A recursive rise control method and system for maglev train suspension system

Abstract

A recursive RISE control method and system for maglev train levitation systems is disclosed. The control method includes: constructing the dynamic equations and voltage balance equations of the electromagnets based on a single-point levitation system, and then constructing a dynamic model of the single-point levitation system accordingly; designing a virtual control law, and then designing a recursive RISE controller based on the backstepping method by combining the dynamic model of the single-point levitation system and the virtual control law; performing stability analysis on the RISE controller to obtain its stability conditions; and, based on satisfying the stability conditions, using the RISE controller to perform real-time control of the levitation gap of the maglev train levitation system. This invention has excellent anti-interference capabilities, reducing the impact of external interference or model uncertainty on levitation accuracy. Furthermore, by handling the nonlinear relationship between voltage and current through the backstepping method, this invention avoids the model mismatch problem caused by linearization.

Description

Technical Field

[0001] This invention relates to the field of suspension system control technology, and in particular to a recursive RISE control method and system for maglev train suspension systems. Background Technology

[0002] Maglev trains, as a novel mode of transportation, offer advantages such as zero mechanical friction, low noise, and a small turning radius, making them a powerful supplement to modern integrated transportation systems. Their levitation control system maintains a constant 8mm gap between the train and the track by adjusting the electromagnet current, thus achieving stable levitation. However, the maglev system is inherently an open-loop unstable nonlinear system; its electromagnetic force is directly proportional to the square of the current and inversely proportional to the square of the levitation gap. In actual operation, the system is also affected by various factors such as external disturbances, uncertainties in model parameters, and sensor noise. Therefore, designing a control algorithm with strong stability and anti-interference capabilities is crucial.

[0003] Currently, commonly used methods in suspension control include PID control, Active Disturbance Rejection Control (ADRC), and cascade control schemes. PID control has a simple structure and performs well under no disturbance or constant disturbance conditions, but it is difficult to achieve steady-state tracking of time-varying disturbances. ADRC estimates and performs feedforward compensation through an extended state observer, which can suppress some disturbances, but it still suffers from problems such as observation phase lag and complex parameter tuning. In addition, most mainstream schemes adopt a cascade control structure combining a gap loop and a current loop. This structure relies on the assumption that the time scale separation of the current loop is much faster than that of the gap loop. Its stability proof is usually limited to the linearization region near the equilibrium point, and the current loop has limited ability to handle disturbances such as electromagnetic interference and current sensor noise.

[0004] In summary, improving the anti-interference capability and global stability of the suspension controller is crucial for achieving higher speeds and greater precision in maglev train operation. Therefore, there is an urgent need for a control method with globally asymptotically stable characteristics and the ability to effectively suppress various disturbances to meet the high-performance control requirements of maglev train suspension systems. Summary of the Invention

[0005] This invention provides a recursive RISE control method and system for maglev train suspension systems to solve the technical problems mentioned in the background.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] This invention provides a recursive RISE control method for maglev train levitation systems, comprising the following steps:

[0008] S1. Taking the single-point suspension system in the maglev train suspension system as the research object, construct the dynamic equation and voltage balance equation of the electromagnet, and then construct the dynamic model of the single-point suspension system based on the dynamic equation and voltage balance equation of the electromagnet.

[0009] S2. Design a virtual control law, and then combine the dynamic model of the single-point suspension system with the virtual control law to design a RISE controller based on backstepping recursion.

[0010] S3. Perform stability analysis on the RISE controller based on backstepping recursion to obtain the stability conditions of the RISE controller.

[0011] S4. Based on the stability conditions, the suspension controller uses a RISE controller based on backstepping recursion to control the suspension gap of the maglev train suspension system in real time.

[0012] Furthermore, step S1 specifically includes the following steps:

[0013] S11. First, taking the single-point suspension system in the maglev train suspension system as the research object, the dynamic equation and voltage balance equation of the electromagnet are constructed, and the expressions are:

[0014] (1)

[0015] in, The total mass of the electromagnet and the mass it carries. The current in the electromagnet winding is... The voltage applied across the electromagnet winding. The levitation gap between the electromagnet and the track. The disturbance force experienced by the electromagnet. This refers to the number of turns in the electromagnet winding. The resistance is for DC. The area of ​​the electromagnet poles; symbol This represents the first derivative of the parameter; symbol This represents the second derivative of the parameter; Indicates the permeability of free space; Represents gravitational acceleration; t Indicates time;

[0016] S12. Define three state variables. , , ,and , , ;

[0017] S13, Using three state variables , , The dynamic equations and voltage balance equations of the electromagnet are rewritten to obtain the dynamic model of the single-point levitation system, as shown in the following expression:

[0018] (2)

[0019] in, , These represent the model uncertainty caused by external force disturbances and the model uncertainty caused by lumped electromagnetic disturbances, respectively.

[0020] Furthermore, step S2 specifically includes the following steps:

[0021] S21, By introducing the desired gap between the electromagnet and the track. Tracking error in constructing the gap between the electromagnet and the track The expression;

[0022] S22, Introducing filter error And construct the filter error The expression;

[0023] S23, Introducing auxiliary variables and construct auxiliary variables The expression;

[0024] S24. Introduce the first user-defined variable. ,and Then based on the first user-defined variable For filter error The expression is rewritten to obtain the filter error. The rewritten expression;

[0025] S25. Dynamic model and auxiliary variables based on single-point suspension system The expression and filter error The rewritten expression for auxiliary variables Rewrite the expression to obtain the auxiliary variable. The rewritten expression;

[0026] S26. Designing Virtual Control Laws Constructing virtual control laws The expression introduces an auxiliary error variable. and And based on the virtual control law Constructing auxiliary error variables The expression, and then based on the auxiliary error variable. Constructing auxiliary error variables The expression;

[0027] S27, Virtual Control Law The expression, auxiliary error variable Substituting the expression into the auxiliary variable The rewritten expression, for auxiliary variables Rewrite the expression to obtain the auxiliary variable. The rewritten expression; then the auxiliary variable Differentiating the rewritten expression yields the auxiliary variable. derivative The expression;

[0028] S28, Based on auxiliary error variables The expression and auxiliary error variable The expression for the auxiliary error variable in the dynamic model of the single-point suspension system. The expression is rewritten to obtain the auxiliary error variable. The rewritten expression;

[0029] S29. Design a RISE controller based on backstepping recursion, obtain the expression for the RISE controller based on backstepping recursion, and substitute the expression for the RISE controller based on backstepping recursion into the auxiliary error variable. The auxiliary error variable is obtained from the rewritten expression. The rewritten expression; then the auxiliary error variable Differentiating the rewritten expression yields the auxiliary error variable. derivative The expression.

[0030] Furthermore, the tracking error of the gap between the electromagnet and the track in S21 The expression is:

[0031] (3)

[0032] The filter error in S22 The expression is:

[0033] (4)

[0034] in, A positive gain coefficient set manually;

[0035] Auxiliary variables in S23 The expression is:

[0036] (5)

[0037] in, A positive gain coefficient set manually;

[0038] Filter error in S24 The rewritten expression is:

[0039] (6)

[0040] Auxiliary variables in S25 The rewritten expression is:

[0041] (7)

[0042] The auxiliary error variable in S26 The expression and auxiliary error variable The expressions are as follows:

[0043] (8)

[0044] (9)

[0045] in, A positive gain coefficient set manually;

[0046] Virtual control law in S26 The expression is as follows:

[0047] (10)

[0048] In the formula, , This indicates a manually set positive control gain. Represents the integral variable; The first derivative of the first user-defined variable corresponds to the known feedforward compensation term; Indicates the desired suspension gap;

[0049] Auxiliary variables in S27 The rewritten expression is:

[0050] (11)

[0051] Auxiliary variables in S27 derivative The expression is:

[0052] (12)

[0053] The auxiliary error variable in S28 The rewritten expression is:

[0054] (13)

[0055] The expression for the RISE controller based on backstepping recursion in S29 is as follows:

[0056] ;(14)

[0057] in, , This indicates a manually set positive control gain.

[0058] The auxiliary error variable in S29 The rewritten expression is:

[0059] (15)

[0060] The auxiliary error variable in S29 derivative The expression is:

[0061] ;(16)

[0062] Furthermore, step S3 specifically includes the following steps:

[0063] S31. Define and construct auxiliary functions and The expression, and then based on the auxiliary function and Choose the Lyapunov function ;

[0064] S32, Regarding auxiliary functions and Differentiating the expressions respectively yields the auxiliary function. derivative Expressions and auxiliary functions derivative The expression;

[0065] S33, Regarding Lyapunov functions By taking the derivative, we obtain the Lyapunov function. derivative The expression;

[0066] S34, Based on filter error Expressions and auxiliary variables The expression and auxiliary error variable The expression is used to construct the tracking error. derivative Filter error derivative and auxiliary error variables derivative The expression;

[0067] S35, Tracking error derivative Expressions and filter errors derivative The expression, auxiliary error variable derivative Expressions and auxiliary variables derivative The expression, auxiliary error variable derivative expressions, auxiliary functions derivative Expressions and auxiliary functions derivative Substituting the expression into the Lyapunov function derivative From the expression, we obtain the Lyapunov function. derivative The rewritten expression;

[0068] S36. According to Young's inequality, for the Lyapunov function... derivative Scaling the rewritten expression yields the Lyapunov function. derivative Inequality after scaling;

[0069] S37, Regarding Lyapunov functions derivative By analyzing the scaled inequalities, the stability conditions of the RISE controller are obtained.

[0070] Furthermore, the Lyapunov function in S31 for:

[0071] (17)

[0072] Auxiliary function in S31 The expression is:

[0073] (18)

[0074] Auxiliary function in S31 The expression is:

[0075] (19)

[0076] Auxiliary function in S32 derivative Expressions and auxiliary functions derivative The expressions are as follows:

[0077] (20)

[0078] The Lyapunov function in S33 derivative The expression is:

[0079] ;(twenty one)

[0080] Tracking error in S34 derivative Filter error derivative and auxiliary error variables derivative The expression is:

[0081] ;(twenty two)

[0082] The Lyapunov function in S35 derivative The rewritten expression is:

[0083] ;(twenty three)

[0084] The Lyapunov function in S36 derivative The inequality after scaling is:

[0085] ; (twenty four)

[0086] in, It is a second user-defined variable, and , Indicates transpose; It is a third user-defined variable, and .

[0087] Furthermore, the stability condition of the RISE controller in S3 is:

[0088] , , , , , , ;

[0089] in, , , , These represent model uncertainties respectively. Upper bound of the absolute value of the first derivative, model uncertainty Upper bound of the absolute value of the first derivative, model uncertainty Upper bound of the absolute value of the second derivative, model uncertainty The upper bound of the absolute value of the second derivative of , and respectively satisfying , , , .

[0090] Furthermore, step S4 specifically includes the following steps:

[0091] S41. Use relevant sensors to collect the current suspension gap in real time. Vehicle acceleration and the current in the electromagnet winding ;

[0092] S42, The suspension controller will collect the suspension gap of the maglev train's suspension system. Vehicle acceleration and the current in the electromagnet winding These signals are converted into state variables. , , , obtain state variables , , The current actual value;

[0093] S43, Transfer state variables Substitute the current actual value into the tracking error The tracking error is obtained from the expression. The current actual value, and then the tracking error Substitute the current actual value into the filter error The filter error is obtained from the expression. The current actual value;

[0094] S44, filter error Substituting the actual value into the virtual control law From the expression, the virtual control law is obtained. The current actual value;

[0095] S45, Virtual Control Law Substitute the current actual value into the auxiliary error variable From the expression, we obtain the auxiliary error variable. The current actual value;

[0096] S46. Virtual control law Current actual value, auxiliary error variable The current actual value is substituted into the RISE controller based on backstepping recursion. The RISE controller based on backstepping recursion calculates the voltage while satisfying the stability condition. The actual value;

[0097] S47, the suspension controller will change the voltage The actual value is input to the chopper of the power amplifier module PWM to realize the driving of the single-point levitation system;

[0098] S48, return to S42 and enter the next control cycle to realize the real-time control of the suspension gap of the maglev train suspension system by the suspension controller.

[0099] Furthermore, the state variables in S42 , , The actual value is:

[0100] ;(25)

[0101] In another aspect, the present invention provides a recursive RISE control system, including a maglev train suspension system, wherein the maglev train suspension system has a plurality of single-point suspension systems built in, and the recursive RISE control system is configured to execute the above-described recursive RISE control method.

[0102] The beneficial effects of this invention are:

[0103] 1. This invention provides a recursive RISE control method for maglev train suspension systems, including a gap loop (for calculating the suspension gap) and a current loop (for calculating the current). In the calculation of RISE feedback (including positive gain coefficient), , , Control gain , , , The presence of these features provides excellent anti-interference capabilities, reducing the impact of external interference or uncertainties in the dynamic model on suspension accuracy.

[0104] 2. The dynamic model of the single-point suspension system used in this invention is a complete nonlinear dynamic model, which fully preserves the nonlinear coupling relationship between electromagnetic force, current, and suspension gap, without making any linearization approximations at the equilibrium point. Furthermore, this invention designs the RISE controller based on the complete nonlinear dynamic model, rather than using a linearized approximation model. This ensures that the designed control law can handle the inherent nonlinearity of the system, achieving globally stable control and completely avoiding the stability range limitation problem caused by model linearization in traditional methods, as well as the model mismatch problem caused by linearization. Attached Figure Description

[0105] Figure 1 This is a schematic diagram of the single-point suspension system in this invention;

[0106] Figure 2 This is a control block diagram of the RISE controller based on backstepping recursion in this invention;

[0107] Figure 3 This is a schematic diagram of the disturbance signal from an external force in an embodiment of the present invention;

[0108] Figure 4 In order to be in Figure 3 The diagram shows the gap response of three different methods under the same external force disturbance.

[0109] Figure 5 This is a schematic diagram of electromagnetic disturbance signals in an embodiment of the present invention;

[0110] Figure 6 In order to be in Figure 5 The diagram shows the gap response of three different methods under the same electromagnetic disturbance.

[0111] Figure 7 In order to be in Figure 3 The same external force disturbance shown and Figure 5 The diagram shows the gap response of three different methods under the same electromagnetic disturbance. Detailed Implementation

[0112] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0113] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0114] Reference Figure 1 and Figure 2 This application provides a recursive RISE control method for maglev train suspension systems, comprising the following steps:

[0115] S1. Taking the single-point suspension system in the maglev train suspension system as the research object, construct the dynamic equation and voltage balance equation of the electromagnet, and then construct the dynamic model of the single-point suspension system based on the dynamic equation and voltage balance equation of the electromagnet.

[0116] Among them, the single-point suspension system is shown below. Figure 1 As shown, it includes an electromagnet, which includes an iron core and a coil wound on the iron core. The electromagnet is positioned below the track.

[0117] S2. Design a virtual control law, and then combine the dynamic model of the single-point suspension system with the virtual control law to design a RISE controller based on backstepping recursion.

[0118] S3. Perform stability analysis on the RISE controller based on backstepping recursion to obtain the stability conditions of the RISE controller.

[0119] S4. Based on the stability conditions, the suspension controller uses a RISE controller based on backstepping recursion to control the suspension gap of the maglev train suspension system in real time.

[0120] This invention addresses the calculation of the gap loop (corresponding to the suspension gap) and the current loop (corresponding to the current). In the calculation, due to the presence of RISE feedback, there is a good anti-interference ability, which reduces the impact of external interference or uncertainty of dynamic model on suspension accuracy.

[0121] Furthermore, the dynamic model of the single-point suspension system used in this invention is a complete nonlinear dynamic model, fully preserving the nonlinear coupling relationship between electromagnetic force, current, and suspension gap, without any linearization approximation at the equilibrium point. Simultaneously, this invention designs the RISE controller based on the complete nonlinear dynamic model, rather than using a linearized approximation model. This ensures that the designed control law can handle the inherent nonlinearity of the system, achieving globally stable control and completely avoiding the stability range limitation problem caused by model linearization in traditional methods, as well as the model mismatch problem caused by linearization.

[0122] In some embodiments, S1 specifically includes the following steps:

[0123] S11. First, taking the single-point suspension system in the maglev train suspension system as the research object, the dynamic equation and voltage balance equation of the electromagnet are constructed, and the expressions are:

[0124] (1)

[0125] in, The total mass of the electromagnet and the mass it carries. The current in the electromagnet winding is... The voltage applied across the electromagnet winding. The levitation gap between the electromagnet and the track. The disturbance force experienced by the electromagnet. This refers to the number of turns in the electromagnet winding. The resistance is for DC. The area of ​​the electromagnet poles; symbol This represents the first derivative of the parameter; symbol This represents the second derivative of the parameter; Indicates the permeability of free space; Represents gravitational acceleration; t Indicates time;

[0126] S12. Define three state variables. , , ,and , , ;

[0127] S13, Using three state variables , , The dynamic equations and voltage balance equations of the electromagnet are rewritten to obtain the dynamic model of the single-point levitation system, as shown in the following expression:

[0128] (2)

[0129] in, , These represent the model uncertainty caused by external force disturbances and the model uncertainty caused by lumped electromagnetic disturbances, respectively.

[0130] In some embodiments, S2 specifically includes the following steps:

[0131] S21, By introducing the desired gap between the electromagnet and the track. Tracking error in constructing the gap between the electromagnet and the track The expression;

[0132] S22, Introducing filter error And construct the filter error The expression;

[0133] S23, Introducing auxiliary variables and construct auxiliary variables The expression;

[0134] S24. Introduce the first user-defined variable. ,and Then based on the first user-defined variable For filter error The expression is rewritten to obtain the filter error. The rewritten expression;

[0135] S25. Dynamic model and auxiliary variables based on single-point suspension system The expression and filter error The rewritten expression for auxiliary variables Rewrite the expression to obtain the auxiliary variable. The rewritten expression;

[0136] S26. Designing Virtual Control Laws Constructing virtual control laws The expression introduces an auxiliary error variable. and And based on the virtual control law Constructing auxiliary error variables The expression, and then based on the auxiliary error variable. Constructing auxiliary error variables The expression;

[0137] S27, Virtual Control Law The expression, auxiliary error variable Substituting the expression into the auxiliary variable The rewritten expression, for auxiliary variables Rewrite the expression to obtain the auxiliary variable. The rewritten expression; then the auxiliary variable Differentiating the rewritten expression yields the auxiliary variable. derivative The expression;

[0138] S28, Based on auxiliary error variables The expression and auxiliary error variable The expression for the auxiliary error variable in the dynamic model of the single-point suspension system. The expression is rewritten to obtain the auxiliary error variable. The rewritten expression;

[0139] S29. Design a RISE controller based on backstepping recursion, obtain the expression for the RISE controller based on backstepping recursion, and substitute the expression for the RISE controller based on backstepping recursion into the auxiliary error variable. The auxiliary error variable is obtained from the rewritten expression. The rewritten expression; then the auxiliary error variable Differentiating the rewritten expression yields the auxiliary error variable. derivative The expression.

[0140] In some embodiments, the tracking error of the gap between the electromagnet and the track in S21 The expression is:

[0141] (3)

[0142] The filter error in S22 The expression is:

[0143] (4)

[0144] in, A positive gain coefficient set manually;

[0145] Auxiliary variables in S23 The expression is:

[0146] (5)

[0147] in, A positive gain coefficient set manually;

[0148] Filter error in S24 The rewritten expression is:

[0149] (6)

[0150] Auxiliary variables in S25 The rewritten expression is:

[0151] (7)

[0152] The auxiliary error variable in S26 The expression and auxiliary error variable The expressions are as follows:

[0153] (8)

[0154] (9)

[0155] in, A positive gain coefficient set manually;

[0156] Virtual control law in S26 The expression is as follows:

[0157] (10)

[0158] In the formula, , This indicates a manually set positive control gain. Represents the integral variable; The first derivative of the first user-defined variable corresponds to the known feedforward compensation term; The desired suspension gap is represented; the first-level RISE integral term in formula (10) is the first part of the RISE (Robust Error Sign Integral) mechanism, used to address model uncertainty. Perform asymptotic compensation;

[0159] Auxiliary variables in S27 The rewritten expression is:

[0160] (11)

[0161] Auxiliary variables in S27 derivative The expression is:

[0162] (12)

[0163] The auxiliary error variable in S28 The rewritten expression is:

[0164] (13)

[0165] The expression for the RISE controller based on backstepping recursion in S29 is as follows:

[0166] ;(14)

[0167] in, , This indicates a manually set positive control gain.

[0168] The auxiliary error variable in S29 The rewritten expression is:

[0169] (15)

[0170] The auxiliary error variable in S29 derivative The expression is:

[0171] ;(16)

[0172] In some embodiments, S3 specifically includes the following steps:

[0173] S31. Define and construct auxiliary functions and The expression, and then based on the auxiliary function and Choose the Lyapunov function ;

[0174] S32, Regarding auxiliary functions and Differentiating the expressions respectively yields the auxiliary function. derivative Expressions and auxiliary functions derivative The expression;

[0175] S33, Regarding Lyapunov functions By taking the derivative, we obtain the Lyapunov function. derivative The expression;

[0176] S34, Based on filter error Expressions and auxiliary variables The expression and auxiliary error variable The expression is used to construct the tracking error. derivative Filter error derivative and auxiliary error variables derivative The expression;

[0177] S35, Tracking error derivative Expressions and filter errors derivative The expression, auxiliary error variable derivative Expressions and auxiliary variables derivative The expression, auxiliary error variable derivative expressions, auxiliary functions derivative Expressions and auxiliary functions derivative Substituting the expression into the Lyapunov function derivative From the expression, we obtain the Lyapunov function. derivative The rewritten expression;

[0178] S36. According to Young's inequality, for the Lyapunov function... derivative Scaling the rewritten expression yields the Lyapunov function. derivative Inequality after scaling;

[0179] S37, Regarding Lyapunov functions derivative By analyzing the scaled inequalities, the stability conditions of the RISE controller are obtained.

[0180] In some embodiments, the Lyapunov function in S31 for:

[0181] (17)

[0182] Auxiliary function in S31 The expression is:

[0183] (18)

[0184] Auxiliary function in S31 The expression is:

[0185] (19)

[0186] For auxiliary functions , Expanding the expression, we get the following expansion:

[0187] ;

[0188] ;

[0189] From the above expansion, it can be seen that when , ,and hour, Right determination; when , ,and hour, Positive definiteness. (Must satisfy...) , The reason for positive definiteness is to make the Lyapunov function... Satisfying the definition, that is );

[0190] Auxiliary function in S32 derivative Expressions and auxiliary functions derivative The expressions are as follows:

[0191] (20)

[0192] The Lyapunov function in S33 derivative The expression is:

[0193] ;(twenty one)

[0194] Tracking error in S34 derivative Filter error derivative and auxiliary error variables derivative The expression is:

[0195] ;(twenty two)

[0196] The Lyapunov function in S35 derivative The rewritten expression is:

[0197] ;(twenty three)

[0198] The Lyapunov function in S36 derivative The inequality after scaling is:

[0199] ; (twenty four)

[0200] in, It is a second user-defined variable, and , Indicates transpose; It is a third user-defined variable, and .

[0201] In some embodiments, the stability condition of the RISE controller in S3 is:

[0202] , , , , , , ;

[0203] in, , , , These represent model uncertainties respectively. Upper bound of the absolute value of the first derivative, model uncertainty Upper bound of the absolute value of the first derivative, model uncertainty Upper bound of the absolute value of the second derivative, model uncertainty The upper bound of the absolute value of the second derivative of , and respectively satisfying , , , .

[0204] In some embodiments, S4 specifically includes the following steps:

[0205] S41. Use relevant sensors to collect the current suspension gap of the maglev train's suspension system in real time. Vehicle acceleration and the current in the electromagnet winding ;

[0206] S42, The suspension controller will collect the suspension gap. Vehicle acceleration and the current in the electromagnet winding These signals are converted into state variables. , , , obtain state variables , , The current actual value;

[0207] S43, Transfer state variables Substitute the current actual value into the tracking error The tracking error is obtained from the expression. The current actual value, and then the tracking error Substitute the current actual value into the filter error The filter error is obtained from the expression. The current actual value;

[0208] S44, filter error Substituting the actual value into the virtual control law From the expression, the virtual control law is obtained. The current actual value; this completes the first step of the reverse step method;

[0209] S45, Virtual Control Law Substitute the current actual value into the auxiliary error variable From the expression, we obtain the auxiliary error variable. The current actual value;

[0210] S46. Virtual control law Current actual value, auxiliary error variable The current actual value is substituted into the RISE controller based on backstepping recursion. The RISE controller based on backstepping recursion calculates the voltage while satisfying the stability condition. The actual value; this completes the second step of the backstepping method; voltage The expression for the actual value is as follows:

[0211] ;

[0212] The second-level RISE integral term is used to handle high-frequency interference and parameter uncertainties at the voltage / current level.

[0213] S47, the suspension controller will change the voltage The actual value is input to the chopper of the power amplifier module PWM to realize the driving of the single-point levitation system;

[0214] S48, return to S42, and enter the next control cycle to achieve high-precision real-time control of the suspension gap of the maglev train's suspension system by the suspension controller. In this embodiment, each control cycle is set to 1 / 4000s.

[0215] In some embodiments, the state variables in S42 , , The actual value is:

[0216] ; (25).

[0217] To verify the effectiveness and superiority of the proposed recursive RISE control method of this invention, a simulation model of the single-point levitation system of the maglev train was built in the Matlab / Simulink environment. The model parameters of the simulation model are shown in Table 1;

[0218] Table 1: Value table of each parameter of the single-point levitation system simulation model;

[0219]

[0220] To simulate the harsh working conditions that the maglev train may encounter during actual operation, between the simulation time t = 25s - t = 75s, a large-amplitude model uncertainty caused by external force disturbance was artificially imposed . As Figure 3 shown, this disturbance signal simulates the gusts, track irregularities or load mutations that the train receives. The amplitude range of its force disturbance is [-760N, 950N], and it has the characteristics of being aperiodic and rapidly changing, which poses extremely high requirements on the anti-interference ability of the levitation controller.

[0221] Figure 4 shows the comparison schematic diagram of the gap responses of three different methods under the disturbance of the same external force; Figure 4 In it, pid corresponds to the PID algorithm using a PID (Proportional-Integral-Differential) controller. Although the PID controller can maintain the stability of the system within a general range, it seems powerless when dealing with various continuously changing sinusoidal disturbances. From Figure 4 it can be seen that when there is no disturbance (t < 25s or t > 75s), the PID algorithm can converge well to the expected gap of 8mm. However, since the PID controller is essentially based on linear error feedback for control, when it faces non-linear disturbances or rapidly changing sinusoidal signals, it shows obvious phase lag and large steady-state error. Figure 4 The tracking fluctuations of the tracking curve (25s < t < 75s) in it are reflected. Under the action of external disturbance, the gap fluctuation of the PID controller is [7.76mm, 8.35mm]. The design of the PID controller is based on the linearized model of the levitation system. It can only achieve stability near the working point. After being disturbed by the time-varying external force, the system is no longer at the working point. On the one hand, the deviation of the system from the working point will make its stability worse. On the other hand, the linearized model is no longer accurate after being far from the working point. The error between the real non-linear model and the linearized model is essentially equivalent to an additional disturbance of model uncertainty.

[0222] Figure 4 The "zhong" ADRC corresponds to the ADRC (Active Disturbance Rejection Control) algorithm. The ADRC algorithm uses an Extended State Observer (ESO) to regard model nonlinearity and external disturbances as "total disturbances" for observation and compensation. However, when facing high-frequency or rapidly changing large disturbances, due to the bandwidth limitation of the observer, the estimated value of the Extended State Observer often lags behind the true disturbance value. This time difference between "observation - compensation" causes the control quantity to be unable to cancel precisely in real time. Therefore, when facing the剧烈变化的力扰动 in this experiment, the ADRC algorithm still shows a certain tracking error. From Figure 4 As shown, compared with PID, the fluctuation amplitude of ADRC is slightly reduced, but it still cannot completely suppress the disturbance. Under the same disturbance conditions, the gap fluctuation of ADRC is [7.86mm, 8.18mm].

[0223] Figure 4 The "zhong" three-step regression RISE corresponds to the recursive RISE control method proposed in this invention. In sharp contrast to the above two methods, during the entire disturbance period (25s < t < 75s), the suspension gap almost always closely adheres to the desired gap of 8mm, the curve is almost straight, and the fluctuation range is [7.997mm - 8.003mm].

[0224] The main reasons are as follows: 1. The advantage of the nonlinear model. This invention is designed based on a complete nonlinear dynamics model without any linearization simplification. Therefore, when the system deviates from the equilibrium point, the control law can still accurately describe the nonlinear coupling relationship between electromagnetic force, current, and gap , so as to maintain high performance within a wide working range. 2. The robustness of RISE feedback: The design of the RISE (Robust Integral of the Sign of the Error) term is specifically for disturbances with bounded derivatives. RISE can generate a continuous control signal through the integral action to asymptotically eliminate the influence of model uncertainties and external additive disturbances.

[0225] In the actual operation of maglev trains, in addition to the changes in the external mechanical environment, the uncertainty of the internal electrical characteristics of the control system is also a key factor affecting the suspension performance. To verify the robustness of this invention at the electrical level, this invention introduces model uncertainties caused by lumped electromagnetic disturbances in the simulation .

[0226] Such as Figure 5 As shown, this invention applies a large-amplitude time-varying voltage disturbance signal during the period of [20s, 70s]. This signal has the following characteristics: high-frequency large-amplitude oscillation: simulating the measurement noise of the current sensor and the output ripple of the power amplifier. The amplitude is in The values ​​fluctuate drastically. Non-zero mean deviation: The simulation shows that the coil resistance fluctuates due to the heat generated by the levitation electromagnet during prolonged operation, causing a mismatch between the model parameters and the actual physical parameters (parameter uncertainty).

[0227] Reference Figure 6 It gives in Figure 5 The diagram shows a comparison of the gap response of three different methods under the same electromagnetic disturbance; although the PID controller demonstrates a certain filtering effect on high-frequency noise using the integral element (the curve is relatively smooth), it has obvious shortcomings in dynamic performance. In the initial stage of simulation... The PID control has a long settling time, and the suspension gap decreases slowly, failing to reach its target value for an extended period. The expected value. This means that reducing the PID gain or bandwidth to suppress noise comes at the cost of sacrificing the system's dynamic response speed. When faced with sudden changes in electrical parameters, the PID struggles to make rapid corrections.

[0228] observe Figure 6 It can be observed that the ADRC algorithm in After the disturbance was introduced, the suspension gap exhibited severe high-frequency jitter with significant fluctuations. Analysis: The ADRC algorithm relies on an extended state observer (ESO) to estimate the system's "total disturbance." However, when the disturbance signal contains a large amount of high-frequency noise, the high-gain observer misinterprets this noise as rapid changes in the system state and compensates for it. This "overcompensation" behavior introduces noise components into the control input, ultimately causing system jitter. This indicates that ADRC faces a dilemma in its bandwidth design when dealing with high-frequency electromagnetic measurement noise: a conflict between "disturbance immunity" and "noise filtering," making it difficult to achieve both simultaneously.

[0229] In comparison, the recursive RISE control method proposed in this invention exhibits superior overall performance. In the initial stage, the system stabilizes without overshoot in a very short time. The operating point and dynamic response speed far exceed those of PID. The most significant advantage is that when... Even after the introduction of intense high-frequency electromagnetic disturbances, the system response curve remains perfectly flat, with almost no fluctuations. This is thanks to the sign function integral term included in the RISE control law. Integration operations inherently possess low-pass filtering characteristics, effectively filtering out... This invention addresses high-frequency noise components and continuously compensates for low-frequency / DC parameter deviations such as resistance temperature rise. Furthermore, because the invention is based on a complete nonlinear model design, it directly handles the nonlinear relationship between voltage and current using the backstepping method, avoiding model mismatch problems caused by linearization.

[0230] To further verify the dynamic response capability of the present invention under complex working conditions, the present invention simultaneously applies the aforementioned model uncertainties to the system. and model uncertainty And requires the levitation system to track a frequency of Amplitude The sine reference trajectory.

[0231] from Figure 7 The simulation curves show that the PID controller performs the worst in dynamic tracking tasks. The response curve under PID control lags significantly behind the reference signal, with huge time delays at both peaks and troughs.

[0232] The jitter problem of ADRC algorithm: Although ADRC algorithm is better than PID algorithm in phase tracking, its performance is still not ideal due to the influence of electromagnetic noise.

[0233] The recursive RISE control method proposed in this invention exhibits superior tracking performance. The system's response curve almost perfectly overlaps with the gray reference trajectory, showing neither phase lag nor amplitude attenuation. Despite the system being subjected to significant force disturbances and electromagnetic noise, this invention maintains an extremely high signal-to-noise ratio, with a smooth and clean curve. This demonstrates that the RISE feedback term not only eliminates steady-state errors but also enables global asymptotic tracking of time-varying signals.

[0234] A second aspect of the present invention also provides a recursive RISE control system, including a maglev train suspension system, wherein the maglev train suspension system has a plurality of single-point suspension systems built in, and the recursive RISE control system is configured to or execute the above-described recursive RISE control method.

[0235] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A recursive RISE control method for a maglev train suspension system, characterized in that, Includes the following steps: S1. Taking the single-point suspension system in the maglev train suspension system as the research object, construct the dynamic equation and voltage balance equation of the electromagnet, and then construct the dynamic model of the single-point suspension system based on the dynamic equation and voltage balance equation of the electromagnet. S2. Design a virtual control law, and then combine the dynamic model of the single-point suspension system with the virtual control law to design a RISE controller based on backstepping recursion. S3. Perform stability analysis on the RISE controller based on backstepping recursion to obtain the stability conditions of the RISE controller. S4. Based on the stability conditions, the suspension controller uses a RISE controller based on backstepping recursion to control the suspension gap of the maglev train suspension system in real time. S1 specifically includes the following steps: S11. First, taking the single-point suspension system in the maglev train suspension system as the research object, the dynamic equation and voltage balance equation of the electromagnet are constructed, and the expressions are: ；（1） in, The total mass of the electromagnet and the mass it carries. The current in the electromagnet winding is... The voltage applied across the electromagnet winding. The levitation gap between the electromagnet and the track. The disturbance force experienced by the electromagnet. This refers to the number of turns in the electromagnet winding. The resistance is for DC. The area of ​​the electromagnet poles; symbol The first derivative of the parameter; symbol Represents the second derivative of the parameter; Indicates the permeability of free space; Represents gravitational acceleration; t Indicates time; S12. Define three state variables. , , ,and , , ; S13, Using three state variables , , The dynamic equations and voltage balance equations of the electromagnet are rewritten to obtain the dynamic model of the single-point levitation system, as shown in the following expression: ；（2） wherein , respectively represent the model uncertainty due to external force disturbance and the model uncertainty due to lumped electromagnetic disturbance.

2. The recursive RISE control method for maglev train suspension system according to claim 1, wherein, S2 specifically includes the following steps: S21, by introducing a desired gap between electromagnet and track Expression of the tracking error of the gap between electromagnet and track Expression of the tracking error of the gap between electromagnet and track S22, introducing filter error and constructing an expression for filter error ​ S23, introduce auxiliary variables and construct an expression for the auxiliary variable ; S24. Introduce the first user-defined variable. ,and Then based on the first user-defined variable For filter error The expression is rewritten to obtain the filter error. The rewritten expression; S25. Dynamic model and auxiliary variables based on single-point suspension system The expression and filter error The rewritten expression for auxiliary variables Rewrite the expression to obtain the auxiliary variable. The rewritten expression; S26. Designing Virtual Control Laws Constructing virtual control laws The expression introduces an auxiliary error variable. and And based on the virtual control law Constructing auxiliary error variables The expression, and then based on the auxiliary error variable. Constructing auxiliary error variables The expression; S27, Virtual Control Law The expression, auxiliary error variable Substituting the expression into the auxiliary variable The rewritten expression, regarding the auxiliary variable Rewrite the expression to obtain the auxiliary variable. The rewritten expression; then the auxiliary variable Differentiating the rewritten expression yields the auxiliary variable. derivative The expression; S28, Based on auxiliary error variables The expression and auxiliary error variable The expression for the auxiliary error variable in the dynamic model of the single-point suspension system. The expression is rewritten to obtain the auxiliary error variable. The rewritten expression; S29. Design a RISE controller based on backstepping recursion, obtain the expression for the RISE controller based on backstepping recursion, and substitute the expression for the RISE controller based on backstepping recursion into the auxiliary error variable. The auxiliary error variable is obtained from the rewritten expression. The rewritten expression; then the auxiliary error variable Differentiating the rewritten expression yields the auxiliary error variable. derivative The expression.

3. The recursive RISE control method for maglev train suspension systems according to claim 2, characterized in that, Tracking error of the gap between the electromagnet and the track in S21 The expression is: ；（3） The filter error in the S22 The expression is: ；（4） wherein a positive gain factor set by a human being; The expression of the auxiliary variable in S23 is: ；（5） wherein a positive gain factor set by a human being; The filter error in S24 The rewritten expression is: ；（6） Auxiliary variables in S25 The rewritten expression is: ；（7） The auxiliary error variable in S26 The expression and auxiliary error variable The expressions are as follows: ；（8） ；（9） wherein a positive gain factor set by a human being; Virtual control law in S26 The expression is as follows: ；（10） In the formula, , This indicates a manually set positive control gain. Represents the integral variable; The first derivative of the first user-defined variable corresponds to the known feedforward compensation term; Indicates the desired suspension gap; The S27 auxiliary variable The rewritten expression is: ；（11） The S27 auxiliary variable derivative is expressed as ；（12） The auxiliary error variable in S28 The rewritten expression is: ；（13） The expression for the RISE controller based on backstepping recursion in S29 is as follows: ； （14） wherein, , represents a control gain of a positive gain set artificially; The S29 auxiliary error variable The rewritten expression is: ；（15） the S29 auxiliary error variable derivative of the expression for ；（16）。 4. The recursive RISE control method for maglev train suspension system according to claim 3, wherein, S3 specifically includes the following steps: S31. Define and construct auxiliary functions and The expression, and then based on the auxiliary function and Choose the Lyapunov function ; S32, Regarding auxiliary functions and Differentiating the expressions respectively yields the auxiliary function. derivative Expressions and auxiliary functions derivative The expression; S33, Regarding Lyapunov functions By taking the derivative, we obtain the Lyapunov function. derivative The expression; S34, Based on filter error Expressions and auxiliary variables The expression and auxiliary error variable The expression is used to construct the tracking error. derivative Filter error derivative and auxiliary error variables derivative The expression; S35, Tracking error derivative Expressions and filter errors derivative The expression, auxiliary error variable derivative Expressions and auxiliary variables derivative The expression, auxiliary error variable derivative Expressions and auxiliary functions derivative Expressions and auxiliary functions derivative Substituting the expression into the Lyapunov function derivative From the expression, we obtain the Lyapunov function. derivative The rewritten expression; S36. According to Young's inequality, for the Lyapunov function... derivative Scaling the rewritten expression yields the Lyapunov function. derivative Inequality after scaling; S37. Regarding Lyapunov functions derivative By analyzing the scaled inequalities, the stability conditions of the RISE controller are obtained.

5. The recursive RISE control method for maglev train suspension system according to claim 4, wherein, The Lyapunov function in S31 is: ； （17） The auxiliary function in the S31 The expression is: ；（18） The auxiliary function in the S31 The expression is: ；（19） Auxiliary function in S32 derivative Expressions and auxiliary functions derivative The expressions are as follows: ； （20） derivative of the lyapunov function s33 is given by​ ； （21） Tracking error in S34 derivative Filter error derivative and auxiliary error variables derivative The expression is: ；（22） derivative of the lyapunov function in s35 the rewritten expression is ；（23） The Lyapunov function in S36 derivative The inequality after scaling is: ； （24） wherein is a second custom variable, and , denotes transpose; is a third custom variable, and .

6. The recursive RISE control method for maglev train suspension system according to claim 5, wherein, The stability condition of the RISE controller in S3 is as follows: 、 、 、 、 、 、 ； in, , , , These represent model uncertainties respectively. Upper bound of the absolute value of the first derivative, model uncertainty Upper bound of the absolute value of the first derivative, model uncertainty Upper bound of the absolute value of the second derivative, model uncertainty The upper bound of the absolute value of the second derivative of , and respectively satisfying , , , .

7. The recursive RISE control method for a maglev train levitation system according to claim 6, characterized in that, S4 specifically includes the following steps: S41. Use relevant sensors to collect the current suspension gap in real time. Vehicle acceleration and the current in the electromagnet winding ; S42, The suspension controller will collect the suspension gap of the maglev train's suspension system. Vehicle acceleration and the current in the electromagnet winding These signals are converted into state variables. , , , obtain state variables , , The current actual value; S43, Change the state variables Substitute the current actual value into the tracking error The tracking error is obtained from the expression. The current actual value, and then the tracking error Substitute the current actual value into the filter error The filter error is obtained from the expression. The current actual value; S44, filter error Substituting the actual value into the virtual control law From the expression, the virtual control law is obtained. The current actual value; S45, Virtual Control Law Substitute the current actual value into the auxiliary error variable From the expression, we obtain the auxiliary error variable. The current actual value; S46. Virtual control law Current actual value, auxiliary error variable The current actual value is substituted into the RISE controller based on backstepping recursion. The RISE controller based on backstepping recursion calculates the voltage while satisfying the stability condition. The actual value; S47, the suspension controller will change the voltage The actual value is input to the chopper of the power amplifier module PWM to realize the driving of the single-point levitation system; S48, return to S42 and enter the next control cycle to realize the real-time control of the suspension gap of the maglev train suspension system by the suspension controller.

8. The recursive RISE control method for maglev train suspension system according to claim 7, characterized in that, The state variable in S42 , , The actual value of the state variable is: ；（25）。 9. A recursive RISE control system, characterized in that, The system includes a maglev train suspension system, which incorporates several single-point suspension systems. The recursive RISE control system is configured to execute the recursive RISE control method as described in any one of claims 1 to 8.

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