Prediction control method for multi-suspension system of maglev train based on event triggering

Abstract

The invention provides a maglev train multi-suspension system predictive control method based on event triggering, which comprises the following steps: establishing a multi-electromagnet suspension system continuous dynamic model based on electromagnet parameters of a maglev train; in combination with the input time delay of the multi-electromagnet suspension system, the continuous dynamic model of the multi-electromagnet suspension system is sequentially processed based on a fourth-order Runge-Kutta method, and a discrete coupling time delay dynamic model of the multi-electromagnet suspension system is obtained; establishing a model prediction controller of the multi-electromagnet suspension system by combining the discrete coupling time delay dynamical model of the multi-electromagnet suspension system and the optimization problem; and updating a control signal of the model prediction controller according to a preset composite event triggering mechanism to obtain an initial control quantity, designing a time delay compensation strategy to carry out input time delay compensation on the initial control quantity, and obtaining a standard control quantity to control the multi-suspension system of the maglev train. According to the method, the system energy consumption is remarkably reduced while the good operation performance of the suspension system in a complex environment is guaranteed.

Description

Technical Field

[0001] The invention relates to the field of magnetic suspension of vehicles, and in particular to a predictive control method of a multi-suspension system of a magnetic suspension train based on event triggering. Background Art

[0002] High-speed maglev trains have the advantages of being green and environmentally friendly and having strong climbing ability, and are one of the important development directions of future ground transportation. The suspension system achieves contactless suspension of the train by precisely controlling the electromagnetic force, and is an important technical basis and one of the core components to ensure the normal operation of high-speed maglev trains. At present, most suspension control research is designed based on a decoupled and simplified single-point suspension system. However, factors such as uneven load distribution in the train and random unevenness of the track cause the dynamic state of one of the suspension modules to change, which in turn directly affects the dynamic state of another suspension module. The maglev train is a complex system with multi-point coupling. If only the control performance of the single-point suspension system is considered and the coupling between the electromagnet modules is ignored, the dynamic control performance of the suspension system will be greatly reduced, affecting the smoothness of the train operation.

[0003] In addition, the suspension system of a high-speed maglev train is a complex nonlinear system with multiple constraints, including the output constraint of the suspension gap and the input constraint of the control current. However, most existing control methods do not fully consider the input and output constraints of the suspension control system, resulting in a decrease in the system control performance. At the same time, in order to ensure the smooth suspension of high-speed maglev trains under complex working conditions, the currently designed intelligent control algorithms usually have complex control structures, consume a lot of computing resources and memory, and have high requirements on the computing power of the system hardware. It is difficult to implement in large-scale systems. Excessive computing resource occupation will increase system energy consumption and further weaken the control performance. In addition, in a multi-module system, there is inevitably input delay due to the inductance lag of the electromagnetic coil. If the delay effect is ignored, the performance of the control system will be seriously affected. Therefore, how to simultaneously consider inherent constraints, limited computing / communication resources, and system delays is of great significance to the research on high-speed maglev high-precision stable suspension.

[0004] The control methods in the existing technology are all based on the time trigger mechanism, which calculates the feasible solution of the optimization problem in real time at each sampling point. It takes up a lot of computing and communication resources under a small sampling time and is difficult to implement in large-scale systems. Summary of the invention

[0005] In view of this, the present invention provides a predictive control method for a multi-suspension system of a maglev train based on event triggering to solve the above problems.

[0006] The present invention provides a predictive control method for a multi-suspension system of a maglev train based on event triggering, comprising: establishing a continuous dynamics model of the multi-electromagnet suspension system based on the electromagnet parameters of the maglev train; linearizing and discretizing the continuous dynamics model of the multi-electromagnet suspension system in sequence based on a fourth-order Runge-Kutta method in combination with the input delay of the multi-electromagnet suspension system to obtain a discrete coupled time-delay dynamics model of the multi-electromagnet suspension system; designing an optimization problem according to the inherent constraints and coupled disturbances of the multi-electromagnet suspension system; establishing a model predictive controller of the multi-electromagnet suspension system in combination with the discrete coupled time-delay dynamics model of the multi-electromagnet suspension system and the optimization problem; updating a control signal obtained by the model predictive controller according to a preset composite event triggering mechanism to obtain an initial control quantity; designing a delay compensation strategy according to a predicted state in an iterative optimization process of the model predictive controller to compensate for the input delay of the initial control quantity to obtain a standard control quantity; and controlling the multi-suspension system of the maglev train using the standard control quantity.

[0007] In another implementation of the present invention, the continuous dynamics model of the multi-electromagnet suspension system is expressed as:

[0008] Where g represents the acceleration due to gravity, and its unit is N / kg ; f d1 (t), f d2 (t) are the disturbance forces on the electromagnets on the left and right sides, respectively, in units of N ; , are the masses of the electromagnets on the left and right sides, respectively, in units of kg ; , are the equivalent spring coefficients of the electromagnets on the left and right sides, in units of N / m ; , are the vertical displacements of the electromagnets on the left and right sides, respectively, in units of m ; M 1 is the mass of the floating frame, in units of kg ; M 2 is the total mass of the air spring and the vehicle body, in units of kg ; μ 0 is the air magnetic permeability unit is H / m ; N is the effective number of turns of the electromagnet coil; A 0 is the effective cross-sectional area of ​​the electromagnet coil, in units of m 2 ; i 1 、i2 are the currents of the electromagnets on the left and right sides, in units of A .

[0009] In another implementation of the present invention, the discrete coupling time-delay dynamics model of the multi-electromagnet suspension system is expressed as:

[0010] in, For the left solenoid module System status at the moment; ; For the right solenoid module System status at the moment; ; represents the current time step; and are the tracking errors of the suspension gaps of the left and right electromagnet modules, in m; is the target value of the suspension clearance, in meters; for The first derivative with respect to time; for First and second derivatives with respect to time; A 1 is the system state parameter matrix of the left electromagnet module, C 21 is the coupling parameter matrix of the multi-electromagnet module, ; A 2 is the system state parameter matrix of the right electromagnet module, C 12 is the coupling parameter matrix of the multi-electromagnet module, ; B 1 is the control input parameter matrix of the left electromagnet module, ; B 2 is the control input parameter matrix of the right electromagnet module. ; D 1 is the external disturbance parameter matrix of the left electromagnet module, D 2 is the external disturbance parameter matrix of the right electromagnet module, ; The left electromagnet module is at the input delay Moment-by-moment prediction of control input sequence; The right side electromagnet module is at the input delay Moment-by-moment prediction of control input sequence; Randomly input delay to the system; For the left solenoid module The external disturbances at any time, ; For the right solenoid module The external disturbances at any time, ; and They are the external disturbance fluctuations of the left and right electromagnet modules compared to the equilibrium point, and the unit is N.

[0011] In order to facilitate controller design, the above formula is simplified as:

[0012] in, for The system status at the moment, ; for The actual system status at the moment, ; For input delay The actual control input of the system at that moment, ; for The external disturbance to the system at that moment, ; is the state parameter of the coupled system, ; is the optimal control quantity set, .

[0013] In another implementation of the present invention, the optimization problem is expressed as:

[0014]

[0015]

[0016]

[0017]

[0018] in, for Predicted system state at a given moment; If there is input delay The optimal control quantity at the moment; For the prediction time domain; To control the time domain; The trigger moment for the event; for Moment The predicted system state of the step; for Moment The predicted state of the step; If there is input delay Moment The optimal control quantity of the step; for The external disturbance to which the system is subjected at any given moment; for Moment The estimated state of the system at step 1; for Moment The predicted system state of the step; for Moment The optimal control quantity of the step; is a positive integer to be designed; is the system state set; Contraction set for preset system state; Predict the set of terminal states for the system.

[0019] In another implementation of the present invention, the preset system state contraction set is expressed as:

[0020] in, To ensure the feedback control gain of the closed loop stability of the system; for Transposition of the system state at a given moment; Q is the positive definite matrix to be selected; is the positive definite matrix to be selected; γ is the normal number to be designed.

[0021] In another implementation of the present invention, the preset compound event trigger mechanism includes an optimization feasibility event trigger mechanism, a system closed-loop stability event trigger mechanism and an energy consumption minimization event trigger mechanism; the control signal obtained by updating the model predictive controller according to the preset compound event trigger mechanism to obtain an initial control quantity includes: when the multi-electromagnet suspension system is in the floating stage and satisfies the optimization feasibility event trigger mechanism and the system closed-loop stability event trigger mechanism, the model predictive controller receives the system state output by the sensor and performs optimization solution to obtain the initial control quantity; when the multi-electromagnet suspension system enters the stable suspension stage and satisfies any one of the optimization feasibility event trigger mechanism, the system closed-loop stability event trigger mechanism and the energy consumption minimization event trigger mechanism, the model predictive controller receives the system state output by the sensor and performs optimization solution to obtain the initial control quantity.

[0022] In another implementation of the present invention, the optimization feasibility event triggering mechanism is expressed as:

[0023] in, for System status at the moment; for Moment The system prediction state of the step; System parameters The Lipschitz constant; for Moment The optimal control input and The maximum value of the optimal control input difference at the moment; is the upper bound of the error norm between the actual system state and the predicted system state; is the Lipschitz constant of the system disturbance; System parameters The Lipschitz constant.

[0024] In another implementation of the present invention, the system closed-loop stability event triggering mechanism is expressed as:

[0025] in, for System state error at time is the contraction set of system states to be designed; for Moment The predicted system state of the step; System parameters The Lipschitz constant; System parameters exist The Lipschitz constant at the moment; is a normal number to be designed and satisfies ; for Moment The system status of the step; m To control the time domain; p For the prediction time domain.

[0026] In another implementation of the present invention, the auxiliary condition of the system closed-loop stability event triggering mechanism is expressed as:

[0027] in, is the system state error parameter; is the initial value of the system state error; is the normal number to be designed.

[0028] In another implementation of the present invention, the energy consumption minimization event triggering mechanism is expressed as:

[0029] in, Trigger the moment for the next event; The trigger moment for the event; The event trigger period.

[0030] The event-triggered predictive control method for a maglev train multi-suspension system of the present invention comprehensively considers the mechanical coupling relationship between electromagnets on the same side and the input-output dual dynamic constraints of the multi-electromagnet suspension system during the controller design process; a maximum delay compensation method is used to compensate for the influence of the system input delay on the stable suspension performance; a composite event trigger mechanism is designed to ensure that the temporary / transient performance of the suspension system remains basically unchanged while reducing the number of system calculations / communications; the system state constraint satisfaction can be guaranteed under random external disturbances and system coupling disturbances, greatly reducing the system conservatism; and the system energy consumption is significantly reduced while ensuring the good operating performance of the suspension system in a complex environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. By reading the detailed description of the following implementations, the advantages and benefits of the solutions become clear to those skilled in the art. The drawings are only used to illustrate the preferred implementations and are not to be considered as limiting the present invention.

[0032] Figure 1 The present invention is a flowchart of a method for predictive control of a multi-suspension system of a maglev train based on event triggering according to an embodiment of the present invention.

[0033] Figure 2 This is a force diagram of a multi-electromagnet suspension system of a high-speed maglev train suspension system according to an embodiment of the present invention.

[0034] Figure 3 This is a diagram showing the change in suspension gap of the left and right electromagnet suspension systems under input delay according to an embodiment of the present invention.

[0035] Figure 4 This is a graph showing changes in control current input of left and right electromagnet suspension systems under input delay according to an embodiment of the present invention.

[0036] Figure 5 This is a diagram of the calculation / communication triggering timing of a multi-electromagnet suspension system under the compound event triggering mechanism of the method of the present invention in one embodiment of the present invention.

[0037] Figure 6 This is a diagram of the calculation / communication triggering timing of a multi-electromagnet suspension system under the event triggering mechanism proposed in the document of one embodiment of the present invention.

[0038] Figure 7 This is a block diagram of a model predictive control system for a high-speed maglev train based on event triggering according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be described clearly and in detail below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in the field based on the embodiments in the embodiments of the present invention should fall within the scope of protection of the embodiments of the present invention.

[0040] Figure 1 A flow chart of a predictive control method for a maglev train multi-suspension system based on event triggering is provided in an embodiment of the present invention, such as Figure 1 As shown, this embodiment mainly includes: S101. Based on the electromagnet parameters of the maglev train, a continuous dynamics model of the multi-electromagnet suspension system is established.

[0041] S102. In combination with the input delay of the multi-electromagnet suspension system, the continuous dynamics model of the multi-electromagnet suspension system is linearized and discretized in sequence based on the fourth-order Runge-Kutta method to obtain a discrete coupled time-delay dynamics model of the multi-electromagnet suspension system.

[0042] S103. Design an optimization problem according to the inherent constraints and coupling disturbances of the multi-electromagnet suspension system.

[0043] S104, establishing a model predictive controller for the multi-electromagnet suspension system in combination with the discrete coupled time-delay dynamics model of the multi-electromagnet suspension system and the optimization problem.

[0044] S105 . Update the control signal obtained by the model predictive controller according to a preset compound event trigger mechanism to obtain an initial control variable.

[0045] S106. Design a time delay compensation strategy to compensate for input time delay of the initial control variable according to the prediction state in the iterative optimization process of the model predictive controller to obtain a standard control variable.

[0046] S107: Use the standard control amount to control the multi-suspension system of the maglev train.

[0047] The event-triggered predictive control method for a maglev train multi-suspension system of the present invention comprehensively considers the mechanical coupling relationship between electromagnets on the same side and the input-output dual dynamic constraints of the multi-electromagnet suspension system during the controller design process; a maximum delay compensation method is used to compensate for the influence of the system input delay on the stable suspension performance; a composite event trigger mechanism is designed to ensure that the temporary / transient performance of the suspension system remains basically unchanged while reducing the number of system calculations / communications; the system state constraint satisfaction can be guaranteed under random external disturbances and system coupling disturbances, greatly reducing the system conservatism; and the system energy consumption is significantly reduced while ensuring the good operating performance of the suspension system in a complex environment.

[0048] In another implementation of the present invention, the continuous dynamics model of the multi-electromagnet suspension system is expressed as:

[0049] Where g represents the acceleration due to gravity, and its unit is N / kg ; f d1 (t), f d2 (t) are the disturbance forces on the electromagnets on the left and right sides, respectively, in units of N ; , are the masses of the electromagnets on the left and right sides, respectively, in units of kg ; , are the equivalent spring coefficients of the electromagnets on the left and right sides, in units of N / m ; , are the vertical displacements of the electromagnets on the left and right sides, respectively, in units of m ; M 1 is the mass of the floating frame, in units of kg ; M 2 is the total mass of the air spring and the vehicle body, in units of kg ; μ 0 is the air magnetic permeability unit is H / m ; N is the effective number of turns of the electromagnet coil; A 0 is the effective cross-sectional area of ​​the electromagnet coil, in units of m 2 ; i 1 、i 2 are the currents of the electromagnets on the left and right sides, in units of A .

[0050] For example, the two electromagnet modules in the lap structure of the high-speed maglev train suspension system are connected by rigid pole plates, which can be simplified to spring damping force. The simplified structural force diagram is shown in Figure 2 As shown, according to Newton's second law, the dynamic equation of the electromagnet module in the vertical direction can be obtained:

[0051] in, , are the masses of the electromagnets on the left and right sides respectively; , are the accelerations of the electromagnets on the left and right sides in the vertical direction respectively; , are the disturbance forces on the electromagnets on the left and right sides respectively; g is the acceleration due to gravity; , are the electromagnetic attraction forces on the electromagnets on the left and right sides respectively; , are the equivalent spring damping forces of the electromagnets on the left and right sides, respectively, which are usually obtained by the following formula:

[0052] in, is the vertical displacement of the floating frame; , are the vertical displacements of the electromagnets on the left and right sides respectively; , are the equivalent spring coefficients of the electromagnets on the left and right sides respectively; , are the equivalent damping coefficients of the electromagnets on the left and right sides respectively; is the vertical speed of the floating frame; , are the vertical velocities of the electromagnets on the left and right sides respectively.

[0053] Since the pole plate is a rigid structure, the damping coefficient is very small and can be ignored. The two electromagnet modules are evenly distributed on both sides of the pole plate. Therefore, the vertical displacement of the suspension frame can be approximately simplified to the average displacement of the electromagnet modules on both sides, that is:

[0054] in, M 1 is the mass of the suspension frame, in kg; M 2 is the total mass of the air spring and the vehicle body, in kg; is the equivalent stiffness coefficient of disc spring.

[0055] For the maglev train suspension system, the number of turns of the electromagnet coils on the left and right sides is equal, and the effective magnetic pole area is equal, and the multi-electromagnet coupling continuous dynamic model is obtained:

[0056] It should be understood that the suspension system is a complex system with multi-point coupling. The electromagnets on the same side are connected by rigid pole plates and have a strong mechanical coupling relationship. When the dynamic state of one electromagnet changes, the dynamic state of the adjacent electromagnet will also change due to the influence of the coupling disturbance. The coupling disturbance between multiple electromagnet modules reduces the dynamic control performance of the suspension system.

[0057] In another implementation of the present invention, the discrete coupling time-delay dynamics model of the multi-electromagnet suspension system is expressed as:

[0058] in, For the left solenoid module System status at the moment; ; For the right solenoid module System status at the moment; ; represents the current time step; and are the tracking errors of the suspension gaps of the left and right electromagnet modules, in m; is the target value of the suspension clearance, in meters; for The first derivative with respect to time; for First and second derivatives with respect to time; A 1 is the system state parameter matrix of the left electromagnet module, C 21 is the coupling parameter matrix of the multi-electromagnet module, ; A 2 is the system state parameter matrix of the right electromagnet module, C 12 is the coupling parameter matrix of the multi-electromagnet module, ; B 1 is the control input parameter matrix of the left electromagnet module, ; B 2 is the control input parameter matrix of the right electromagnet module. ; D 1 is the external disturbance parameter matrix of the left electromagnet module, D 2 is the external disturbance parameter matrix of the right electromagnet module, ; The left electromagnet module is at the input delay Moment-by-moment prediction of control input sequence; The right side electromagnet module is at the input delay Moment-by-moment prediction of control input sequence; Randomly input delay to the system; For the left solenoid module The external disturbances at any time, ; For the right solenoid module The external disturbances at any time, ; and They are the external disturbance fluctuations of the left and right electromagnet modules compared to the equilibrium point, and the unit is N.

[0059] In order to facilitate controller design, the above formula is simplified as:

[0060] in, for The system status at the moment, ; for The actual system status at the moment, ; For input delay The actual control input of the system at that moment, ; for The external disturbance to the system at that moment, ; is the state parameter of the coupled system, ; is the optimal control quantity set, .

[0061] Exemplarily, the obtained multi-electromagnet coupled continuous dynamics model is linearized near the equilibrium point to obtain a linearized model of the multi-electromagnet module:

[0062] in, and are the tracking errors of the suspension gap of the left and right electromagnet modules, and They are The first and second derivatives with respect to time, and They are First and second derivatives with respect to time; and are the difference in control current of the left and right electromagnet modules, and They are the external disturbance fluctuations of the left and right electromagnet modules compared to the equilibrium point, is the target value of the suspension clearance, is the control current of the left electromagnet module at the equilibrium point, is the control current of the right electromagnet module at the equilibrium point; is the electromagnetic coefficient; , are the displacement coefficients of the left and right electromagnet modules respectively; , They are the current coefficients of the left and right electromagnet modules respectively.

[0063] ; ; ; ;

[0064] in, , are the current values ​​of the left and right electromagnet modules at the balance point respectively; , They are the suspension gaps of the left and right electromagnet modules at the balance point.

[0065] The fourth-order Runge-Kutta method is used to discretize the linearized model of the multi-electromagnet suspension module to obtain a discrete dynamic model:

[0066] in, , , , , , , , , and are the difference in control current of the left and right electromagnet modules, , .

[0067] Considering the system input delay caused by the inductance lag of the electromagnetic coil, the multi-electromagnet discrete coupling time-delay dynamic model is obtained:

[0068] In order to facilitate the controller design, the multi-electromagnet discrete coupling time-delay dynamics model is simplified as:

[0069] In another implementation of the present invention, the optimization problem is expressed as:

[0070]

[0071]

[0072]

[0073]

[0074] in, for Predicted system state at a given moment; If there is input delay The optimal control quantity at the moment; For the prediction time domain; To control the time domain; The trigger moment for the event; for Moment The predicted system state of the step; for Moment The predicted state of the step; If there is input delay Moment The optimal control quantity of the step; for The external disturbance to which the system is subjected at any given moment; for Moment The estimated state of the system at step 1; for Moment The predicted system state of the step; for Moment The optimal control quantity of the step; is a positive integer to be designed; is the system state set; Contraction set for preset system state; Predict the set of terminal states for the system.

[0075] Exemplarily, the multi-electromagnet suspension system has output constraints caused by an extremely small working range and input constraints caused by output power limitations of the power supply device, so a model predictive controller is used to handle the dual dynamic constraints of input and output of the multi-electromagnet suspension system.

[0076] Considering the input and output constraints of the multi-electromagnet suspension system, a multi-constraint optimization problem is designed. Aiming at the dynamic coupling disturbance and random external disturbance in the high-speed maglev multi-electromagnet suspension system, a new state constraint set tightening method is proposed. The system state contraction set is introduced to ensure the satisfaction of the system state constraints under time-varying external disturbance and system coupling disturbance.

[0077] In another implementation of the present invention, the preset system state contraction set is expressed as:

[0078] in, To ensure the feedback control gain of the closed loop stability of the system; for Transposition of the system state at a given moment; Q is the positive definite matrix to be selected; is the positive definite matrix to be selected; γ is the normal number to be designed.

[0079] For example, the system state shrink set It plays an important role in optimization solution and system closed-loop stability, and can reduce the conservatism of system design.

[0080] In another implementation of the present invention, due to the existence of input delay, the optimization problem The optimal control quantity at the moment is Acting on the system all the time, causing system performance degradation and instability. In order to compensate for the impact of input delay on system performance, set The control quantity actually acting on the system at any moment is ,in, is the maximum value of the input delay, .

[0081] The present invention fully considers the random input delay of the subsystem in the coupled system, and adopts the maximum delay compensation strategy based on the predicted state to reduce the influence of the input delay on the stable suspension performance. The proposed delay compensation algorithm has good robust compensation performance even under coupling interference. This is a control algorithm for multi-electromagnet coupled suspension system that considers both input delay and inherent constraints.

[0082] In another implementation of the present invention, the preset compound event trigger mechanism includes an optimization feasibility event trigger mechanism, a system closed-loop stability event trigger mechanism, and an energy consumption minimization event trigger mechanism; the control signal obtained by updating the model predictive controller according to the preset compound event trigger mechanism to obtain the initial control quantity includes: Figure 7As shown, the system status is monitored in real time by sensors. When the multi-electromagnet suspension system is in the floating stage and satisfies the optimization feasibility event trigger mechanism and the system closed-loop stability event trigger mechanism, the model predictive controller receives the system status output by the sensor and performs optimization solution to obtain the initial control quantity; when the multi-electromagnet suspension system enters the stable suspension stage and satisfies any one of the optimization feasibility event trigger mechanism, the system closed-loop stability event trigger mechanism and the energy consumption minimization event trigger mechanism, the model predictive controller receives the system status output by the sensor and performs optimization solution to obtain the initial control quantity.

[0083] For example, the model predictive controller calculates the feasible solution of the optimization problem in real time at each sampling point, which takes up a lot of computing and communication resources and is difficult to implement in large-scale systems. Event-triggered control will update the control signal only when the pre-designed trigger mechanism is met, greatly reducing unnecessary signal transmission, saving communication resources and computing resources, and reducing energy consumption.

[0084] Based on this, a composite event trigger mechanism is designed to save system communication resources. The composite event trigger mechanism that considers the feasibility of iterative optimization, system closed-loop stability and energy consumption minimization ensures that the temporary / transient performance of the suspension system remains basically unchanged while significantly reducing the computing / communication resources.

[0085] In another implementation of the present invention, in order to ensure that there is a feasible solution to the optimization problem, the following event triggering mechanism is designed to ensure the feasibility of iterative optimization. The optimization feasibility event triggering mechanism is expressed as:

[0086] in, for System status at the moment; for Moment The system prediction state of the step; System parameters The Lipschitz constant; for Moment The optimal control input and The maximum value of the optimal control input difference at the moment; is the upper bound of the error norm between the actual system state and the predicted system state; is the Lipschitz constant of the system disturbance; System parameters The Lipschitz constant.

[0087] In another implementation of the present invention, the system closed-loop stability event triggering mechanism is expressed as:

[0088] in, for System state error at time is the contraction set of system states to be designed; for Moment The predicted system state of the step; System parameters The Lipschitz constant; System parameters exist The Lipschitz constant at the moment; is a normal number to be designed and satisfies ; for Moment The system status of the step; m To control the time domain; p For the prediction time domain.

[0089] In another implementation of the present invention, in the presence of random external interference and system mechanical coupling interference, the above event trigger mechanism is easily satisfied, resulting in frequent system triggering and a large waste of resources. In order to reduce the event triggering frequency, the following auxiliary conditions are adopted. The auxiliary conditions of the system closed-loop stability event trigger mechanism are expressed as:

[0090] in, is the system state error parameter; is the initial value of the system state error; is the normal number to be designed.

[0091] In another implementation of the present invention, after the system reaches a stable suspension state, its event triggering frequency requirement is significantly reduced. To further optimize computing resources, the following event triggering mechanism is designed to monitor the state fluctuation of the system in the stable suspension stage. The energy consumption minimization event triggering mechanism is expressed as:

[0092] in, Trigger the moment for the next event; The trigger moment for the event; The event trigger period.

[0093] It should be understood that the composite event trigger mechanism proposed in the present invention provides parallel detection to ensure closed-loop stability, recursive feasibility and event triggering mechanism with minimized energy consumption, thereby improving system computing / communication efficiency and significantly reducing system energy consumption.

[0094] In another implementation of the present invention, the above control method is applied to a multi-electromagnet suspension module of a high-speed maglev train, and the system parameters and simulation initial values ​​are configured, and the following two sets of simulations are performed in MATLAB.

[0095] 1) System delay compensation.

[0096] 2) Compound event trigger mechanism.

[0097] Figure 3 and Figure 4 The following are the changes in the suspension gap and the control quantity under the system input delay. The model predictive control method without time delay compensation is selected for comparison in the simulation. The results show that the suspension gap of the system has large fluctuations under the influence of input delay without the delay compensation method. However, by adopting the proposed delay compensation strategy, the multi-electromagnet suspension system can better converge to the target air gap and has better dynamic performance. In addition, from Figure 3 and Figure 4 It can be seen that the method proposed in the present invention effectively ensures that the system input and output are always within the constraint conditions, thereby ensuring the smooth operation of the multi-electromagnet coupled suspension system.

[0098] Figure 5 and Figure 6 They are respectively the calculation / communication frequency of the multi-suspension system under the composite event trigger mechanism proposed in the present invention and the event trigger mechanism proposed in the literature [Y. Yan, R. Wang, SH Yu, CL Wang, TS Li, ​​“Event-triggered output feedback sliding mode control of mechanical systems,” Nonlinear Dynamics, vol. 107, pp. 3543–3555, Jan. 2022, doi:10.1007 / s11071-021-07152-1.]. It can be seen that in the first 100 moments, compared with the 52 trigger moments of the control algorithm in the literature, the composite event trigger mechanism proposed in the present invention was only triggered 22 times, with lower calculation and communication loads.

[0099] The event-triggered predictive control method for the multi-suspension system of a maglev train proposed in the present invention is applied to the multi-electromagnet suspension module model of a high-speed maglev train, and simulations are performed under different conditions. The simulation results show that the control method proposed in the present invention has better dynamic performance under the system input delay and inherent constraints, and can ensure that the temporary / transient performance of the suspension system remains basically unchanged while significantly reducing computing / communication resources and system energy consumption.

[0100] In another aspect of the present invention, an electronic device includes: a processor, a memory, a communication bus, and a communication interface.

[0101] in: The processor, memory and communication interface communicate with each other through a communication bus.

[0102] Communication interface, used to communicate with other electronic devices or servers.

[0103] The processor is used to execute the program, and specifically can execute the steps of any one of the event-triggered predictive control methods for a maglev train multi-suspension system in the above-mentioned embodiments.

[0104] Specifically, the program may include program codes including computer operation instructions.

[0105] The processor may be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application. The one or more processors included in the smart device may be processors of the same type, such as one or more CPUs; or processors of different types, such as one or more CPUs and one or more ASICs.

[0106] Memory is used to store programs. The memory may include high-speed RAM memory and may also include non-volatile memory, such as at least one disk storage.

[0107] The program can be specifically used to enable the processor to execute to implement the steps of any event-triggered predictive control method for a maglev train multi-suspension system described in the embodiment. The specific implementation of each step in the program can refer to the corresponding descriptions in the steps and units executed by any event-triggered predictive control method for a maglev train multi-suspension system in the above steps, which will not be repeated here. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the above-described equipment and modules can refer to the corresponding process description in the aforementioned method embodiment.

[0108] The exemplary embodiments of the present application also provide a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a computer to execute the methods of the various embodiments of the present application.

[0109] The method according to the embodiment of the present invention described above may be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded through a network and will be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that a computer, a processor, a microprocessor controller or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, a processor or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0110] Thus far, specific embodiments of the present invention have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired results. Additionally, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing may be advantageous.

[0111] It should be noted that all directional indications (such as up, down, left, right, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0112] In the description of the present invention, the terms "first" and "second" are only used to facilitate the description of different components or names, and cannot be understood as indicating or implying a sequential relationship, relative importance, or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features.

[0113] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0114] It should be noted that although the specific embodiments of the present invention are described in detail in conjunction with the accompanying drawings, it should not be understood as limiting the scope of protection of the present invention. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still belong to the scope of protection of the present invention.

[0115] The examples of the embodiments of the present invention are intended to concisely illustrate the technical features of the embodiments of the present invention so that those skilled in the art can intuitively understand the technical features of the embodiments of the present invention, and are not intended to be improper limitations of the embodiments of the present invention.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A predictive control method for a maglev train multi-suspension system based on event triggering, characterized in that: include: Based on the electromagnet parameters of the maglev train, a continuous dynamics model of the multi-electromagnet suspension system is established; Combined with the input delay of the multi-electromagnet suspension system, the continuous dynamic model of the multi-electromagnet suspension system is linearized and discretized in turn based on the fourth-order Runge-Kutta method to obtain a discrete coupled time-delay dynamic model of the multi-electromagnet suspension system; Designing an optimization problem based on the inherent constraints and coupled disturbances of the multi-electromagnet suspension system; In combination with the discrete coupling time-delay dynamics model of the multi-electromagnet suspension system and the optimization problem, a model predictive controller of the multi-electromagnet suspension system is established; Update the control signal obtained by the model predictive controller according to a preset composite event trigger mechanism to obtain an initial control amount; According to the prediction state in the iterative optimization process of the model predictive controller, a delay compensation strategy is designed to compensate the input delay of the initial control quantity to obtain a standard control quantity; The multi-suspension system of the maglev train is controlled using the standard control quantity.

2. The method according to claim 1, characterized in that: The continuous dynamics model of the multi-electromagnet suspension system is expressed as: Where g represents the acceleration due to gravity, and its unit is N / kg ; f d1 (t), f d2 (t) are the disturbance forces on the electromagnets on the left and right sides, respectively, in units of N ; , are the masses of the electromagnets on the left and right sides, respectively, in units of kg ; , are the equivalent spring coefficients of the electromagnets on the left and right sides, in units of N / m ; , are the vertical displacements of the electromagnets on the left and right sides, respectively, in units of m ; M 1 is the mass of the floating frame, in units of kg ; M 2 is the total mass of the air spring and the vehicle body, in units of kg ; μ 0 is the air magnetic permeability unit is H / m ; N is the effective number of turns of the electromagnet coil; A 0 is the effective cross-sectional area of ​​the electromagnet coil, in units of m 2 ; i 1 、i 2 are the currents of the electromagnets on the left and right sides, in units of A .

3. The method according to claim 2, characterized in that The discrete coupling time-delay dynamics model of the multi-electromagnet suspension system is expressed as: in, For the left solenoid module System status at the moment; ; For the right solenoid module System status at the moment; ; represents the current time step; and are the tracking errors of the suspension gaps of the left and right electromagnet modules, in m; is the target value of the suspension clearance, in meters; for The first derivative with respect to time; for First and second derivatives with respect to time; A 1 is the system state parameter matrix of the left electromagnet module, C 21 is the coupling parameter matrix of the multi-electromagnet module, ; A 2 is the system state parameter matrix of the right electromagnet module, C 12 is the coupling parameter matrix of the multi-electromagnet module, ; B 1 is the control input parameter matrix of the left electromagnet module, ; B 2 is the control input parameter matrix of the right electromagnet module. ; D 1 is the external disturbance parameter matrix of the left electromagnet module, D 2 is the external disturbance parameter matrix of the right electromagnet module, ; The left electromagnet module is at the input delay Moment-by-moment prediction control input sequence; For input delay, the right side electromagnet module is Moment-by-moment prediction control input sequence; Randomly input delay to the system; For the left solenoid module The external disturbances at any time, ; For the right solenoid module The external disturbances at any time, ; and They are the external disturbance fluctuations of the left and right electromagnet modules compared to the equilibrium point, in N; In order to facilitate controller design, the above formula is simplified as: in, for The system status at the moment, ; for The actual system status at the moment, ; For input delay The actual control input of the system at that moment, ; for The external disturbance to the system at that moment, ; is the state parameter of the coupled system, ; is the optimal control quantity set, .

4. The method according to claim 3, characterized in that: The optimization problem is expressed as: in, for Predicted system state at a given moment; If there is input delay The optimal control quantity at the moment; For the prediction time domain; To control the time domain; The trigger moment for the event; for Moment The predicted system state of the step; for Moment The predicted state of the step; If there is input delay Moment The optimal control quantity of the step; for The external disturbance to which the system is subjected at any given moment; for Moment The estimated state of the system at step 1; for Moment The predicted system state of the step; for Moment The optimal control quantity of the step; is a positive integer to be designed; is the system state set; Contraction set for preset system state; Predict the set of terminal states for the system.

5. The method according to claim 4, characterized in that The preset system state contraction set is expressed as: in, To ensure the feedback control gain of the closed loop stability of the system; for Transposition of the system state at a given moment; Q is the positive definite matrix to be selected; is the positive definite matrix to be selected; γ is the normal number to be designed.

6. The method according to claim 1, characterized in that The preset compound event trigger mechanism includes an optimization feasibility event trigger mechanism, a system closed-loop stability event trigger mechanism, and an energy consumption minimization event trigger mechanism; The method of updating the control signal obtained by the model predictive controller according to the preset composite event trigger mechanism to obtain the initial control amount includes: When the multi-electromagnet suspension system is in the floating stage and satisfies the optimization feasibility event triggering mechanism and the system closed-loop stability event triggering mechanism, the model predictive controller receives the system state output by the sensor and performs optimization and solution to obtain an initial control quantity; When the multi-electromagnet suspension system enters the stable suspension stage and satisfies any one of the optimization feasibility event triggering mechanism, the system closed-loop stability event triggering mechanism and the energy consumption minimization event triggering mechanism, the model predictive controller receives the system state output by the sensor and performs optimization solution to obtain the initial control quantity.

7. The method according to claim 6, characterized in that The optimization feasibility event triggering mechanism is expressed as: in, for System status at the moment; for Moment The system prediction state of the step; System parameters The Lipschitz constant; for Moment The optimal control input and The maximum value of the optimal control input difference at the moment; is the upper bound of the error norm between the actual system state and the predicted system state; is the Lipschitz constant of the system disturbance; System parameters The Lipschitz constant.

8. The method according to claim 6, characterized in that The system closed-loop stability event triggering mechanism is expressed as: in, for System state error at time is the contraction set of system states to be designed; for Moment The predicted system state of the step; System parameters The Lipschitz constant; System parameters exist The Lipschitz constant at the moment; is a normal number to be designed and satisfies ; for Moment The system status of the step; m To control the time domain; p For the prediction time domain.

9. The method according to claim 8, characterized in that The auxiliary condition of the system closed-loop stability event triggering mechanism is expressed as: in, is the system state error parameter; is the initial value of the system state error; is the normal number to be designed.

10. The method according to claim 6, characterized in that The energy consumption minimization event triggering mechanism is expressed as: in, Trigger the moment for the next event; The trigger moment for the event; The event trigger period.

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