A Predictive Control Method for a Multi-Levitation System of Maglev Trains Based on Event Triggering

Abstract

The present invention provides a predictive control method for a multi-levitation system of a maglev train based on event triggering, including: establishing a continuous dynamic model of a multi-electromagnet levitation system based on the electromagnet parameters of the maglev train; combining the input time delay of the multi-electromagnet levitation system, and sequentially processing the continuous dynamic model of the multi-electromagnet levitation system based on the fourth-order Runge-Kutta method to obtain a discrete coupled time-delay dynamic model of the multi-electromagnet levitation system; combining the discrete coupled time-delay dynamic model of the multi-electromagnet levitation system and the optimization problem to establish a model predictive controller for the multi-electromagnet levitation system; updating the control signal of the model predictive controller according to a preset composite event triggering mechanism to obtain an initial control quantity, designing a time-delay compensation strategy to perform input time-delay compensation on the initial control quantity, and obtaining a standard control quantity to control the multi-levitation system of the maglev train. The method of the present invention significantly reduces the system energy consumption while ensuring the good operating performance of the levitation system in a complex environment.

Description

Technical Field

[0001] The present invention relates to the field of maglev of vehicles, and particularly to a predictive control method for a multi-suspension system of a maglev 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, etc., and are one of the important development directions of future ground transportation. The suspension system realizes the non-contact suspension of the train by precisely controlling the electromagnetic force, and is one of the important technical bases and core components to ensure the normal operation of high-speed maglev trains. At present, most of the suspension control research is designed based on a single-point suspension system after decoupling and simplification. However, factors such as uneven load distribution inside the train and random unevenness of the track cause changes in the dynamic state of one suspension module, which in turn directly affects the dynamic state of another suspension module. A maglev train is a complex multi-point coupled system. If only the control performance of the single-point suspension system is considered and the coupling effect between the electromagnet modules is ignored, the dynamic control performance of the suspension system will be greatly reduced, affecting the running smoothness of the train.

[0003] In addition, the suspension system of high-speed maglev trains is a complex non-linear system with multiple constraints, including output constraints of the suspension gap and input constraints of the control current. However, most of the existing control methods do not fully consider the input and output constraints of the suspension control system, resulting in a decline 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 large amount of computing resources and memory, require high computing power of the system hardware, and are difficult to implement in large-scale systems. Excessive occupation of computing resources will increase the system energy consumption and further weaken the control performance. In addition, there is inevitably an input delay in the multi-module system due to the inductance lag of the electromagnetic coil. If the time delay effect is ignored, it will seriously affect the performance of the control system. Therefore, how to consider problems such as inherent constraints, limited computing / communication resources, and system time delay at the same time is of great significance for carrying out high-precision and stable suspension research on high-speed maglev.

[0004] The control methods in the prior art are all based on the time-triggered mechanism, and the feasible solutions of the optimization problem are calculated in real time at each sampling point. A large amount of computing and communication resources are occupied under a small sampling time, and it is difficult to implement in a large-scale system. 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-levitation system of a maglev train based on event triggering, including: establishing a continuous dynamic model of a multi-electromagnet levitation system based on the electromagnet parameters of the maglev train; combining the input time delay of the multi-electromagnet levitation system, and performing linearization and discretization processing on the continuous dynamic model of the multi-electromagnet levitation system in sequence based on the fourth-order Runge-Kutta method to obtain a discrete coupled time-delay dynamic model of the multi-electromagnet levitation system; designing an optimization problem according to the inherent constraints and coupled disturbances of the multi-electromagnet levitation system; combining the discrete coupled time-delay dynamic model of the multi-electromagnet levitation system and the optimization problem to establish a model predictive controller for the multi-electromagnet levitation system; updating the control signal obtained by the model predictive controller according to a preset composite event triggering mechanism to obtain an initial control quantity; designing a time-delay compensation strategy to compensate the input time delay of the initial control quantity according to the predicted state in the iterative optimization process of the model predictive controller to obtain a standard control quantity; and using the standard control quantity to control the multi-levitation system of the maglev train.

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

[0008]

[0009] where g represents the acceleration due to gravity, and the unit is N / kg ; f d1 (t), f d2 (t) are the disturbing forces received by the left and right electromagnets respectively, and the unit is N ; , are the masses of the left and right electromagnets respectively, and the unit is kg ; , are the equivalent spring coefficients of the left and right electromagnets respectively, and the unit is N / m ; , are the displacements of the left and right electromagnets in the vertical direction respectively, and the unit is m ; M 1 is the mass of the suspension frame, and the unit is kg ; M 2 is the total mass of the air spring and the car body, and the unit is kg ; μ 0 is the air permeability, and the unit is H / m ; N is the effective number of turns of the electromagnet coil; A 0is the effective cross-sectional area of the electromagnet coil, with the unit of m 2 ; i 1 、i 2 are the currents of the left and right electromagnets respectively, with the unit of A .

[0010] In another implementation of the present invention, the discrete coupling time-delay dynamic model of the multi-electromagnet suspension system is expressed as:

[0011]

[0012] where is the system state of the left electromagnet module at time; ; is the system state of the right electromagnet module at time; ; represents the current time step; and are the tracking errors of the suspension gaps of the left and right electromagnet modules respectively, with the unit of m; is the target value of the suspension gap, with the unit of m; is the first derivative with respect to time; is the 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, ; is the left electromagnet module at the input time delay The predicted control input sequence at the moment; For the right electromagnet module under input time delay at The predicted control input sequence at the moment; Is the system random input time delay; For the left electromagnet module at The external disturbance received at the moment, ; For the right electromagnet module at The external disturbance received at the moment, ; And Are the external disturbance fluctuations of the left and right electromagnet modules compared with the equilibrium point, with the unit of N.

[0013] For the convenience of controller design, the above formula is abbreviated as:

[0014]

[0015] Among them, Is The system state at the moment, ; Is The actual system state at the moment, ; For The actual control input of the system at the moment under input time delay, ; Is The external disturbance received by the system at the moment, ; Is the coupling system state parameter, ; Is the optimal control quantity set, .

[0016] In another implementation manner of the present invention, the optimization problem is expressed as:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] Among them, Is The predicted system state at the moment; For The optimal control quantity at a moment; is the prediction time domain; is the control time domain; is the event trigger moment; is the predicted system state at the step at the predicted state at the step at the moment with input time delay; the optimal control quantity at the is the external disturbance suffered by the system at the is the estimated system state at the step at the predicted system state at the step at the optimal control quantity at the is a positive integer to be designed; is the system state set; is the preset system state contraction set; is the system predicted terminal state set.

[0023] In another implementation manner of the present invention, the preset system state contraction set is expressed as:

[0024]

[0025] where is the feedback control gain that can ensure the closed-loop stability of the system; is the transpose of the system state at the Q is a positive definite matrix to be selected; is a positive definite matrix to be selected; γ is a positive constant to be designed.

[0026] In another implementation of the present invention, the preset composite event triggering mechanism includes an optimized feasibility event triggering mechanism, a system closed-loop stability event triggering mechanism, and an energy consumption minimization event triggering mechanism; obtaining an initial control quantity according to the control signal obtained by updating the model predictive controller according to the preset composite event triggering mechanism includes: when the multi-electromagnet suspension system is in the floating stage and both the optimized feasibility event triggering mechanism and the system closed-loop stability event triggering mechanism are satisfied, the model predictive controller receives the system state output by the sensor and performs optimization to obtain the initial control quantity; when the multi-electromagnet suspension system enters the stable suspension stage and any one of the optimized feasibility event triggering mechanism, the system closed-loop stability event triggering mechanism, and the energy consumption minimization event triggering mechanism is satisfied, the model predictive controller receives the system state output by the sensor and performs optimization to obtain the initial control quantity.

[0027] In another implementation of the present invention, the optimized feasibility event triggering mechanism is expressed as:

[0028]

[0029] Wherein, is the system state at time is the system predicted state at the -th step at time is the system parameter Lipschitz constant; is the maximum value of the difference between the optimal control input at the -th step at time and the optimal control input at time 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; is the system parameter Lipschitz constant.

[0030] In another implementation of the present invention, the system closed-loop stability event triggering mechanism is expressed as:

[0031]

[0032] Wherein, is is the system state error at time is the system state contraction set to be designed; is at the Predict the system state at the step; is the system parameter Lipschitz constant; is the system parameter at Lipschitz constant at the moment; is a positive constant to be designed and satisfies ; is system state at the step at the moment; m is the control time domain; p is the prediction time domain.

[0033] In another implementation of the present invention, the auxiliary condition of the system closed-loop stability event-triggering mechanism is expressed as:

[0034]

[0035] where is the system state error parameter; is the initial value of the system state error; is a positive constant to be designed.

[0036] In another implementation of the present invention, the energy consumption minimization event-triggering mechanism is expressed as:

[0037]

[0038] where is the next event-triggering moment; is the event-triggering moment; is the event-triggering period.

[0039] The event-triggered predictive control method for the maglev train multi-suspension system of the present invention comprehensively considers the mechanical coupling relationship between the electromagnets on the same side and the input-output double dynamic constraints of the multi-electromagnet suspension system during the controller design process; adopts the maximum time-delay compensation method to compensate for the influence of the system input time delay on the stable suspension performance; designs a composite event-triggering mechanism to ensure that the transient / steady-state performance of the suspension system remains basically unchanged while reducing the system calculation / communication times; can also ensure the system state constraint satisfaction under random external disturbances and system coupling disturbances, greatly reducing the system conservatism; and significantly reduces the system energy consumption while ensuring the good operation performance of the suspension system in a complex environment. Description of the Drawings

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. By reading the detailed description of the following embodiments, the advantages and benefits in the solutions become clear to those skilled in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention.

[0041] Figure 1 Schematic diagram of the predictive control method for the multi-levitation system of a maglev train based on event triggering, which is an embodiment of the present invention.

[0042] Figure 2 Schematic diagram of the forces on the multi-electromagnet levitation system of the high-speed maglev train levitation system, which is an embodiment of the present invention.

[0043] Figure 3 Variation diagram of the levitation gap of the left and right electromagnet levitation systems under input time delay, which is an embodiment of the present invention.

[0044] Figure 4 Variation diagram of the control current input of the left and right electromagnet levitation systems under input time delay, which is an embodiment of the present invention.

[0045] Figure 5 Calculation / communication trigger time diagram of the multi-electromagnet levitation system under the composite event trigger mechanism of the method of the present invention, which is an embodiment of the present invention.

[0046] Figure 6 Calculation / communication trigger time diagram of the multi-electromagnet levitation system under the event trigger mechanism proposed in the literature, which is an embodiment of the present invention.

[0047] Figure 7 Block diagram of the model predictive control of the multi-levitation system of a high-speed maglev train based on event triggering, which is an embodiment of the present invention. Detailed implementation manners

[0048] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the following will clearly and detailedly describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art shall fall within the scope of protection of the embodiments of the present invention.

[0049] Figure 1 Schematic diagram of the predictive control method for the multi-levitation system of a maglev train based on event triggering provided by the embodiment of the present invention. As Figure 1 shown, this embodiment mainly includes:

[0050] S101. Establish a continuous dynamic model of the multi-electromagnet suspension system based on the electromagnet parameters of the maglev train.

[0051] S102. Combine the input time delay of the multi-electromagnet suspension system, and based on the fourth-order Runge-Kutta method, linearly and discretely process the continuous dynamic model of the multi-electromagnet suspension system in sequence to obtain a discrete coupled time-delay dynamic model of the multi-electromagnet suspension system.

[0052] S103. Design an optimization problem according to the inherent constraints and coupled disturbances of the multi-electromagnet suspension system.

[0053] S104. Combine the discrete coupled time-delay dynamic model of the multi-electromagnet suspension system and the optimization problem to establish a model predictive controller for the multi-electromagnet suspension system.

[0054] S105. Update the control signal obtained by the model predictive controller according to a preset composite event trigger mechanism to obtain an initial control quantity.

[0055] S106. Design a time-delay compensation strategy according to the predicted state in the iterative optimization process of the model predictive controller to perform input time-delay compensation on the initial control quantity to obtain a standard control quantity.

[0056] S107. Use the standard control quantity to control the multi-suspension system of the maglev train.

[0057] The predictive control method for the multi-suspension system of the maglev train based on event triggering according to the present invention comprehensively considers the mechanical coupling relationship between the electromagnets on the same side and the input-output dual dynamic constraints of the multi-electromagnet suspension system during the controller design process; adopts the maximum time-delay compensation method to compensate for the influence of the system input time delay on the stable suspension performance; designs a composite event trigger mechanism to reduce the system calculation / communication times while ensuring that the transient / transient performance of the suspension system remains basically unchanged; can also ensure the system state constraint satisfaction degree under random external disturbances and system coupling disturbances, greatly reducing the system conservativeness; and significantly reduces the system energy consumption while ensuring the good operation performance of the suspension system in a complex environment.

[0058] In another implementation manner of the present invention, the continuous dynamic model of the multi-electromagnet suspension system is expressed as:

[0059]

[0060] where g represents the acceleration due to gravity, and the unit is N / kg ; f d1 (t), f d2 (t) are the disturbing forces received by the electromagnets on the left and right sides respectively, and the unit is N; and are the masses of the left and right electromagnets respectively, with the unit of kg ; and are the equivalent spring constants of the left and right electromagnets respectively, with the unit of N / m ; and are the displacements of the left and right electromagnets in the vertical direction respectively, with the unit of m ; M 1 is the mass of the suspension frame, with the unit of kg ; M 2 is the total mass of the air spring and the car body, with the unit of kg ; μ 0 is the air permeability, with the unit of 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, with the unit of m 2 ; i 1 、i 2 are the currents of the left and right electromagnets respectively, with the unit of A .

[0061] Exemplarily, in the lap joint structure of the high-speed maglev train suspension system, the two electromagnet modules are connected by a rigid plate and can be simplified to spring damping forces. The force diagram of the simplified structure is as shown in Figure 2 . According to Newton's second law, the dynamic equation of the electromagnet module in the vertical direction can be obtained as follows:

[0062]

[0063] where and are the masses of the left and right electromagnets respectively; and are the accelerations of the left and right electromagnets in the vertical direction respectively; and are the disturbing forces acting on the left and right electromagnets respectively; g is the acceleration due to gravity; and are the electromagnetic attractions acting on the left and right electromagnets respectively; and are the equivalent spring damping forces of the left and right electromagnets respectively, which are usually obtained by the following formula:

[0064]

[0065] Among them, is the displacement of the floating frame in the vertical direction; , are the displacements of the left and right electromagnets in the vertical direction respectively; , are the equivalent spring coefficients of the left and right electromagnets respectively; , are the equivalent damping coefficients of the left and right electromagnets respectively; is the velocity of the floating frame in the vertical direction; , are the velocities of the left and right electromagnets in the vertical direction respectively.

[0066] Since the electrode plate is a rigid structure and the damping coefficient is very small and can be ignored, and the two electromagnet modules are evenly distributed on both sides of the electrode plate, the displacement of the floating frame in the vertical direction can be approximately simplified as the average value of the displacements of the two electromagnet modules on both sides, that is:

[0067]

[0068] Among them, M 1 is the mass of the floating frame, with the unit of kg; M 2 is the total mass of the air spring and the car body, with the unit of kg; is the equivalent stiffness coefficient of the disc spring.

[0069] For the maglev train suspension system, the number of turns of the coils of the left and right electromagnets is equal, and the effective pole areas are equal, obtaining a multi-electromagnet coupled continuous dynamics model:

[0070]

[0071] 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 electrode plates and have a strong mechanical coupling relationship. When the dynamic state of one electromagnet changes, the adjacent electromagnets will be affected by the coupling disturbance and their dynamic states will also change. The coupling disturbance between multiple electromagnet modules reduces the dynamic control performance of the suspension system.

[0072] In another implementation manner of the present invention, the discrete coupling time-delay dynamics model of the multi-electromagnet suspension system is expressed as:

[0073]

[0074] Among them, is the system state of the left electromagnet module at time; ; is the system state of the right electromagnet module at moment; ; represents the current time step; and are the tracking errors of the suspension gaps of the left and right electromagnet modules respectively, with the unit of m; is the target value of the suspension gap, with the unit of m; is the first derivative with respect to time; is the 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, ; is the predicted control input sequence of the left electromagnet module at moment under input time delay; is the predicted control input sequence of the right electromagnet module at moment under input time delay; is the system random input time delay; is the external disturbance received by the left electromagnet module at moment, ; is the external disturbance received by the right electromagnet module at moment, ; and are the external disturbance fluctuations of the left and right electromagnet modules compared with the equilibrium point respectively, with the unit of N.

[0075] For the convenience of controller design, the above formula is abbreviated as:

[0076]

[0077] wherein, is the system state at time ; is the actual system state at time ; is the actual control input of the system at time under the input time delay; is the external disturbance on the system at time ; is the coupling system state parameter ; is the optimal control quantity set .

[0078] Exemplarily, linearize the obtained multi-electromagnet coupling continuous dynamics model near the equilibrium point to obtain the linearized model of the multi-electromagnet module:

[0079]

[0080] wherein, and are respectively the tracking errors of the suspension gaps of the left and right electromagnet modules, and are respectively the first derivative and the second derivative with respect to time, and are respectively the first derivative and the second derivative with respect to time; and are respectively the differences in the control currents of the left and right electromagnet modules, and are respectively the external disturbance fluctuations of the left and right electromagnet modules relative to the equilibrium point, is the target value of the suspension gap, 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 respectively the displacement coefficients of the left and right electromagnet modules; , are respectively the current coefficients of the left and right electromagnet modules.

[0081] ; ; ; ;

[0082] Among them, and are the current values of the left and right electromagnet modules at the equilibrium point, respectively; and are the suspension gaps of the left and right electromagnet modules at the equilibrium point, respectively.

[0083] The linearized model of the multi-electromagnet suspension module is discretized using the fourth-order Runge-Kutta method to obtain a discrete dynamic model:

[0084]

[0085] Among them, , , , , , , , , and are the differences in the control currents of the left and right electromagnet modules, respectively, , .

[0086] Considering the system input delay caused by the inductance lag of the electromagnetic coil, a discrete coupled time-delay dynamic model of the multi-electromagnet is obtained:

[0087]

[0088] For the convenience of controller design, the discrete coupled time-delay dynamic model of the multi-electromagnet is abbreviated as:

[0089]

[0090] In another implementation manner of the present invention, the optimization problem is expressed as:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] Among them, is the predicted system state at time is the optimal control quantity at time with input time delay; is the prediction horizon; is the control horizon; is the event trigger time; is the step prediction system state at time is the step prediction state at time is the optimal control quantity at time with input time delay and at the step; is the external disturbance on the system at time is the step system estimated state at time is the step prediction system state at time is the step optimal control quantity at time is a positive integer to be designed; is the system state set; is the preset system state contraction set; is the system prediction terminal state set.

[0097] Exemplarily, the multi - electromagnet suspension system has output constraints caused by a very small working range and input constraints caused by the output power limitation of the power supply device. Therefore, a model predictive controller is used to handle the input - output dual - dynamic constraint problem of the multi - electromagnet suspension system.

[0098] Considering the input - output constraints of the multi - electromagnet suspension system, a multi - constraint optimization problem is designed. A new method for tightening the state constraint set is proposed for the dynamic coupling disturbance and random external disturbance in the high - speed maglev multi - electromagnet suspension system. The system state contraction set is introduced to ensure the satisfaction of the system state constraints under time - varying external disturbances and system coupling disturbances.

[0099] In another implementation manner of the present invention, the preset system state contraction set is expressed as:

[0100]

[0101] where, is the feedback control gain that can ensure the closed - loop stability of the system; is the transpose of the system state at time Qis a positive definite matrix to be selected; is a positive definite matrix to be selected; γ is a positive constant to be designed.

[0102] Exemplarily, the system state contraction set plays an important role in optimization solving and system closed-loop stability, and can reduce the conservatism of system design.

[0103] In another implementation manner of the present invention, due to the existence of input time delay, the optimization problem The optimal control quantity obtained at time acts on the system at time, resulting in a decline in system performance and instability. In order to compensate for the influence of input time delay on system performance, it is set that The control quantity actually acting on the system at time is , where is the maximum value of the input time delay, .

[0104] The present invention fully considers the random input delay of the subsystems in the coupled system, and adopts the maximum time delay compensation strategy based on the predicted state to reduce the influence of input time delay on the stable suspension performance. The proposed delay compensation algorithm has good robust compensation performance even under coupled disturbances, which is a control algorithm for a multi-electromagnet coupled suspension system considering both input delay and inherent constraints.

[0105] In another implementation manner of the present invention, the preset composite event triggering mechanism includes an optimization feasibility event triggering mechanism, a system closed-loop stability event triggering mechanism, and an energy consumption minimization event triggering mechanism; the control signal obtained by updating the model predictive controller according to the preset composite event triggering mechanism to obtain an initial control quantity includes: As Figure 7 shown, the system state is monitored in real time through a sensor. When the multi-electromagnet suspension system is in the floating stage and both the optimization feasibility event triggering mechanism and the system closed-loop stability event triggering mechanism are satisfied, the model predictive controller receives the system state output by the sensor and performs optimization solving to obtain an initial control quantity; when the multi-electromagnet suspension system enters the stable suspension stage and 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 is satisfied, the model predictive controller receives the system state output by the sensor and performs optimization solving to obtain an initial control quantity.

[0106] Exemplarily, the model predictive controller calculates the feasible solution of the optimization problem in real time at each sampling point, which occupies a large amount of computing and communication resources and is difficult to implement in large-scale systems. The event-triggered control updates the control signal only when the pre-designed triggering mechanism is satisfied, greatly reducing unnecessary signal transmission, saving communication resources and computing resources, and reducing energy consumption.

[0107] Based on this, a composite event-triggering mechanism is designed to save the system communication resources. The composite event-triggering mechanism considering iterative optimization feasibility, system closed-loop stability, and energy consumption minimization ensures that the transient / steady-state performance of the suspension system remains basically unchanged while significantly reducing the computing / communication resources.

[0108] In another implementation manner of the present invention, in order to ensure the existence of 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:

[0109]

[0110] where is the system state at time is the predicted system state at the -th step at time is the system parameter Lipschitz constant; is the maximum value of the difference between the optimal control input at the -th step at time and the optimal control input at time is the upper bound of the error norm of the actual system state and the predicted system state; is the Lipschitz constant of the system disturbance; is the system parameter Lipschitz constant.

[0111] In another implementation manner of the present invention, the system closed-loop stability event-triggering mechanism is expressed as:

[0112]

[0113] where is is the system state error at time is the system state contraction set to be designed; is the predicted system state at the -th step at time is the system parameter The Lipschitz constant; is the system parameter At the Lipschitz constant at time; is a positive constant to be designed and satisfies ; is the system state at the step at time; m is the control time domain; p is the prediction time domain.

[0114] In another implementation of the present invention, in the presence of random external disturbances and system mechanical coupling disturbances, the above event-triggering mechanism is easily satisfied, resulting in frequent triggering of the system and wasting a large amount of resources. To reduce the event-triggering frequency, the following auxiliary conditions are adopted. The auxiliary conditions for the system closed-loop stability event-triggering mechanism are expressed as:

[0115]

[0116] where is the system state error parameter; is the initial value of the system state error; is a positive constant to be designed.

[0117] In another implementation of the present invention, after the system reaches the stable suspension state, the requirement for its event-triggering frequency is significantly reduced. To further optimize the computing resources, the following event-triggering mechanism is designed to monitor the state fluctuations of the system during the stable suspension stage. The energy consumption minimization event-triggering mechanism is expressed as:

[0118]

[0119] where is the next event-triggering time; is the event-triggering time; is the event-triggering period.

[0120] It should be understood that the composite event-triggering mechanism proposed by the present invention parallelly detects the event-triggering mechanisms that ensure closed-loop stability, recursive feasibility, and energy consumption minimization, thereby improving the system computing / communication efficiency and significantly reducing the system energy consumption.

[0121] In another implementation of the present invention, the above control method is applied to the multi-electromagnet suspension module of a high-speed maglev train, and the system parameters and simulation initial values are configured, and the following two groups of simulations are carried out in MATLAB.

[0122] 1) System time delay compensation.

[0123] 2) Composite event-triggering mechanism.

[0124] Figure 3 and Figure 4 are respectively the variation diagrams of the suspension gap and the control quantity under the system input time delay. In the simulation, the model predictive control method without time-delay compensation is selected for comparison. It can be seen from the results that under the influence of input delay, there are large fluctuations in the suspension gap of the system without the delay compensation method. By adopting the proposed time-delay compensation strategy, the multi-electromagnet suspension system can converge to the target air gap better 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 range, thus ensuring the stable operation of the multi-electromagnet coupled suspension system.

[0125] Figure 5 and Figure 6 are respectively the calculation / communication frequencies of the multi-suspension system under the action of the composite event-triggered mechanism proposed in the present invention and the event-triggered mechanism proposed in the literature [Y. Yan, R. Wang, S.H. Yu, C. L. Wang, T. S. 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-triggered mechanism proposed in the present invention is only triggered 22 times, with lower calculation and communication loads.

[0126] The predictive control method for the multi-suspension system of maglev trains based on event triggering proposed in the present invention is applied to the model of the multi-electromagnet suspension module of high-speed maglev trains for simulation under different conditions. The simulation results show that: the control method proposed in the present invention has better dynamic performance under system input time delay and inherent constraints, and can ensure that the transient / steady-state performance of the suspension system remains basically unchanged while significantly reducing the calculation / communication resources and system energy consumption.

[0127] On the other hand, the electronic device includes: a processor, a memory, and a communication bus and a communication interface.

[0128] Wherein:

[0129] A processor, a memory, and a communication interface communicate with each other via a communication bus.

[0130] The communication interface is used to communicate with other electronic devices or servers.

[0131] The processor is used to execute a program, specifically, it can execute the steps of any one of the above-mentioned predictive control methods for the multi-levitation system of maglev trains triggered by events in the embodiments.

[0132] Specifically, the program may include program code, and the program code includes computer operation instructions.

[0133] The processor may be a central processing unit (CPU), or a specific integrated circuit (ASIC) (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of the present application. One or more processors included in the intelligent device may be of the same type of processor, such as one or more CPUs; or they may be of different types of processors, such as one or more CPUs and one or more ASICs.

[0134] The memory is used to store the program. The memory may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk memory.

[0135] Specifically, the program can be used to cause the processor to execute to implement the steps of any one of the predictive control methods for the multi-levitation system of maglev trains triggered by events described in the embodiments. For the specific implementation of each step in the program, reference can be made to the corresponding descriptions in the steps and units of any one of the above-mentioned predictive control methods for the multi-levitation system of maglev trains triggered by events, which will not be elaborated here. Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes of the above-described devices and modules can refer to the corresponding process descriptions in the foregoing method embodiments.

[0136] An exemplary embodiment of the present application further provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause a computer to execute the methods of the embodiments of the present application.

[0137] The method according to an embodiment of the present invention can be implemented in hardware, firmware, or be implemented 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 be implemented as computer code that is originally stored in a remote recording medium or a non-transitory machine-readable medium and downloaded through a network and will be stored in a local recording medium, so that the method described herein can be stored on such a software process on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It can be understood that a computer, a processor, a microprocessor controller, or programmable hardware includes a storage component (such as a RAM, a ROM, a flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by the computer, the processor, or the 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.

[0138] So 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 can be performed in a different order and still achieve the desired result. Additionally, the processes depicted in the figures do not necessarily require the particular order or sequential order shown to achieve the desired result. In certain embodiments, multitasking and parallel processing may be advantageous.

[0139] It should be noted that all directional indications (such as up, down, left, right, back...) in the embodiments of the present invention are only used to explain the relative positional relationship and movement conditions between components in a specific posture (as shown in the drawings). If the specific posture changes, the directional indications will change accordingly.

[0140] In the description of the present invention, the terms "first" and "second" are only used for convenience in describing different components or names, and cannot be understood as indicating or implying an order relationship, relative importance, or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features.

[0141] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. The terms used in the description of the present invention herein are only for the purpose of describing specific embodiments, and are not intended to limit the present invention.

[0142] It should be noted that although the specific embodiments of the present invention have been described in detail with reference to the accompanying drawings, it should not be construed as a limitation on the protection scope of the present invention. Within the scope described in the claims, various modifications and deformations that can be made by those skilled in the art without creative efforts still fall within the protection scope of the present invention.

[0143] The examples of the embodiments of the present invention are intended to briefly 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 do not serve as an improper limitation on the embodiments of the present invention.

[0144] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate 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; The control signal obtained by the model predictive controller is updated according to a preset composite event trigger mechanism to obtain an initial control amount, including: 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; 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 a 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 and solution 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 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, 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; For 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 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.

7. The method according to claim 1, 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.

8. The method according to claim 7, 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.

9. The method according to claim 1, 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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