynamics, considering input time delay and actuator failure; at this point, the train adhesion dynamics model is:

[0030]

[0031] The unknown input time delay h satisfies the following condition:

[0032] 0≤h≤h m (6)

[0033] Where: g is the acceleration due to gravity; J is the moment of inertia of the wheel; ζ is the coefficient of viscous friction; h m This represents the upper bound of the time delay; during train operation, the running resistance f r (v(t))=c0+c1v(t)+c2v(t) 2 c0…c2 are drag coefficients.

[0034] u(th) represents the control input; ρ is the traction / braking efficiency: ρ = 0 means that the train has completely lost its traction or braking ability, 0 < ρ < 1 means that the train has partially lost its traction or braking efficiency, and ρ = 1 corresponds to the healthy operation of the traction / braking system; θ represents the partially uncontrolled action of the actuator.

[0035] Step 1.3: Detail the analysis of the train adhesion dynamics model based on the train traction and braking conditions; under the train traction condition, differentiate the creep rate λ(t):

[0036]

[0037] The adhesion dynamics model of the train traction condition is obtained:

[0038]

[0039] in:

[0040]

[0041] Similarly, for the train braking control phase:

[0042]

[0043] Thus, the adhesion dynamics model for train braking conditions is obtained:

[0044]

[0045] in:

[0046]

[0047] Furthermore, in step 2, during the train's cruise phase, it operates under traction conditions. The adhesion dynamics model of the train under traction conditions is linearized to obtain:

[0048]

[0049] Where: u cr (th) indicates the controller during the cruise phase;

[0050]

[0051] In step 3, the desired speed v for the train's cruise operation phase is selected. d and expected creep rate λ d Therefore, the train's speed deviation at time t is v. e (t)=v(t)-v d The creep rate deviation is λ e (t)=λ(t)-λ d The dynamic equation for the error during the train's cruise phase is:

[0052]

[0053] in:

[0054]

[0055] Furthermore, step 4 includes the following steps:

[0056] Step 4.1: Analyze system (15), combining the parameter a1(v) in equation (14) d ,λ d ...a3(v d ,λ d )have to:

[0057]

[0058] According to the train system (8), during the cruise phase therefore:

[0059] a1(v d ,λ d )v d +a2(v d ,λ d )λ d +a3(v d ,λ d )=0 (18)

[0060] At this point, system (15) is rewritten as:

[0061]

[0062] Step 4.2: According to relation (18), the formula for calculating the expected creep rate during the train cruise phase is:

[0063]

[0064] Where: v d It is the desired velocity, λ d It is the expected creep rate.

[0065] Furthermore, step 5 includes the following steps:

[0066] Step 5.1: Design the virtual controller for the train cruise phase as follows:

[0067]

[0068] The linear system at this point is:

[0069]

[0070] Design a memoryless state feedback controller:

[0071]

[0072] Where K = [k1, k2], E(t) = [v e (t),λe (t)] T .

[0073] Substitute the controller (23) into the system (22):

[0074]

[0075] Step 5.2: Denote system (24) as:

[0076]

[0077] in:

[0078]

[0079] Furthermore, step 6 includes the following steps:

[0080] Step 6.1: The designed Lyapunov functional is:

[0081] V cr (E t )=V1+V2+V3 (27)

[0082] in:

[0083]

[0084] L = L T >0, W = W T ≥0 and R=R T >0 is an undetermined 2×2 matrix.

[0085] Step 6.2: The system stability conditions during the train cruise operation phase are as follows:

[0086] There exist symmetric positive definite matrices L and R of appropriate dimensions, a semi-symmetric positive definite matrix W, a matrix V, and a symmetric matrix. And matrices M1 and M2, such that the following matrix inequalities hold;

[0087]

[0088] here:

[0089]

[0090] Furthermore, in step 7, the nonlinear matrix inequality condition (29) is first transformed into a linear matrix inequality condition, and then the controller parameters and the corresponding time-delay stability upper bound are solved using the linear matrix inequality toolbox, including the following steps:

[0091] Step 7.1: Equation (29) is a nonlinear matrix inequality, which needs to be transformed into a linear matrix inequality for solution; let R = εL, and substitute it into equation (29) to get:

[0092]

[0093] Multiply Λ by diag(III / h) on both the left and right sides. m ),have to:

[0094]

[0095] in:

[0096]

[0097] In equation (31), take Y 12 =0, substituting into equation (32) yields:

[0098]

[0099] To solve for the maximum time-delay stability upper bound h m That is, the smallest ι, introduces an additional 2×2 matrix Y. i =Y i T ≥0, i=1,2,3, satisfying:

[0100]

[0101] Substituting equation (35) into equation (34), we get:

[0102]

[0103] Step 7.2: Solve for the upper bound of the time-delay stability h m The corresponding controller feedback matrix K can then be transformed into an optimization problem:

[0104]

[0105] st

[0106]

[0107]

[0108]

[0109] Given a scalar ε, by solving equation (37), the values ​​of L, V, W, and M are calculated. i i = 1, 2, Y 11 Y 22 and Y iLet i = 1, 2, 3 be the smallest ι of the variables, and finally use h m =1 / l to find the upper bound of the time delay stability, and the feedback gain K = VL -1 .

[0110] Furthermore, in step 8, the train cruise operation phase controller is:

[0111]

[0112] Predicted values ​​of error variables:

[0113]

[0114] It has an initial value:

[0115]

[0116] Furthermore, in step 10, the anti-slip controller during the train traction acceleration phase is as follows:

[0117]

[0118] Where: u ac (t) represents the traction acceleration phase controller, k ac >0,y2,y3 are defined in system (9).

[0119] Predicted values ​​of state variables:

[0120]

[0121] It has an initial value:

[0122]

[0123] Furthermore, in step 11, the anti-slip controller for the train braking phase, designed based on creep speed, is as follows:

[0124]

[0125] Where: u de (t) represents the train braking phase controller, k de >0, z1, z2, z3 are defined in (12), and the target creep velocity v s * (t+h) is a function of v(t+h).

[0126] Predicted values ​​of state variables:

[0127]

[0128] It has an initial value:

[0129]

[0130] The beneficial technical effects of this invention are as follows:

[0131] 1. Due to limitations in train communication network capabilities, the speed and other collected information used by the train control system does not match the real-time train operating status information, resulting in input time lag. Input time lag causes existing anti-slip controllers to fail and can even cause the train system to lose stability. The control algorithm proposed in this invention can handle the adverse effects of input time lag, ensuring train operation safety.

[0132] 2. In train control systems, actuator failures can affect the system's structure and jeopardize the entire train system's control strategy. Therefore, the fault-tolerant controller developed in this invention can still achieve the anti-skid control objective of train operation even when an actuator fails. Attached Figure Description

[0133] Figure 1 This is a flowchart of the high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to the present invention.

[0134] Figure 2 This is a train speed response curve provided in an embodiment of the present invention.

[0135] Figure 3 This is a train creep rate response curve provided in an embodiment of the present invention. Detailed Implementation

[0136] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0137] The flowchart of a high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to the present invention is as follows: Figure 1 As shown, the specific steps include:

[0138] Step 1: Based on the wheel-rail adhesion mechanism and dynamic laws, establish a train adhesion dynamic model with input time delay and actuator failure, and refine it into a traction / braking model.

[0139] Step 1.1: For wheel-rail creep, calculate the wheel-rail adhesion force based on the wheel-rail adhesion mechanism:

[0140] f a =μ(λ(t))mg (1)

[0141] Where: m represents the mass of the train; g is the acceleration due to gravity; μ(λ(t)) represents the adhesion coefficient, which is a function of the creep rate λ(t):

[0142]

[0143] Where λ(t)>0 corresponds to train traction operation, and λ(t)<0 corresponds to train braking operation; different values ​​of coefficients a, b, and c represent different track surfaces; and the creep rate is defined as:

[0144]

[0145] Where v(t) represents the vehicle speed; v w (t) is the tangential velocity of the wheel circumference, that is:

[0146] v ω (t)=ω(t)r (4)

[0147] In the formula, ω(t) and r are the wheel angular velocity and radius, respectively.

[0148] Step 1.2: Establish a train adhesion dynamics model based on the laws of dynamics, considering input time delay and actuator failure; at this point, the train adhesion dynamics model is:

[0149]

[0150] The unknown input time delay h satisfies the following condition:

[0151] 0≤h≤h m (6)

[0152] Where: g is the acceleration due to gravity; J is the moment of inertia of the wheel; ζ is the coefficient of viscous friction; h m This represents the upper bound of the time delay; during train operation, the running resistance f r (v(t))=c0+c1v(t)+c2v(t) 2 c0…c2 are drag coefficients.

[0153] u(th) represents the control input; ρ is the traction / braking efficiency: ρ = 0 means that the train has completely lost its traction or braking ability, 0 < ρ < 1 means that the train has partially lost its traction or braking efficiency, and ρ = 1 corresponds to the healthy operation of the traction / braking system; θ represents the partially uncontrolled action of the actuator.

[0154] Step 1.3: Detail the analysis of the train adhesion dynamics model based on the train traction and braking conditions; under the train traction condition, differentiate the creep rate λ(t):

[0155]

[0156] The adhesion dynamics model of the train traction condition is obtained:

[0157]

[0158] in:

[0159]

[0160] Similarly, for the train braking control phase:

[0161]

[0162] Thus, the adhesion dynamics model for train braking conditions is obtained:

[0163]

[0164] in:

[0165]

[0166] Step 2: For the train cruise operation phase, linearization technology is used to process the train model to obtain an approximate model for the train cruise operation phase.

[0167] During the train's cruise phase, it operates under traction conditions. Linearizing the car adhesion dynamics model under traction conditions yields:

[0168]

[0169] Where: u cr (th) indicates the controller during the cruise phase;

[0170]

[0171] When a train is typically in the cruise phase, its operating state varies within a small neighborhood of the desired cruise target value. Therefore, linearization techniques can be used to process the train system during this period.

[0172] Step 3: Based on the desired speed and desired creep rate of the selected cruise operation phase, calculate the deviation of the train's operating state to obtain the error dynamic model of the train's cruise operation phase.

[0173] Selected train cruise operation phase desired speed v d and expected creep rate λ d Therefore, the train's speed deviation at time t is v. e (t)=v(t)-v d The creep rate deviation is λ e (t)=λ(t)-λ d The dynamic equation for the error during the train's cruise phase is:

[0174]

[0175] in:

[0176]

[0177] Step 4: Analyze the error dynamic model for the train cruise operation phase to obtain the coupling relationship between the expected speed and the expected creep rate during the train cruise operation phase, and further obtain the method for calculating the expected creep rate during the cruise phase.

[0178] Step 4.1: Analyze system (15), combining the parameter a1(v) in equation (14) d ,λ d ...a3(v d ,λ d )have to:

[0179]

[0180] According to the train system (8), during the cruise phase therefore:

[0181] a1(v d ,λ d )v d +a2(v d ,λ d )λ d +a3(v d ,λ d )=0 (18)

[0182] At this point, system (15) is rewritten as:

[0183]

[0184] Step 4.2: According to relation (18), the formula for calculating the expected creep rate during the train cruise phase is:

[0185]

[0186] Where: v d It is the desired velocity, λ d It is the expected creep rate.

[0187] Step 5: Design a virtual controller, and based on this, matrix-encode the error dynamic model of the train cruise operation phase.

[0188] Step 5.1: Design the virtual controller for the train cruise phase as follows:

[0189]

[0190] The linear system at this point is:

[0191]

[0192] Design a memoryless state feedback controller:

[0193]

[0194] Where K = [k1, k2], E(t) = [v e (t),λ e (t)] T .

[0195] Substitute the controller (23) into the system (22):

[0196]

[0197] Step 5.2: Denote system (24) as:

[0198]

[0199] in:

[0200]

[0201] Step 6: Design the Lyapunov functional, and combine it with the dynamic error model of the train cruise operation phase to analyze and derive the system stability conditions during the train cruise operation phase.

[0202] Step 6.1: The designed Lyapunov functional is:

[0203] V cr (E t )=V1+V2+V3 (27)

[0204] in:

[0205]

[0206] L = L T >0, W = W T ≥0 and R=R T >0 is an undetermined 2×2 matrix.

[0207] Step 6.2: The system stability conditions during the train cruise operation phase are as follows:

[0208] There exist symmetric positive definite matrices L and R of appropriate dimensions, a semi-symmetric positive definite matrix W, a matrix V, and a symmetric matrix. And matrices M1 and M2, such that the following matrix inequalities hold;

[0209]

[0210] here:

[0211]

[0212] Step 7: Using Matlab / Simulink software, calculate the controller parameters and corresponding upper bounds of time delay stability to ensure stable operation of the train during the cruise phase.

[0213] First, the nonlinear matrix inequality condition (29) is transformed into a linear matrix inequality condition. Then, the controller parameters and the corresponding time-delay stability upper bound are solved using the linear matrix inequality toolbox, including the following steps:

[0214] Step 7.1: Equation (29) is a nonlinear matrix inequality, which needs to be transformed into a linear matrix inequality for solution; let R = εL, and substitute it into equation (29) to get:

[0215]

[0216] Multiply Λ by diag(III / h) on both the left and right sides. m ),have to:

[0217]

[0218] in:

[0219]

[0220] In equation (31), take Y 12 =0, substituting into equation (32) yields:

[0221]

[0222] To solve for the maximum time-delay stability upper bound h m That is, the smallest ι, introduces an additional 2×2 matrix Y. i =Y i T ≥0, i=1,2,3, satisfying:

[0223]

[0224] Substituting equation (35) into equation (34), we get:

[0225]

[0226] Step 7.2: Solve for the upper bound of the time-delay stability h m The corresponding controller feedback matrix K can then be transformed into an optimization problem:

[0227]

[0228] st

[0229]

[0230]

[0231]

[0232] Given a scalar ε, by solving equation (37), the values ​​of L, V, W, and M are calculated. i i = 1, 2, Y 11 Y 22 and Y i Let i = 1, 2, 3 be the smallest ι of the variables, and finally use h m =1 / ι to find the upper bound of the time delay stability, and the feedback gain K = VL -1 .

[0233] Step 8: Obtain the train cruise phase controller through the virtual controller, wherein: the obtained upper bound of the time delay stability is used as the input time delay and compensated by the predictor.

[0234] The train cruise operation phase controller is:

[0235]

[0236] Predicted values ​​of error variables:

[0237]

[0238] It has an initial value:

[0239]

[0240] Step 9: Use the obtained upper bound of the time delay stability as the input time delay for the entire train operation process.

[0241] Step 10: Using the optimal creep rate as the expected creep rate for the train traction acceleration phase, design the controller for the train traction phase based on the backstepping method, where the input time delay is compensated by a predictor.

[0242] The anti-slip controller during the train's traction acceleration phase is as follows:

[0243]

[0244] Where: u ac (t) represents the traction acceleration phase controller, k ac >0,y2,y3 are defined in system (9).

[0245] Predicted values ​​of state variables:

[0246]

[0247] It has an initial value:

[0248]

[0249] Step 11: Design the desired creep speed during the train braking phase. With creep speed tracking as the control objective, design the controller for the train braking operation phase. Similarly, the input time delay is compensated by the predictor.

[0250] The anti-slip controller for train braking based on creep speed is as follows:

[0251]

[0252] Where: u de (t) represents the train braking phase controller, k de >0, z1, z2, z3 are defined in (12), and the target creep velocity v s * (t+h) is a function of v(t+h).

[0253] Predicted values ​​of state variables:

[0254]

[0255] It has an initial value:

[0256]

[0257] Step 12: The developed train anti-skid control algorithm with time delay compensation and actuator fault tolerance is simulated and verified on a computer. By setting the simulation environment and designing the controller parameters, the purpose of train anti-skid control is achieved.

[0258] The train speed response curve provided in this embodiment is as follows: Figure 2 As shown, the train creep response curve is as follows: Figure 3 As shown.

[0259] from Figure 2-3 It can be seen that: under the action of the traction acceleration controller, the train achieves optimal creep rate λ opt To control the target and fully utilize maximum adhesion, the train accelerates from an initial velocity v(0) = 3 m / s in approximately 31.1 s, reaching a cruising speed of 70 m / s. Afterward, due to inertia, the train speed slightly exceeds 70 m / s. The control system switches to the cruise phase controller when the train reaches the cruising speed of 70 m / s, and the train enters the cruise operation phase. During the cruise phase, the train speed and creep rate gradually track the desired speed and creep rate under the action of the cruise controller. After 300 s, the train enters the braking and stopping phase, and after approximately 85 s, the train speed drops to zero under the action of the braking controller. Throughout the entire control process, the control algorithm provided by this invention can adjust the train's traction / braking torque in a timely manner, ensuring it tracks the desired values ​​at each operating stage effectively. Furthermore, the train speed changes smoothly, and the creep rate never exceeds the optimal creep rate λ.opt (The creep rate limit for stable train operation) indicates that the wheels did not slip.

[0260] Step 13: Load the designed control algorithms for each stage of train operation into the ATO (Automatic Train Operation) onboard equipment to achieve anti-skid operation control of the train in the event of input time delay and actuator failure.

[0261] In summary, this embodiment establishes an adhesion dynamics model with input time delay and actuator failure based on the wheel-rail adhesion mechanism and dynamic laws, and refines it into a traction / braking model. For the train cruise operation phase, a linearization technique is used to process the train model to obtain an approximate model. A controller for the train cruise operation phase is designed based on the approximate model, and the corresponding upper bound of the time delay stability is obtained. The obtained upper bound of the time delay stability is used as the input time delay for the entire train operation process, and compensation is performed through a predictor to develop an anti-slip control strategy for the train's traction acceleration, cruise, and braking operation phases. Compared with existing anti-slip control strategies, this invention can handle the adverse effects of input time delay and actuator failure, improving train operation safety.

Claims

1. A high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance, characterized in that, The method comprises the following steps: Step 1: based on wheel-rail adhesion mechanism and dynamics law, a train adhesion dynamics model with input time delay and actuator fault is established, and is refined into a traction / braking model; Step 2: for the train cruising operation stage, a linearization technique is used to process the train model, and an approximate model of the train cruising operation stage is obtained; Step 3: according to the selected expected speed and expected creep rate of the cruising operation stage, the deviation of the train operation state is calculated, so as to obtain an error dynamic model of the train cruising operation stage; Step 4: the error dynamic model of the train cruising operation stage is analyzed, the coupling relationship between the expected speed and the expected creep rate of the train cruising operation stage is obtained, and a method for calculating the expected creep rate of the cruising stage is further obtained; Step 5: a virtual controller is designed, and the error dynamic model of the train cruising operation stage is matrixed on the basis of the virtual controller; Step 6: a Lyapunov functional is designed, and the system stability condition of the train cruising operation stage is obtained by combining the error dynamic model of the train cruising operation stage; Step 7: based on the Matlab / Simulink software, the controller parameters and the corresponding time delay stability upper limit ensuring the stable operation of the train cruising stage are calculated; Step 8: the train cruising stage controller is obtained through the virtual controller, wherein the obtained time delay stability upper limit is taken as an input time delay, and the predictor is used for compensation; Step 9: the obtained time delay stability upper limit is taken as an input time delay of the whole train operation process; Step 10: the optimal creep rate is taken as the expected creep rate of the train traction acceleration stage, and a controller of the train traction stage is designed based on the backstepping method, wherein the input time delay is compensated through the predictor; Step 11: the expected creep speed of the train braking stage is designed, the creep speed tracking is taken as a control target, a controller of the train braking operation stage is designed, and the input time delay is also compensated through the predictor; Step 12: the developed train anti-skid control algorithm with the time delay compensation function and the actuator fault tolerance capability is simulated on a computer, the simulation environment is set, the controller parameters are designed, and the purpose of the train anti-skid control is achieved; Step 13: the control algorithm of each operation stage of the train designed is loaded into the ATO on-board equipment, so that the train anti-skid operation control in the input time delay and the actuator fault is realized.

2. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 1, characterized in that, The step 1 comprises the following steps: Step 1.1: for the wheel-rail creep phenomenon, the wheel-rail adhesion force is calculated based on the wheel-rail adhesion mechanism: （1） where: denotes the train mass; is the gravitational acceleration; denotes the adhesion coefficient, which is a function of the creep rate : （2） wherein corresponding to a train traction operation, corresponding to a train braking operation; coefficient , , different values represent different track surfaces; and, the creep rate is defined as: （3） wherein represents the vehicle speed; is the tangential velocity of the wheel circumference, i.e.: （4） wherein and are the wheel angular velocity and radius, respectively; Step 1.2: a train adhesion dynamics model is established based on the dynamics law, wherein the input time delay and the actuator fault are considered; at this time, the train adhesion dynamics model is: （5） unknown input time delay satisfies the following conditions: （6） wherein: is the gravitational acceleration; is the wheel rotational inertia; is the viscous friction coefficient; denotes the time delay upper bound; during the train operation, the running resistance , is the resistance coefficient; denotes a control input; for traction / braking efficiency: the case where the train has completely lost its traction or braking capacity, denotes a partial loss of traction or braking efficiency of the train, corresponds to the case where the traction / braking system is operating correctly; denotes a partial action where the actuator is completely out of control; Step 1.3: Detailed analysis of the train adhesion dynamics model according to the train traction and braking conditions; in the train traction condition, the creep rate derivation: （7） The train adhesion dynamics model in the traction working condition is obtained: （8） Wherein: （9） For the train braking control stage: （10） Thus, the train adhesion dynamics model in the braking working condition is obtained: （11） Wherein: （12）。 3. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 2, characterized in that, In the step 2, the train cruising stage runs in the traction working condition, the train adhesion dynamics model in the traction working condition is linearized, and the following is obtained: （13） wherein: represents a controller for the cruise phase; （14） The desired speed of the selected train cruising phase in step 3 and the desired creep rate ; therefore, the speed deviation of the train at time t is , the creep rate deviation is , and the error dynamic equation of the train cruising phase is: （15） Wherein: （16）。 4. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 3, characterized in that, The step 4 comprises the following steps: Step 4.1: Analyzing the error dynamic equation (15) of the train cruising phase, combining the parameters in equation (14) we have: （17） According to the train traction working condition adhesion dynamics model (8), in the cruise stage Therefore: （18） At this time, the train cruising stage error dynamic equation (15) is rewritten as: （19） Step 4.2: according to the relationship (18), the expected creep rate calculation formula of the train cruising stage is: Step 4.2: according to the relationship (18), the expected creep rate calculation formula of the train cruising stage is: （20） wherein: is the desired speed, is the desired creep rate.

5. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 4, characterized in that, The step 5 comprises the following steps: Step 5.1: design the virtual controller for the train cruising phase as: （21） The linear system at this time is: （22） Design the memoryless state feedback controller: （23） wherein , ; Substitute the controller (23) into the linear system (22): （24） Step 5.2: record the linear system (24) as: （25） Wherein: （26）。 6. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 5, characterized in that, The step 6 comprises the following steps: Step 6.1: the designed Lyapunov functional is: （27） Wherein: （28） , and are pending 2x2 matrices; Step 6.2: the system stability condition for the train cruising phase is: there exists a symmetric positive definite matrix of appropriate dimension , a semi-symmetric positive definite matrix , a matrix , a symmetric matrix , and a matrix such that the following matrix inequality holds; , （29） Here: （30）。 7. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 6, characterized in that, In the step 7, firstly, the nonlinear matrix inequality (29) condition is converted into a linear matrix inequality condition, and then the controller parameters and the corresponding time delay stability upper limit are solved through the linear matrix inequality toolbox, comprising the following steps: Step 7.1: Equation (29) is a nonlinear matrix inequality, which needs to be converted into a linear matrix inequality for solution; let Substitute into equation (29) to get: , （31） Let Left multiply right multiply , we get: （32） Wherein: （33） In formula (31), take , into formula (32) to obtain: （34） To solve the maximal delay-stable upper bound , i.e. the minimal , introduce the additional 2x2 matrix , satisfying: （35） Substitute formula (35) into formula (34): （36） Step 7.2: Solving the time-delay stability upper bound and its corresponding controller feedback matrix which can be transformed into an optimization problem: ； ； ； （37） Given scalar , by solving equation (37), the minimum , , , , , and are calculated with as variable. Finally, the time-delay stability upper bound is obtained with and the feedback gain .

8. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 7, characterized in that, In the step 8, the controller for the train cruising phase is: （38） The error variable predictor model is: （39） With the initial value: （40）。 9. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 8, characterized in that, In the step 10, the anti-slip controller for the train traction acceleration phase is: （41） wherein: denotes the traction acceleration phase controller, defined in equation (9). The state variable prediction value is: （42） With the initial value: （43）。 10. The high-speed train anti-skid control method with input time delay compensation and actuator fault tolerance according to claim 9, characterized in that, In the step 11, the anti-slip controller for the train braking phase is designed based on the creep speed: （44） wherein: denotes the train braking phase controller, The target creep speed is a function of the train speed The state variable prediction value is: （45） With the initial value: （46）。

Images