Interference Suppression Levitation Control Method and System for Maglev Train

Abstract

The present invention provides a disturbance rejection suspension control method and system for a maglev train, belonging to the technical field of maglev train suspension control. The vertical dynamic equation of the maglev train suspension system is established to obtain the nonlinear dynamic model of the maglev train suspension system, and the tracking error model of the suspension system is obtained according to the tracking target. Using the feedback linearization method, the tracking error model of the maglev train suspension system is linearized to obtain the linear tracking error model of the maglev train suspension system. A disturbance observer is designed to actively compensate for the disturbance. According to the tracking error model of the disturbed maglev train suspension system, a tube model predictive controller is designed to calculate the robust tightening constraint. The disturbance observer and the tube model predictive controller are used to control the suspension system of the maglev train within the safe air gap range and keep it stable. The present invention solves the influence of vertical disturbance on the maglev train and realizes the stable suspension of the maglev train within the safe range.

Description

Technical Field

[0001] The present invention relates to the technical field of maglev train suspension control, and particularly to a disturbance rejection suspension control method and system for a maglev train. Background Art

[0002] How to improve the performance of maglev trains such as safety, reliability, and comfort is a research direction that has attracted attention today. Therefore, the control problem of maglev trains has drawn extensive attention. Among them, the most important problem is how to ensure that the train is stably suspended within the safe clearance between the track and the ground during the high-speed operation of the maglev train, preventing excessive magnetic force from attracting it to the track or the magnetic force being less than the vehicle weight and contacting the ground. Summary of the Invention

[0003] The purpose of the present invention is to provide a disturbance rejection suspension control method and system for a maglev train affected by vertical disturbances, so as to solve at least one of the technical problems existing in the above background art.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions:

[0005] In the first aspect, the present invention provides a disturbance rejection suspension control method for a maglev train, including:

[0006] Based on the force analysis of the vertical motion of the maglev train considering vertical disturbances, establish the vertical dynamic equation of the maglev train suspension system, obtain the nonlinear dynamic model of the maglev train suspension system, and obtain the tracking error model of the suspension system according to the tracking target;

[0007] Use the feedback linearization method to linearize the tracking error model of the maglev train suspension system to obtain the linear tracking error model of the maglev train suspension system;

[0008] Based on the disturbance observer, actively compensate for the disturbance;

[0009] According to the tracking error model of the disturbed maglev train suspension system, design a tube model predictive controller and calculate the robust tightening constraint;

[0010] Use the disturbance observer and the tube model predictive controller to control the suspension system of the maglev train within the safe air gap range and keep it stable.

[0011] Further, the vertical dynamic equation of the maglev train suspension system is:

[0012]

[0013] Among them, F(i(t), δ(t)) is the electromagnetic force at time t; m is the mass of the electromagnet; g is the acceleration due to gravity; δ(t) is the suspension air gap at time t; is the vertical acceleration of the suspension system at time t; f d (t) is the vertical disturbance caused by the load or wind force at time t; i(t) is the current value passing through the coil at time t; μ0, A m and N are the air permeability, the pole area of the electromagnet, and the number of turns of the coil respectively; F(i(0), δ(0)) is the boundary condition at the equilibrium point;

[0014] Select the air gap value δ(t) and the vertical velocity of the suspension system as the state variables, i 2 (t) as the control input; assume the state at the equilibrium point is δ eq , where The state - space equation of the tracking error is expressed as:

[0015]

[0016] Furthermore, calculate the Lie bracket to obtain that the matrix [g, ad f g] is full - rank and satisfies the involutivity condition; define n(z) = z1, and calculate that the Lie derivative satisfies the condition L g n(z) = 0, L g L f n(z)≠0;

[0017] Define the new state as and the auxiliary control input where and to obtain the linear - system model:

[0018]

[0019] where and satisfy the constraint conditions:

[0020] χ 1min ≤χ1(t)≤χ 1max , χ 2min ≤χ2(t)≤χ 2max , ω min ≤ω(t)≤ω max

[0021] Among them,

[0022] Furthermore, the control input ω(t) is defined as:

[0023]

[0024] where ω dob (t) and ω tmplc (t) are the disturbance compensation and the TMPLC input, respectively;

[0025] Design a disturbance observer to estimate the mismatched disturbance d:

[0026]

[0027]

[0028] where L < 0 is the observer gain and ν is the auxiliary variable, is the disturbance estimate,

[0029] Define the disturbance estimation error as Obtain:

[0030]

[0031] Therefore, it can be designed as:

[0032]

[0033] Substitute the disturbance compensation into the formula to obtain the closed-loop system:

[0034]

[0035] Furthermore, design the nominal MPLC controller ω mplc (t):

[0036] According to the nominal form of the linear system model:

[0037]

[0038] where, is the state of the nominal system. Define the sampling interval as τ (τ = t k+1 - t k , t0 = 0);

[0039] Under the constant prediction horizon T, the nominal finite-horizon optimization problem is expressed as:

[0040]

[0041] Satisfy the conditions:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Among them, is the cost function, and are the stage cost function and the terminal cost function respectively, with Q, P, R > 0; is the predicted state corresponding to time ; and are the robust tightening constraints, which are calculated in the next step; is the terminal state constraint set, where ε is a positive constant; by solving the optimization problem the trajectory of the optimal control input and the corresponding optimal predicted state trajectory are obtained. Therefore, the control input of the nominal MPLC is defined as:

[0048]

[0049] Furthermore, an auxiliary controller ω ac (t) is designed:

[0050] The state feedback controller ω ac is generated from the error between the true state affected by the disturbance and the nominal state:

[0051] where the feedback gain K ac makes be Hurwitz. The TMPLC controller is composed of the nominal MPLC controller and the auxiliary controller, and is expressed as:

[0052]

[0053] Substituting the ω tmplc (t) controller and the disturbance compensation input ω dob (t) into the formula, the composite closed-loop system is obtained:

[0054]

[0055] Calculate the robust tightening constraints:

[0056] Since the error between the state of the composite closed-loop system under the disturbance and the nominal state satisfies the inequality where

[0057] Using Minkowski set subtraction, the tightened constraint sets of the state and control input are calculated respectively:

[0058]

[0059]

[0060] In a second aspect, the present invention provides an interference suppression suspension control system for a maglev train, including:

[0061] A construction module, configured to establish a vertical dynamic equation of the maglev train suspension system based on the force analysis of the vertical motion of the maglev train considering vertical interference, obtain a non-linear dynamic model of the maglev train suspension system, and obtain a tracking error model of the suspension system according to the tracking target;

[0062] A linear module, configured to linearize the tracking error model of the maglev train suspension system by using the feedback linearization method to obtain a linear tracking error model of the maglev train suspension system;

[0063] A compensation module, configured to actively compensate for disturbances based on a disturbance observer;

[0064] A calculation module, configured to design a tube model predictive controller according to the tracking error model of the maglev train suspension system affected by disturbances and calculate robust tightened constraints;

[0065] A control module, configured to use the disturbance observer and the tube model predictive controller to control the suspension system of the maglev train within a safe air gap range and keep it stable.

[0066] In a third aspect, the present invention provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the interference suppression suspension control method of the maglev train as described in the first aspect is implemented.

[0067] In a fourth aspect, the present invention provides a computer device, including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the interference suppression suspension control method of the maglev train as described in the first aspect.

[0068] In a fifth aspect, the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device runs, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the interference suppression suspension control method of the maglev train as described in the first aspect.

[0069] Advantages of the present invention: effectively suppressing the influence of vertical interference on the maglev train suspension system; effectively enabling the maglev train suspension control to meet the air gap and vertical speed constraints; enabling the maglev train suspension system to have good suspension air gap and vertical speed tracking performance.

[0070] The advantages of additional aspects of the present invention will be more clearly given in the following description part, or understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0072] Figure 1 It is a flowchart of the interference suppression tubular model predictive suspension control method based on the maglev train described in the embodiments of the present invention.

[0073] Figure 2 It is a schematic diagram of the vertical force analysis of the suspension system described in the embodiments of the present invention.

[0074] Figure 3 It is a schematic diagram of the error tracking curves of the air gap and vertical speed of the suspension system based on the PI control, TMPLC, and DO-TMPLC algorithms described in the embodiments of the present invention.

[0075] Figure 4 It is a schematic diagram of the actual curves of the air gap and vertical speed of the suspension system based on the PI control, TMPLC, and DO-TMPLC algorithms described in the embodiments of the present invention.

[0076] Figure 5 It is a schematic diagram of the control input and current curves of the suspension system based on the PI control, TMPLC, and DO-TMPLC algorithms described in the embodiments of the present invention.

[0077] Figure 6 It is a schematic diagram of the interference estimation and interference estimation error curves in the interference suppression tubular model predictive suspension control method based on the maglev train described in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described through the drawings are exemplary and are only used to explain the present invention, and cannot be construed as a limitation to the present invention.

[0079] Those skilled in the art of the present technology can understand that, unless otherwise defined, all terms used herein (including technical terms and scientific terms) have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs.

[0080] It should also be understood that terms such as those defined in a general dictionary should be understood as having a meaning consistent with their meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined as herein.

[0081] Those skilled in the art of the present technology can understand that, unless specifically stated, the singular forms "a", "an", "the", and "said" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the description of the present invention means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0082] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. Without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0083] To facilitate the understanding of the present invention, the following will further explain the present invention with specific embodiments in conjunction with the accompanying drawings, and the specific embodiments do not constitute a limitation to the embodiments of the present invention.

[0084] Those skilled in the art should understand that the drawings are only schematic diagrams of the embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0085] The present invention proposes a tube model predictive control strategy based on a disturbance observer for this situation, effectively solving the influence of vertical disturbances on the train, keeping the suspension air gap within the specified range, with strong realizability and being beneficial to improving economic benefits.

[0086] Embodiment 1

[0087] In Embodiment 1, a disturbance rejection suspension control system for a maglev train is first provided, including: a construction module, configured to establish a vertical dynamic equation of the maglev train suspension system based on the force analysis of the vertical motion of the maglev train considering vertical disturbances, obtain a non-linear dynamic model of the maglev train suspension system, and obtain a tracking error model of the suspension system according to the tracking target; a linearization module, configured to linearize the tracking error model of the maglev train suspension system by using the feedback linearization method to obtain a linear tracking error model of the maglev train suspension system; a compensation module, configured to actively compensate for disturbances by a disturbance observer; a calculation module, configured to design a tube model predictive controller according to the tracking error model of the disturbed maglev train suspension system and calculate the robust tightening constraint; and a control module, configured to use the disturbance observer and the tube model predictive controller to control the suspension system of the maglev train within the safe air gap range and maintain stability.

[0088] In Embodiment 1, by using the above system, a disturbance rejection suspension control method for a maglev train affected by vertical disturbances is implemented. The method includes the following steps:

[0089] S1. Conduct a force analysis on the vertical motion of the maglev train considering vertical disturbances, establish a vertical dynamic equation of the maglev train suspension system, obtain a non-linear dynamic model of the maglev train suspension system, and obtain a tracking error model of the suspension system according to the tracking target;

[0090] S2. Use the feedback linearization method to linearize the tracking error model of the maglev train suspension system to obtain a linear tracking error model of the maglev train suspension system;

[0091] S3. Design a disturbance observer to actively compensate for disturbances;

[0092] S4. Design a tube model predictive controller (TMPLC) according to the tracking error model of the disturbed maglev train suspension system and calculate the robust tightening constraint;

[0093] S5. Prove the recursive feasibility and input-state stability of the closed-loop system, and then use the disturbance observer and the controller to control the suspension system of the maglev train within the safe air gap range and maintain stability.

[0094] The vertical dynamic equation of the maglev train suspension system in step S1 is:

[0095]

[0096] where F(i(t), δ(t)) is the electromagnetic force at time t; m is the mass of the electromagnet; g is the acceleration due to gravity; δ(t) is the suspension air gap at time t, satisfying the constraint condition is the vertical acceleration of the suspension system at time t; f d (t) is the vertical disturbance caused by the load or wind force at time t, satisfying i(t) is the current value passing through the coil at time t, satisfying the constraint condition i(t) ∈ {i(t)∣i min ≤ i(t) ≤ i max , i min ≥ 0}; μ0, A m and N are the air permeability, the magnetic pole area of the electromagnet, and the number of turns of the coil, respectively, where is the boundary condition at the equilibrium point.

[0097] Select the air gap value δ(t) and the vertical velocity of the suspension system as state variables, and i 2 (t) as the control input. Let the state at the equilibrium point be δ eq , where The state - space equation of the tracking error can be expressed as:

[0098]

[0099] The above equation can be abbreviated as:

[0100]

[0101] where

[0102] [[ID= forty - five]]Step S2 further includes the following sub - steps:

[0103] S2.1. Calculate the Lie bracket It can be obtained that the matrix [g, ad f g] is full - rank and satisfies the involutivity condition; define n(z) = z1, and calculate the Lie derivative to satisfy the condition L g n(z) = 0, L g L f n(z) ≠ 0, so the system (1) can be linearized.

[0104] S2.2. According to the above calculation and the input - state linearization rule, define the new state as and the auxiliary control input where and Obtain the linear system model:

[0105]

[0106] where and satisfy the constraint condition:

[0107] χ1min ≤ χ1(t) ≤ χ 1max ,χ 2min ≤ χ2(t) ≤ χ 2max ,ω min ≤ ω(t) ≤ ω max

[0108] wherein,

[0109] the control input ω(t) is defined as:

[0110]

[0111] where ω dob (t) and ω tmplc (t) are the disturbance compensation and the TMPLC input, respectively.

[0112] Design a disturbance observer to estimate the mismatched disturbance d:

[0113]

[0114]

[0115] where L < 0 is the observer gain and ν is the auxiliary variable, is the disturbance estimate, define the disturbance estimation error as It can be obtained that:

[0116]

[0117] Therefore, it can be designed as:

[0118]

[0119] Substitute the disturbance compensation into the formula to obtain the closed-loop system:

[0120]

[0121] Step S4 further includes the following sub-steps:

[0122] S4.1. Design the nominal MPLC controller ω mplc (t):

[0123] According to the nominal form of (2):

[0124]

[0125] wherein, is the state of the nominal system, and define the sampling interval as τ (τ = t k+1 - t k, with \(t_0 = 0\). Under the constant prediction horizon \(T\), the nominal finite-horizon optimization problem is expressed as:

[0126]

[0127] Subject to the conditions:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Where, is the cost function, and are the stage cost function and the terminal cost function respectively, with \(Q, P, R>0\). is the predicted state corresponding to time . and are the robust tightening constraints, which are calculated in the next step. is the terminal state constraint set, where \(\varepsilon\) is a positive constant. By solving the optimization problem the trajectory of the optimal control input and the corresponding optimal predicted state trajectory can be obtained. Therefore, the control input of the nominal MPLC is defined as:

[0134]

[0135] S4.2. Design the auxiliary controller \(\omega\) ac (t):

[0136] The state feedback controller \(\omega\) ac is generated from the error between the true state affected by the disturbance and the nominal state:

[0137]

[0138] where the feedback gain \(K\) ac makes be Hurwitz.

[0139] The TMPLC controller is composed of the nominal MPLC controller and the auxiliary controller, and is expressed as:

[0140]

[0141] S4.3. Substitute ω tmplc (t) controller and disturbance compensation input ω dob (t) into the formula to obtain the composite closed-loop system:

[0142]

[0143] S4.4. Calculate the robust tightening constraints:

[0144] Since the state error of the composite closed-loop system under disturbance and the nominal state satisfies the inequality where Using Minkowski set subtraction, the tightened constraint sets of the state and control input are calculated respectively as follows:

[0145]

[0146]

[0147] Step S5 further includes the following sub-steps:

[0148] S5.1. Prove the recursive feasibility of the proposed DO-TMPLC algorithm:

[0149] The process of online recursive solution of the optimization problem completely depends on the nominal system and does not depend on the disturbance components involved after compensation by the disturbance observer. By selecting appropriate weight matrices and terminal domains, the recursive feasibility of the DO-TMPLC algorithm can be guaranteed.

[0150] S5.2. Prove the input-to-state stability of the proposed DO-TMPLC algorithm:

[0151] By choosing appropriate parameters, it can be guaranteed that the nominal closed-loop system (3) exhibits asymptotic stability under the control input ω tmplc . Therefore, there exists a class of functions such that:

[0152]

[0153] Thus, it can be obtained that:

[0154]

[0155] Therefore, for the closed-loop system (2), it is input-to-state stable under the action of the DO-TMPLC controller. From this, it can be inferred that for the closed-loop system (1) under the control input ω(t), input-to-state stability is also achieved. And the suspension air-gap tracking error and speed tracking error of the suspension system converge to 0, that is, the system has good suspension air-gap and speed tracking characteristics, and the actual suspension air-gap and speed asymptotically track the desired air-gap and speed.

[0156] Embodiment 2

[0157] The composite control method based on the maglev train suspension system provided in this Embodiment 2 is used for the air gap and speed tracking control of the suspension system under vertical interference. As Figure 1 shown, this method includes the following steps:

[0158] S1. Analyze the forces acting on the vertical motion of the maglev train considering vertical interference, establish the vertical dynamic equation of the maglev train suspension system, obtain the nonlinear dynamic model of the maglev train suspension system, and obtain the tracking error model of the suspension system according to the tracking target;

[0159] S2. Use the feedback linearization method to linearize the tracking error model of the maglev train suspension system, and obtain the linear tracking error model of the maglev train suspension system, which is convenient for the design of the controller;

[0160] S3. Design a disturbance observer to actively compensate for the disturbance;

[0161] S4. According to the tracking error model of the maglev train suspension system under disturbance, design a tube model predictive controller and calculate the robust tightening constraint;

[0162] S5. Prove the recursive feasibility and input-state stability of the closed-loop system, and then use the disturbance observer and the controller to control the suspension system of the maglev train within the safe air gap range and keep it stable.

[0163] In step S1, combining with Figure 2 the force analysis diagram of the vertical direction of the maglev train suspension system shown, the dynamic equation of its vertical motion is:

[0164]

[0165] where F(i(t), δ(t)) is the electromagnetic force at time t; m is the mass of the electromagnet; g is the acceleration due to gravity; δ(t) is the suspension air gap at time t, satisfying the constraint condition is the vertical acceleration of the suspension system at time t; f d (t) is the vertical interference caused by the load or wind at time t, satisfying i(t) is the current value passing through the coil at time t, satisfying the constraint condition i(t) ∈ {i(t)∣i min ≤ i(t) ≤ i max , i min ≥ 0}; μ0, A m and N are the air magnetic permeability, the electromagnet pole area, and the number of coil turns respectively, where is the boundary condition at the equilibrium point.

[0166] Select the air gap value δ(t) and vertical velocity of the suspension system is the state variable, i 2 (t) is the control input. Assume that the state at the equilibrium point is δ eq , in The state space equation of the tracking error can be expressed as:

[0167]

[0168] The above formula can be simplified as:

[0169]

[0170] in

[0171] Step S2 further includes the following sub-steps:

[0172] S2.1. Calculate Lie brackets We can get the matrix [g,ad f g] full rank, satisfying the involution condition; defining n(z) = z1, calculating the Lie derivative to satisfy the condition L g n(z)=0,L g L f n(z)≠0, so the suspension system (3) can be linearized.

[0173] S2.2. Based on the above calculation and input-state linearization rule, define the new state as and auxiliary control inputs in and Get the linear system model:

[0174]

[0175] in And satisfy the constraints:

[0176] χ 1min ≤χ1(t)≤χ 1max (5a)

[0177] χ 2min ≤χ2(t)≤χ 2max (5b)

[0178] ω min ≤ω(t)≤ω max (5c)

[0179] in,

[0180] In step S3, the control input ω(t) is defined as:

[0181]

[0182] where ω dob (t) and ω tmplc (t) are the disturbance compensation and the TMPLC input, respectively.

[0183] Design a disturbance observer to estimate the mismatched disturbance d:

[0184]

[0185]

[0186] where L < 0 is the observer gain, ν is the auxiliary variable, is the disturbance estimate, Define the disturbance estimation error as We can get:

[0187]

[0188] Therefore, it can be designed as:

[0189]

[0190] Substitute the disturbance compensation into formula (4) to obtain the closed-loop system:

[0191]

[0192] Step S4 further includes the following sub-steps:

[0193] S4.1. Design the nominal MPLC controller ω mplc (t):

[0194] According to the nominal form of (4):

[0195]

[0196] where, is the state of the nominal system. Define the sampling interval as τ (τ = t k+1 - t k , t0 = 0). Under the constant prediction horizon T, the nominal finite-horizon optimization problem is expressed as:

[0197]

[0198] Subject to the conditions:

[0199]

[0200]

[0201]

[0202]

[0203]

[0204] wherein,

[0205]

[0206] is the cost function, and are the stage cost function and the terminal cost function respectively, and Q, P, R > 0. is the predicted state corresponding to the time . and are robust tightening constraints, which are calculated in the next step. is the terminal state constraint set, where ε is a positive constant. By solving the optimization problem the trajectory of the optimal control input and the corresponding optimal predicted state trajectory can be obtained.

[0207]

[0208] S4.2. Design the auxiliary controller ω ac (t):

[0209] The state feedback controller ω ac is generated from the error between the true state affected by the disturbance and the nominal state:

[0210]

[0211] where the feedback gain K ac makes [[ID=II]] Hurwitz.

[0212] The TMPLC controller is composed of the nominal MPLC controller and the auxiliary controller, and is expressed as:

[0213]

[0214] S4.3. Substitute the ω tmplc (t) controller and the disturbance compensation input ω dob (t) into the formula to obtain the composite closed-loop system:

[0215] It should be noted that there seems to be a mistake in the original text where "makes [[ID=II]] Hurwitz." might have an incorrect "II" tag. I've translated it as best as possible based on the overall context.

[0216] S4.4. Calculate the robust tightening constraints:

[0217] Since the state error of the composite closed-loop system under disturbances and the state under nominal conditions satisfies the inequality where Using Minkowski set subtraction, the tightened constraint sets for the state and control input are calculated respectively as follows:

[0218]

[0219]

[0220] Step S5 further includes the following sub-steps:

[0221] S5.1. Prove the recursive feasibility of the proposed DO-TMPLC algorithm:

[0222] The process of online recursive solution of the optimization problem completely depends on the nominal system and does not depend on the disturbance components involved after being compensated by the disturbance observer. By selecting appropriate weight matrices and terminal domains, the recursive feasibility of the DO-TMPLC algorithm can be guaranteed.

[0223] S5.2. Prove the input-to-state stability of the proposed DO-TMPLC algorithm:

[0224] By choosing appropriate parameters, it can be ensured that the nominal closed-loop system (11) exhibits asymptotic stability under the control input ω tmplc Therefore, there exists a class of functions such that:

[0225]

[0226] Thus, it is obtained that:

[0227]

[0228] Therefore, the closed-loop system (4) is input-to-state stable under the action of the TMPLC controller based on the disturbance observer. From this, it can be inferred that the closed-loop system (3) also achieves input-to-state stability under the control input ω(t). Moreover, the suspension air-gap tracking error and speed tracking error of the suspension system converge to 0, that is, the system has good suspension air-gap and speed tracking characteristics, and the actual suspension air-gap and speed asymptotically track the desired air-gap and speed.

[0229] To verify the effectiveness of the anti-disturbance control method for the maglev train suspension system affected by vertical disturbances provided in this embodiment, MATLAB is used for simulation experiments and detailed descriptions are made.

[0230] The single-electromagnet suspension system model of the maglev train provided in this embodiment comprehensively considers the influence of safety constraints and vertical disturbances on the suspension air gap and vertical speed tracking performance of the maglev train. The tubular model predictive controller based on the disturbance observer is used to make the closed-loop system asymptotically stable, with good suspension air gap and speed tracking performance, and good disturbance suppression and robustness.

[0231] In the simulation experiment, the mass m of the single-electromagnet suspension system is 320 kg, and the gravitational acceleration g is 9.8 m / s 2 , the pole area A of the electromagnet m = 0.02 m 2 , the number of turns N of the coil is 320, and the air permeability μ0 is 4π×10 -7 H / m. The initial state suspension air gap δ0 is set to 0.016 m, the vertical speed v0 is 0 m / s, the expected suspension air gap value δ eq = 0.012 m, and the vertical speed is 0 m / s. According to the equality of the electromagnetic force and the gravity at the equilibrium point, the expected current value i eq = 26.5 A. Considering safety factors, the suspension air gap constraint 0.008 ≤ δ ≤ 0.016 m and the vertical speed constraint -0.1 ≤ v ≤ 0.1 m / s are set. From this, the current constraint 24.7 ≤ i ≤ 28.3 A can be obtained. Considering the vertical disturbance, a sine wave disturbance with a period of 2 s and an amplitude of 0.001 m is set. The sampling time is set to τ = 0.05 s, and the total time t p = 20 s.

[0232] To highlight the advantages of the proposed control strategy, the DO-TMPLC control strategy is compared with the PI control strategy and the TMPLC control strategy. Among them, the PI controller parameters are selected as Kp out = Kp in = 30, Ki out = Ki in = 50; the DO-TMPLC controller parameters are as follows: the sampling time τ = 0.05 s, the prediction time domain T = 20τ, the disturbance observer gain L = -100, the weight matrix Q of the cost function is I 2×2 , R = 0.1, and according to the calculation, K = K ac = [3.1623, 4.0404], P = [1.2777, 0.3162; 1.3162, 0.4040], ε = 0.004. The TMPLC controller sets the disturbance compensation to ω dob (t) = 0, and the other parameters are the same as those of the DO-TMPLC control strategy.

[0233] Based on the above parameters, the composite control strategy proposed in this embodiment is verified by simulation, and Figures 3-6 . Among them, Figure 3 andFigure 4 It shows the error tracking curves and actual curves of the air gap and vertical velocity of the suspension system under the PI control, TMPLC, and DO-TMPLC algorithms. Figure 5 It shows the control input and actual current curves of the suspension system under the PI control, TMPLC, and DO-TMPLC algorithms. Figure 6 It shows the disturbance estimation and disturbance estimation error curves in the disturbance rejection tubular model predictive suspension control method for the maglev train. According to Figure 3 it can be obtained that the suspension air gap tracking error and vertical velocity tracking error of the suspension system tend to 0; according to Figure 4 and Figure 5 it can be obtained that the suspension air gap, vertical velocity, and current value of the suspension system tend to the expected values at the equilibrium point, that is, the system has good suspension air gap tracking performance and vertical velocity tracking performance.

[0234] Through the above analysis, the effectiveness of the anti-disturbance tubular model predictive suspension control strategy for the maglev train provided in this embodiment is proved.

[0235] Embodiment 3

[0236] This Embodiment 3 provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the disturbance rejection suspension control method for the maglev train as described above is implemented. The method includes:

[0237] Based on the force analysis of the vertical motion of the maglev train considering the vertical disturbance, establish the vertical dynamic equation of the maglev train suspension system, obtain the nonlinear dynamic model of the maglev train suspension system, and obtain the tracking error model of the suspension system according to the tracking target;

[0238] Use the feedback linearization method to linearize the tracking error model of the maglev train suspension system to obtain the linear tracking error model of the maglev train suspension system;

[0239] Based on the disturbance observer, actively compensate for the disturbance;

[0240] According to the tracking error model of the disturbed maglev train suspension system, design a tubular model predictive controller and calculate the robust tightening constraints;

[0241] Use the disturbance observer and the tubular model predictive controller to control the suspension system of the maglev train within the safe air gap range and keep it stable.

[0242] Embodiment 4

[0243] Embodiment 4 provides a computer device, including a memory and a processor. The processor communicates with the memory. The memory stores program instructions executable by the processor. The processor calls the program instructions to execute the interference suppression suspension control method of the maglev train as described above. The method includes:

[0244] Based on the force analysis of the vertical motion of the maglev train considering vertical interference, establish the vertical dynamic equation of the maglev train suspension system, obtain the nonlinear dynamic model of the maglev train suspension system, and obtain the tracking error model of the suspension system according to the tracking target;

[0245] Use the feedback linearization method to linearize the tracking error model of the maglev train suspension system, and obtain the linear tracking error model of the maglev train suspension system;

[0246] Based on the disturbance observer, actively compensate for the disturbance;

[0247] According to the tracking error model of the maglev train suspension system affected by interference, design a tube model predictive controller and calculate the robust tightening constraint;

[0248] Use the disturbance observer and the tube model predictive controller to control the suspension system of the maglev train within the safe air gap range and keep it stable.

[0249] Embodiment 5

[0250] Embodiment 5 provides an electronic device, including: a processor, a memory, and a computer program. Among them, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device runs, the processor executes the computer program stored in the memory, so that the electronic device executes the instructions to implement the interference suppression suspension control method of the maglev train as described above. The method includes:

[0251] Based on the force analysis of the vertical motion of the maglev train considering vertical interference, establish the vertical dynamic equation of the maglev train suspension system, obtain the nonlinear dynamic model of the maglev train suspension system, and obtain the tracking error model of the suspension system according to the tracking target;

[0252] Use the feedback linearization method to linearize the tracking error model of the maglev train suspension system, and obtain the linear tracking error model of the maglev train suspension system;

[0253] Based on the disturbance observer, actively compensate for the disturbance;

[0254] According to the tracking error model of the maglev train suspension system affected by interference, design a tube model predictive controller and calculate the robust tightening constraint;

[0255] Use a disturbance observer and a tube model predictive controller to control the levitation system of a maglev train within a safe air gap range and keep it stable.

[0256] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer-usable program code.

[0257] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0258] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device realizes the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0259] These computer program instructions can also be loaded onto a computer or other programmable data processing device to perform a series of operation steps on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0260] Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that based on the technical solutions disclosed in the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts should be covered within the protection scope of the present invention.

Claims

1. A disturbance suppression suspension control method for a maglev train, characterized in that, including: Based on the force analysis of the vertical motion of the maglev train considering vertical interference, establish the vertical dynamic equation of the maglev train suspension system, obtain the non-linear dynamic model of the maglev train suspension system, and obtain the tracking error model of the suspension system according to the tracking target; Using the feedback linearization method, linearize the tracking error model of the maglev train suspension system to obtain the linear tracking error model of the maglev train suspension system; Based on the disturbance observer, actively compensate for the disturbance; According to the tracking error model of the maglev train suspension system under disturbance, design a tube model predictive controller and calculate the robust tightening constraints; Using the disturbance observer and the tube model predictive controller to control the suspension system of the maglev train within the safe air gap range and keep it stable; where The vertical dynamic equation of the maglev train suspension system is: Among them, F(i(t), δ(t)) is the electromagnetic force at time t; m is the mass of the electromagnet; g is the acceleration due to gravity; δ(t) is the suspension air gap at time t; is the vertical acceleration of the suspension system at time t; f d (t) is the vertical disturbance caused by the load or wind force at time t; i(t) is the current value passing through the coil at time t; μ0, A m and N are the air magnetic permeability, the pole area of the electromagnet, and the number of turns of the coil respectively; F(i(0), δ(0)) is the boundary condition at the equilibrium point; Select the air gap value δ(t) and the vertical velocity of the suspension system as state variables, and i 2 (t) as the control input; assume the state at the equilibrium point is where The state - space equation of the tracking error is expressed as: Calculate the Lie bracket Obtain the matrix [g, ad f g] with full rank and satisfying the involutivity condition; Define n(z) = z1, and calculate that the Lie derivative satisfies the condition L g n(z) = 0, L g L f n(z) ≠ 0; Define the new state as and the auxiliary control input where and Obtain the linear system model: Among them and satisfy the constraint conditions: χ 1min ≤ χ1(t) ≤ χ 1max ,χ 2min ≤ χ2(t) ≤ χ 2max ,ω min ≤ ω(t) ≤ ω max Among them, 2. The interference suppression suspension control method for a maglev train according to claim 1, wherein The control input ω(t) is defined as: where ω dob (t) and ω tmplc (t) are the interference compensation and the TMPLC input, respectively; Design a disturbance observer to estimate the mismatched disturbance d: where \(L\lt0\) is the observer gain, \(\nu\) is the auxiliary variable, is the disturbance estimate, Define the interference estimation error as Obtain: Therefore, it can be designed as: Substitute the disturbance compensation into the formula to obtain the closed-loop system:

3. The interference suppression suspension control method for a maglev train according to claim 2, characterized in that Design nominal MPLC controller ω mplc (t): According to the nominal form of the linear system model: Among them, is the state of the nominal system, and the sampling interval is defined as τ (τ = t k+1 - t k , t0 = 0); Under the constant prediction horizon T, the nominal finite-horizon optimization problem is expressed as: Satisfy the conditions: where, is the cost function, are the stage cost function and the terminal cost function respectively, with Q, P, R > 0; is the predicted state corresponding to time ; and are the robust tightening constraints, which are calculated in the next step; is the terminal state constraint set, where ε is a positive constant; the optimal control input trajectory is obtained by solving the optimization problem and the corresponding optimal predicted state trajectory Therefore, the control input of the nominal MPLC is defined as:

4. The interference suppression suspension control method for a maglev train according to claim 3, characterized in that, Design assistant controller ω ac (t): State feedback controller ω ac Generated from the error between the true state and the nominal state affected by disturbances: where the feedback gain K ac makes be Hurwitz; The TMPLC controller is composed of a nominal MPLC controller and an auxiliary controller, expressed as: Substitute ω tmplc (t) controller and disturbance compensation input ω dob (t) into the formula, and the composite closed-loop system is obtained: Calculate the robust tightening constraints: Since the state error of the composite closed-loop system under disturbance and the state under nominal satisfy the inequality Using Minkowski set subtraction, calculate the tightened constraint sets of the state and the control input respectively:

5. A disturbance suppression suspension control system for a maglev train, characterized in that, including: A construction module for establishing the vertical dynamic equation of the maglev train suspension system based on the force analysis of the vertical motion of the maglev train considering vertical interference, obtaining the non-linear dynamic model of the maglev train suspension system, and obtaining the tracking error model of the suspension system according to the tracking target; A linear module for linearizing the tracking error model of the maglev train suspension system using the feedback linearization method to obtain the linear tracking error model of the maglev train suspension system; A compensation module for actively compensating for the disturbance based on the disturbance observer; A calculation module for designing a tube model predictive controller according to the tracking error model of the maglev train suspension system under disturbance and calculating the robust tightening constraints; A control module for using the disturbance observer and the tube model predictive controller to control the suspension system of the maglev train within the safe air gap range and keep it stable; where The vertical dynamic equation of the maglev train suspension system is: Among them, F(i(t), δ(t)) is the electromagnetic force at time t; m is the mass of the electromagnet; g is the acceleration due to gravity; δ(t) is the suspension air gap at time t; is the vertical acceleration of the suspension system at time t; f d (t) is the vertical disturbance caused by the load or wind force at time t; i(t) is the current value passing through the coil at time t; μ0, A m and N are the air magnetic permeability, the pole area of the electromagnet, and the number of turns of the coil respectively; F(i(0), δ(0)) is the boundary condition at the equilibrium point; Select the air gap value δ(t) and the vertical velocity of the suspension system as state variables, and i 2 (t) as the control input; assume that the state at the equilibrium point is where The state space equation of the tracking error is expressed as: Calculate the Lie bracket to obtain the matrix [g, ad f g] with full rank, satisfying the involutivity condition; define n(z) = z1, and calculate that the Lie derivative satisfies the condition L g n(z) = 0, L g L f n(z) ≠ 0; Define the new state as and the auxiliary control input where and obtain the linear system model: Among them and satisfy the constraint conditions: χ 1min χ1(t) ≤ χ 1max ,χ 2min χ2(t) ≤ χ 2max ,ω min ω(t) ≤ ω max Among them, 6. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the disturbance suppression suspension control method of the maglev train as described in any one of claims 1-4 is implemented.

7. A computer device, characterized in that, Including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the disturbance suppression suspension control method of the maglev train as described in any one of claims 1-4.

8. An electronic device, characterized in that, including: A processor, a memory, and a computer program; wherein, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device operates, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the interference suppression suspension control method of the maglev train according to any one of claims 1-4.

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