A magnetic suspension control method based on a regularized data-driven strategy optimization

Abstract

The application discloses a magnetic suspension control method based on a regularized data-driven strategy optimization, force analysis is performed on a minimum suspension unit of a maglev train, nonlinear dynamic equations are established, input and output data of the unit in a time interval of {0, 1,..., k} are collected, a sample covariance matrix is constructed based on the data, and the suspension system dynamic equations are rewritten through covariance parameterization; subsequently, a regularization term is introduced into an LQR cost function, and a direct data-driven LQR optimization problem with a regularization constraint is constructed; finally, a strategy parameter matrix is updated through a projection gradient descent algorithm, a covariance matrix and its inverse matrix are recursively updated in combination with a rank-one update rule, online control gain updating is realized, and suspension control of the maglev train is completed. The application does not require accurate dynamic modeling, solves the problems of complicated modeling and inaccurate parameters in traditional model-based control, the regularization term greatly improves the robustness of the system to complex disturbances and noises, and system instability in the minimum working condition of the air gap constraint is effectively avoided.

Description

Technical Field

[0001] This invention relates to the field of maglev train suspension control technology, and in particular to a maglev control method based on regularized data-driven strategy optimization. Background Technology

[0002] Maglev trains, as a new generation of high-speed rail transit, have become one of the important directions for future rail transit development due to their outstanding advantages such as low noise, frictionless operation, and strong climbing ability. Currently, commercial maglev trains can reach speeds of up to 430 km / h, and experimental prototypes have exceeded 600 km / h. The levitation control system is one of the core technologies of maglev trains. Its principle is to adjust the excitation current of the levitation electromagnets to control the balance between electromagnetic force and vehicle gravity, thereby achieving non-contact levitation.

[0003] In terms of suspension control, existing research has proposed various solutions, including model-based control methods, traditional PID controllers, and data-driven control methods. However, the maglev train suspension system is exposed to complex operating conditions for a long time, resulting in dynamic and time-varying system characteristics. Model parameters are difficult to obtain accurately, leading to significant model inaccuracies. Model-based control schemes are cumbersome to design and difficult to implement in practice. While traditional PID controllers are simple in structure and easy to implement in engineering, their control gain is a fixed value, which cannot adapt to the aforementioned dynamic changes. This can easily lead to excessive air gap, system instability, or even derailment or rail contact, seriously threatening the safety and efficiency of train operation.

[0004] Data-driven control methods, based on Willems' fundamental lemma, can bypass precise modeling and have led to the development of schemes such as data-enabled predictive control and data-driven level-quantum control (LQR). However, their computational complexity increases linearly with data length, making it difficult to meet the real-time online requirements of maglev trains. While covariance parameterization methods have shown potential in systems such as bicycles, their application to noise-sensitive, narrow-air-gap maglev suspension modules still faces challenges due to insufficient robustness caused by environmental noise, parasitic dynamics, and time-varying parameters. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art or related art.

[0006] Therefore, the purpose of this invention is to provide a magnetic levitation control method based on regularized data-driven strategy optimization, which can bypass precise modeling and directly optimize the control strategy of the magnetic levitation module online using real-time operating data.

[0007] To achieve the above objectives, the present invention provides a magnetic levitation control method based on regularized data-driven strategy optimization, comprising the following steps:

[0008] S1, perform force analysis on the minimum suspension unit system of the maglev train and establish the nonlinear dynamic equation of the minimum suspension unit;

[0009] S2, collect the input and output data of the smallest suspension unit of the maglev train within the time interval {0,1,…,k}, the input and output data including the control input corresponding to the historical control current, the suspension air gap, and the acceleration integral;

[0010] S3. Based on the collected input and output data, construct the sample covariance matrix and rewrite the dynamic equation of the suspension system using the covariance parameterization method.

[0011] S4. Introduce a regularization term into the cost function of the linear quadratic regulator LQR to construct a direct data-driven LQR optimization problem with regularization constraints.

[0012] S5 employs a data-driven strategy optimization method, updating the strategy parameter matrix through the projection gradient descent algorithm, and recursively updating the covariance matrix and its inverse matrix based on the rank-one update rule, thereby achieving online updating of the control gain and completing the levitation control of the maglev train.

[0013] In the above technical solution, preferably, the nonlinear dynamic equation of the minimum suspension unit established in S1 is:

[0014] ;

[0015] in, The load capacity of the smallest suspension unit, It is the acceleration due to gravity; and These are the air gaps between the two suspension points before and after the smallest suspension unit. and These represent the rate of change of the air gap between the two suspension points, one before and one after. is the electromagnetic force coefficient, where air permeability, The effective magnetic pole area of ​​the electromagnet. This represents the number of turns in the electromagnet coil. and For system control input, where and These are the control currents for the electromagnets at the front and rear suspension points, respectively.

[0016] In any of the above technical solutions, preferably, the input and output data collected in S2 are used to construct a data matrix in the following form:

[0017] ;

[0018] In the formula, This is the historical accumulation matrix of suspended air gap states. The historical control input is a stacked matrix. The historical acceleration integral stacked matrix, This is the current state stacking matrix of the suspended air gap; the above data matrix satisfies the dynamic relationship of the discrete system:

[0019] ;

[0020] in, For the state matrix of a discrete system, Input matrix for discrete system; simultaneously construct data block matrix The data block matrix The conditions for sustained incentives must be met, namely It has full row order.

[0021] In any of the above technical solutions, preferably, the sample covariance matrix constructed in S3 is:

[0022] ;

[0023] In the formula, The duration of data collection; simultaneously based on the input / output data matrix and the data block matrix. The covariance term is defined as follows:

[0024] ;

[0025] In the formula, For historical air gap state covariance term, For historical control input covariance terms, For the acceleration integral covariance term, This is the covariance term for the current air gap state.

[0026] In any of the above technical solutions, preferably, the step of rewriting the dynamics of the suspension system by covariance parameterization in S3 is as follows: based on the data block matrix Given the full row rank characteristic, the sample covariance matrix Ψ is a positive definite matrix. The closed-loop control gain is correlated with the policy parameter matrix through covariance parameterization.

[0027] ;

[0028] In the formula, This is the closed-loop control gain matrix. for An identity matrix of order 1. Let be the strategy parameter matrix to be optimized; based on the covariance parameterization relationship, the discrete system dynamics of the maglev train are rewritten as:

[0029] .

[0030] In any of the above technical solutions, preferably, in step S4, based on the principle of deterministic equivalence, the unmeasurable noise term is ignored. At that time, the basic direct data-driven LQR optimization problem is: ;

[0031] ;

[0032] In the formula, Let cost function be This is the trace operation of a matrix; The state weight matrix is... To control the input weight matrix; The solution to the Lyapunov equation satisfies

[0033] ;

[0034] Closed-loop control gain satisfies

[0035] .

[0036] In any of the above technical solutions, preferably, in step S4, after introducing a regularization term into the cost function, the constructed regularized direct data-driven LQR optimization problem is:

[0037] ;

[0038] ;

[0039] ;

[0040] In the formula, This is a regularization parameter used to enhance the robust stability of the system against noise and disturbances.

[0041] In any of the above technical solutions, preferably, in step S5, the formula for updating the policy parameter matrix using the projection gradient descent algorithm is:

[0042] ;

[0043] In the formula, For iterative index, The cost function is regularized. For the cost function at the th The gradient at the nth iteration, where η>0 is the constant step size of gradient descent. For projection operators, for The Moore-Penrose pseudoinverse and projection operator are used to ensure that the updated policy parameters satisfy the constraints. .

[0044] In the above technical solution, preferably, in step S5, the formula for recursively updating the covariance matrix and its inverse matrix, and the optimization strategy parameter matrix based on the rank-one update rule is as follows:

[0045] ;

[0046] In the formula, Let be the input state vector at the current time, given by the th... Time control input and suspended air gap state composition; For the first The inverse of the covariance matrix of the next iteration. For the first The policy parameter matrix updated by projective gradient descent in the next iteration.

[0047] In the above technical solution, preferably, in step S5, the formula for the online updated closed-loop control gain is:

[0048] ;

[0049] In the formula, For the first The control input covariance term updated in the next iteration For the first The policy parameter matrix updated by projective gradient descent in the next iteration.

[0050] Compared with existing technologies, the magnetic levitation control method based on regularized data-driven strategy optimization provided by this invention has the following advantages: The data-driven strategy optimization control technology with a regularized magnetic levitation module described in this invention does not rely on precise dynamic modeling, solving the problems of cumbersome modeling and inaccurate parameters in traditional model-based control. By introducing a regularization term into the cost function, the robustness of the system to various complex disturbances and noises is significantly improved, avoiding system instability under conditions of minimal air gap constraints. The technology employs recursive data updates and projected gradient descent design, resulting in high computational efficiency. It can adaptively adjust the control strategy and gain online based on real-time data, and can quickly restore the air gap to an equilibrium state when parameters change abruptly, accurately constraining it within the engineering safety range, adapting to the actual needs of conditions such as train climbing. This technology can be integrated with traditional PID initial control schemes, exhibiting good compatibility and engineering feasibility. Compared with fixed-parameter PID control and data-driven control schemes without regularization, it significantly improves the stability, adaptability, and practicality of magnetic levitation train levitation control. Attached Figure Description

[0051] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0052] Figure 1 A flowchart of the magnetic levitation control method according to an embodiment of the present invention is shown;

[0053] Figure 2 The system parameters for implementing the minimum suspension unit in this invention are varied;

[0054] Figure 3 The suspension gap and speed of the minimum suspension unit are implemented in this invention;

[0055] Figure 4 The control current for implementing the minimum levitation unit in this invention;

[0056] Figure 5 The suspension gap and velocity of the smallest suspension unit under the control scheme proposed in this invention;

[0057] Figure 6 To compare the implementation method of this invention, the suspension gap and velocity of the smallest suspension unit under the unregularized scheme are analyzed. Detailed Implementation

[0058] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0059] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0060] like Figure 1 As shown, a magnetic levitation control method based on regularized data-driven strategy optimization according to an embodiment of the present invention includes the following steps:

[0061] S1, perform force analysis on the minimum suspension unit system of the maglev train and establish the nonlinear dynamic equation of the minimum suspension unit;

[0062] S11, Construct the nonlinear dynamic equations:

[0063] Force analysis was performed on the levitation module system of the maglev train. A nonlinear dynamic equation was established focusing on the smallest levitation unit. This equation accurately characterizes the dynamic relationship between the electromagnetic force, load, levitation air gap, and air gap velocity of the levitation unit. Specifically:

[0064] ;

[0065] in, The load capacity of the smallest suspension unit, It is the acceleration due to gravity; and These are the air gaps between the two suspension points before and after the smallest suspension unit. and These represent the rate of change of the air gap between the two suspension points, one before and one after. and These represent the first derivatives of the air gaps between the front and rear suspension points, respectively. and These represent the first derivatives of the rate of change of the air gap at the suspension point before and after; is the electromagnetic force coefficient, where air permeability, The effective magnetic pole area of ​​the electromagnet. This represents the number of turns in the electromagnet coil. and For system control input, where and These are the control currents of the electromagnets at the front and rear suspension points, respectively, and are essentially the square of the control current.

[0066] In practical engineering applications, suspended air gaps and Strictly constrained within a safe range of 0~0.02m, the midpoint of this range, 10mm, is typically chosen as the operational equilibrium point for the suspension unit. At this point, the equilibrium state of the smallest suspension unit is:

[0067] ;

[0068] The control current in the corresponding equilibrium state satisfies: and ,in, and These are the balance air gaps between the front and rear suspension points, respectively. The load capacity of the smallest suspension unit.

[0069] S12, Linearization of the dynamic equations:

[0070] To adapt to the modeling requirements of subsequent data-driven control, a linearization technique is used near the aforementioned equilibrium state to transform the nonlinear dynamic equations into a linear model, specifically in the following form:

[0071] In the formula, This refers to the unmodeled dynamics and noise generated during the linearization process of the magnetic levitation system. For the control strategy, the linear matrices A and B are respectively:

[0072] ;

[0073] in This is the electromagnetic force coefficient.

[0074] S13, Discretization of the linear model:

[0075] To facilitate its application in the digital control system of maglev trains, the continuous linear system is converted into a discrete system based on the Nyquist-Shannon sampling theorem to avoid signal aliasing. A sampling period of [missing information] is selected. Sampling rate The frequency should be no less than twice the maximum frequency component of the original signal. Using Euler's formula, the continuous linear model is discretized to obtain:

[0076] ;

[0077] In the formula, For discrete-time indexing, For the state variables of the floating module, To control the input, The noise term is the discretized value. , These are the state matrix and input matrix of the discrete system, respectively. It is an identity matrix.

[0078] In traditional feedback control, if it is possible to obtain , With precise information, control laws can be designed. To ensure the stability of the Shure system, among other things, It is feedback control gain. However, the levitation module of the maglev train is in a complex magnetic field and variable operating conditions for a long time, and the discretized model has been simplified many times, which can easily lead to... , The information is inaccurate; when system parameters change over time, the system identification process needs to be repeated, resulting in poor adaptability. This invention solves the above-mentioned technical problems by bypassing the precise system modeling process through a data-driven approach.

[0079] S2, collect the input and output data of the smallest suspension unit of the maglev train within the time interval {0,1,…,k}, the input and output data including the control input corresponding to the historical control current, the suspension air gap, and the acceleration integral;

[0080] S21, Collect and construct the input / output data matrix:

[0081] The input / output data of the minimum levitation module of the maglev train are collected within the time interval {0,1,…,k}, including historical control current, levitation air gap, and acceleration integral, and a data matrix is ​​constructed in the following form:

[0082] ;

[0083] In the formula, This is the historical accumulation matrix of suspended air gap states. The historical control input is a stacked matrix. The historical acceleration integral stacked matrix, This is the current state stacking matrix of the suspended air gap; the above data matrix satisfies the dynamic relationship of the discrete system:

[0084] ;

[0085] in, For the state matrix of a discrete system, Input matrix for discrete system;

[0086] Simultaneously construct the data block matrix And assume that the data block matrix satisfies the continuous stimulus condition, i.e. It has full rank. This assumption is engineeringly reasonable because the levitation control of a maglev train is divided into three stages: levitation start-up (static levitation), levitation maintenance during travel, and levitation stop at the station. The levitation air gap has a large overshoot during the levitation start-up stage, and the data collected during this stage naturally meets the requirements for continuous excitation.

[0087] S22, Construct the sample covariance matrix and covariance terms:

[0088] Based on the above data matrix and data block matrix, construct the sample covariance matrix of the current / air gap data:

[0089] In the formula, The duration of data collection;

[0090] Simultaneously based on the data matrix and data block matrix The product of these terms is defined as follows: The sample covariance term is used for subsequent rewriting of the system dynamics:

[0091] ;

[0092] In the formula, For historical air gap state covariance term, For historical control input covariance terms, For the acceleration integral covariance term, This is the covariance term for the current air gap state.

[0093] S23, Covariance parameterization rewriting of system dynamics:

[0094] Based on data block matrix The full row rank property allows us to derive the sample covariance matrix. Since it is a positive definite matrix, the closed-loop control gain and the policy parameter matrix are correlated through covariance parameterization, in the form of:

[0095] ;

[0096] In the formula, This is the closed-loop control gain matrix. for An identity matrix of order 1. The matrix represents the strategy parameters to be optimized.

[0097] Further combining the definition of the sample covariance term and the aforementioned covariance parameterization relationship, the discrete system dynamics of the maglev train are rewritten as a form characterized solely by the covariance term and the strategy parameter matrix, achieving consistency with the original system matrix. , The decoupling lays the foundation for direct data-driven control, and the rewritten dynamic equations are:

[0098] ;

[0099] In the formula, K represents the closed-loop control gain matrix.

[0100] S3. Based on the collected input and output data, a sample covariance matrix is ​​constructed, and the dynamic equations of the suspension system are rewritten using the covariance parameterization method:

[0101] Based on the deterministic equivalence principle, unmeasurable noise terms are ignored. The direct data-driven control problem is transformed into a linear quadratic regulator (LQR) optimization problem. Using the policy parameter matrix L as the optimization variable, the basic optimization problem is:

[0102] ;

[0103] ;

[0104] In the formula, Let cost function be This is the trace operation of a matrix; To find the minimum value with L as the optimization variable; These are constraints; The solution to the Lyapunov equation satisfies

[0105] ; The state weight matrix is... The input weight matrix is ​​used to balance the control accuracy of the levitation gap with the energy consumption of the control current; the closed-loop control gain satisfies... .

[0106] S4. Introduce a regularization term into the cost function of the linear quadratic regulator (LQR) to construct a direct data-driven LQR optimization problem with regularization constraints:

[0107] The levitation system of maglev trains inevitably suffers from noise interference, and the control range of the levitation air gap is only 0~0.02m. This limited adjustment space amplifies the impact of noise on the system, reducing the feasibility of the basic data-driven LQR problem. Therefore, a regularization term is introduced into the cost function to enhance the robustness and stability of the system, transforming the basic optimization problem into a regularized direct data-driven LQR problem, specifically in the following form:

[0108] ;

[0109] ;

[0110] ;

[0111] In the formula, This is a regularization parameter that can be adaptively adjusted according to the noise intensity and system disturbance level under actual operating conditions, thereby enhancing the robust stability of the system against noise and disturbances.

[0112] S5 employs a data-driven strategy optimization method, updating the strategy parameter matrix through the projection gradient descent algorithm, and recursively updating the covariance matrix and its inverse matrix based on the rank-one update rule, thereby realizing online updating of the control gain and completing the levitation control of the maglev train.

[0113] This step updates the policy parameter matrix using the projected gradient descent algorithm, and recursively updates the covariance matrix and its inverse matrix based on the rank-one update rule, thereby achieving online real-time updating of the control gain and ultimately completing the levitation closed-loop control of the maglev train. The specific implementation sub-steps are as follows:

[0114] S51, Construct the closed-form expression for the gradient of the cost function:

[0115] Assume a set of feasible strategies Not empty, of which Let be the spectral radius of the matrix; combining this with the series expansion of the Lyapunov equation, the regularized cost function is transformed into a solution to the new Lyapunov equation. The trace operation form:

[0116] ;in The unique positive definite solution to the new Lyapunov equation satisfies:

[0117] ;

[0118] For the new Lyapunov equation Taking the derivative, we get:

[0119] ;

[0120] ;

[0121] because ρ(⋅) is the spectral radius of the matrix, from which we can obtain:

[0122] ;

[0123] Furthermore, we can obtain:

[0124] ;

[0125] ;

[0126] Derive the cost function The closed-form expression for the gradient provides a theoretical basis for subsequent projective gradient descent updates. The gradient expression is:

[0127] ;

[0128] In the formula, and They are respectively And the solutions to the new Lyapunov equation; Cost function The gradient with respect to the policy parameter L.

[0129] S42, Update the policy parameter matrix based on projective gradient descent:

[0130] Since a feasible strategy set S exists Due to the constraints, direct gradient descent can easily lead to the updated parameters violating the constraints. Therefore, the gradient of the cost function is projected onto... The null space is used to update the policy parameter matrix using the projective gradient descent algorithm, ensuring parameter feasibility. The update formula is:

[0131] ;

[0132] in, It is an iterative index. For the cost function at the th The gradient at the next iteration; This is a constant step size for gradient descent, which can be adjusted according to the convergence speed requirements of the system. For projection operators, Covariance term Moore-Penrose pseudo-reverse.

[0133] S43, Recursively update the covariance matrix and strategy parameters based on the rank-one update rule:

[0134] The control scheme of this invention possesses recursive characteristics, enabling rapid updates of the covariance matrix and its inverse matrix based on real-time acquired data, without requiring a full recalculation, thus significantly improving computational efficiency. (Covariance matrix and its inverse matrix) All updates use the rank-one update rule, and further optimize the policy parameter matrix by combining it with the current input state vector. The update formula is as follows:

[0135] ;

[0136] In the formula, Let be the input state vector at the current time, given by the th... Time control input and suspension gap state composition; and These are the inverse of the covariance matrix obtained from the previous iteration and the policy parameter matrix updated by projective gradient descent, respectively.

[0137] S44, online update of control gain and implementation of floating closed-loop control:

[0138] Based on the updated strategy parameter matrix obtained from the above steps, the closed-loop control gain is updated online in real time. The update method is as follows:

[0139] ;

[0140] In the formula, For the first The control input covariance term updated in the next iteration For the first The policy parameter matrix updated by projective gradient descent in the next iteration.

[0141] Updated control gain Substitute into the closed-loop control law , The control gain matrix at time k. The state vector of the suspension unit at time k is used to realize the online adaptive suspension control of the smallest suspension unit of the maglev train, so that the suspension air gap is always constrained within the safe operating range. Specific Implementation

[0142] To verify the effectiveness of the maglev train control method based on regularization and direct data-driven strategy optimization proposed in this invention, MATLAB was used for simulation experiments. The smallest levitation unit of the maglev train was taken as the control object, and two operating scenarios, nominal and actual, were simulated to compare the control effects of the schemes with and without regularization.

[0143] Experimental parameter settings

[0144] Minimum levitation unit basic parameters: gravitational acceleration =9.8m / s 2 The levitation unit has a load capacity of M = 500 kg, and the initial value of the electromagnetic force coefficient is... =1000N⋅m 2 / A 2 air permeability =4π×10 −7 H / m, effective magnetic pole area A=0.01m 2 The number of coil turns N = 1000;

[0145] Suspension air gap parameters: The desired nominal suspension air gap value is 10mm, and the suspension air gap constraint range is 0-20mm; under actual working conditions, the desired air gap at the front suspension point is 10.3mm, and the desired air gap at the rear suspension point is 9.8mm; initial air gap. =14mm, =13mm, initial air gap velocity = =0;

[0146] Control parameters: State weight matrix Q = diag[20, 0.005, 20, 0.005], where diag[⋅] is a diagonal matrix, and input weight matrix R = 0.01I. 2 Regularization parameter λ=10, projected gradient descent step size η=2×10 −5 Sampling period Δ=1×10 −4 s;

[0147] Interference settings: Inject a composite signal consisting of a sine wave of 500sin(10πt) and white noise into the system to simulate electromagnetic parameters. The time-varying characteristics, such as Figure 2 As shown; at the same time, strong white noise is injected into the actual working conditions to simulate complex environmental interference;

[0148] Data acquisition: The smallest suspension unit is stabilized near the equilibrium point using a PID controller, and suspension data of 0.1s is collected as initial training data to meet the continuous excitation condition.

[0149] Simulation conditions and results analysis

[0150] Operating Condition 1: Nominal Operating Condition

[0151] Under nominal operating conditions, the desired air gap between the front and rear suspension points is 10mm, with no additional strong noise interference. The only issue is the time-varying characteristics of the electromagnetic parameter ke. The simulation results are as follows: Figure 3 , Figure 4 As shown:

[0152] Figure 3 The display shows that the suspended air gap oscillates violently near the equilibrium point 0.1s before the controller of this invention is started 0.1s, and the air gap quickly converges to the expected reference value of 10mm; after the electromagnetic parameters change abruptly at 0.5s, the air gap fluctuates slightly, but quickly recovers to the equilibrium state within 0.1s. The air gap velocity is always kept within a small range and there is no obvious overshoot.

[0153] Figure 4 The display shows that the control current quickly converges to a stable value after the controller starts up, and only makes small adjustments when parameters change abruptly, without drastic fluctuations, thus effectively constraining energy consumption.

[0154] The above results show that the method of the present invention can quickly achieve stable control of the suspended air gap under nominal operating conditions, has good adaptive ability to time-varying system parameters, and has excellent control performance.

[0155] Operating Condition 2: Actual Operating Condition

[0156] Under actual operating conditions, the desired air gap between the front and rear suspension points is inconsistent (10.3mm at the front and 9.8mm at the rear). Simulating train climbing conditions, strong white noise is injected into the system to simulate complex environmental interference. The system is controlled using both the regularized and unregularized schemes of this invention. The simulation results are as follows: Figure 5 , Figure 6 As shown:

[0157] Figure 5 The results show that, under the regularization scheme, the front suspension point air gap converges stably to about 10.3 mm, and the rear suspension point air gap converges stably to about 9.8 mm. Although there is a slight steady-state error due to the equilibrium point deviation, the air gap is always constrained within a safe range, the air gap velocity does not oscillate violently, and the system maintains stable operation.

[0158] Figure 6 The results show that without regularization, the combined effects of strong noise and time-varying parameters cause severe oscillations in the suspended air gap, the air gap deviation continues to increase, exceeding the safe operating range, the air gap velocity fluctuates greatly, the system becomes completely unstable, and normal suspension control cannot be achieved.

[0159] The above results show that the present invention effectively enhances the robustness of the system by introducing a regularization term, and can maintain system stability under actual operating conditions with complex noise interference and time-varying parameters, and constrain the levitation air gap within a safe range. In contrast, conventional data-driven control schemes without regularization cannot meet the actual operating requirements of maglev trains.

[0160] Experimental conclusions

[0161] Simulation results verify the effectiveness and superiority of the maglev train control method based on regularization and direct data-driven strategy optimization proposed in this invention. This method can bypass the precise modeling process and directly use real-time data to achieve online optimization of the control strategy. It has good adaptability and robustness to time-varying system parameters and complex noise interference, and can strictly constrain the suspension air gap within the safe operating range, significantly improving the stability and safety of the maglev train suspension module. It has good engineering application value.

[0162] Industrial applicability

[0163] The maglev train control method based on regularization-driven direct data optimization of the present invention does not rely on precise dynamic modeling of the maglev system. It has high computational efficiency, strong robustness, and good adaptability. It can effectively cope with time-varying parameters and complex noise interference during the operation of maglev trains, and keep the suspension air gap stably constrained within a safe range. It can be directly applied to the suspension control system of maglev trains, and can also be adapted to different suspension modules of medium-low speed and high-speed maglev trains. It has broad industrial application prospects and promotion value.

[0164] Based on the above, Figure 1 Accordingly, this application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the magnetic levitation control method based on regularized data-driven strategy optimization of any of the above embodiments.

[0165] Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of this application.

[0166] Based on the above, Figure 1 To achieve the above objectives, this application also provides a computer device, including a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to implement the steps of the magnetic levitation control method based on regularized data-driven strategy optimization of any of the above embodiments.

[0167] Optionally, the computer device may also include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, input units such as a keyboard, etc., and optional user interfaces may also include USB ports, card reader ports, etc. The network interface may optionally include standard wired interfaces, wireless interfaces (such as Bluetooth interfaces, Wi-Fi interfaces), etc.

[0168] Those skilled in the art will understand that the computer device structure provided in this embodiment does not constitute a limitation on the computer device, and may include more or fewer components, or combine certain components, or have different component arrangements.

[0169] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages and stores the hardware and software resources of a computer device, supporting the operation of information processing programs and other software and / or programs. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software within the physical device.

[0170] In this invention, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more unless otherwise explicitly defined. The terms "install," "connect," "link," and "fix" should be interpreted broadly. For example, "connect" can be a fixed connection, a detachable connection, or an integral connection; "link" can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0171] In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," "front," "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or unit referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0172] In the description of this specification, the terms "one embodiment," "some embodiments," "specific embodiment," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0173] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A magnetic levitation control method based on regularized data-driven strategy optimization, characterized in that, Includes the following steps: S1, perform force analysis on the minimum suspension unit system of the maglev train and establish the nonlinear dynamic equation of the minimum suspension unit; S2, collect the input and output data of the smallest suspension unit of the maglev train within the time interval {0,1,…,k}, the input and output data including the control input corresponding to the historical control current, the suspension air gap, and the acceleration integral; S3. Based on the collected input and output data, construct the sample covariance matrix and rewrite the dynamic equation of the suspension system using the covariance parameterization method. S4. Introduce a regularization term into the cost function of the linear quadratic regulator LQR to construct a direct data-driven LQR optimization problem with regularization constraints. S5 employs a data-driven strategy optimization method, updating the strategy parameter matrix through the projection gradient descent algorithm, and recursively updating the covariance matrix and its inverse matrix based on the rank-one update rule, thereby realizing online updating of the control gain and completing the levitation control of the maglev train. The formula for updating the policy parameter matrix using the projective gradient descent algorithm is: ； In the formula, For iterative index, The cost function is regularized. For the cost function at the th The gradient at the nth iteration, where η>0 is the constant step size of gradient descent. For projection operators; Indicates the first The policy parameter matrix at the next iteration Indicates the first The policy parameter matrix updated by projective gradient descent in the next iteration. for The Moore-Penrose pseudoinverse and projection operator are used to ensure that the updated policy parameters satisfy the constraints. , For historical air gap state covariance term, The matrix represents the strategy parameters to be optimized. The formula for recursively updating the covariance matrix, its inverse matrix, and the optimization strategy parameter matrix based on the rank-one update rule is as follows: ； In the formula, Let be the input state vector at the current time, given by the th... Time control input and suspended air gap state composition; For the first The inverse of the covariance matrix of the next iteration. For the first The policy parameter matrix updated by projective gradient descent in the next iteration; The formula for the online updated closed-loop control gain is: ； In the formula, For the first The control input covariance term updated in the next iteration For the first The policy parameter matrix updated by projective gradient descent in the next iteration; Let be the control gain matrix at time k.

2. The magnetic levitation control method based on regularized data-driven strategy optimization according to claim 1, characterized in that, The nonlinear dynamic equation of the minimum suspension unit established in S1 is: ； in, The load capacity of the smallest suspension unit, It is the acceleration due to gravity; and These are the air gaps between the two suspension points before and after the smallest suspension unit. and These represent the rate of change of the air gap between the two suspension points, one before and one after. and These represent the first derivatives of the air gaps between the front and rear suspension points, respectively. and These represent the first derivatives of the rate of change of the air gap at the suspension point before and after; is the electromagnetic force coefficient, where air permeability, The effective magnetic pole area of ​​the electromagnet. This represents the number of turns in the electromagnet coil. and For system control input, where and These are the control currents for the electromagnets at the front and rear suspension points, respectively.

3. The magnetic levitation control method based on regularized data-driven strategy optimization according to claim 2, characterized in that, The input and output data collected in S2 are used to construct a data matrix in the following form: ； In the formula, This is the historical accumulation matrix of suspended air gap states. The historical control input is a stacked matrix. The historical acceleration integral stacked matrix, This is the current accumulation matrix of the suspended air gap state. These represent the historical suspended air gap states from the 0th to the (k-1th)th; These represent the 0th to the (k-1)th historical control inputs, respectively. These represent the historical acceleration integrals from the 0th to the (k-1th)th time; These represent the suspended air gap states at time points 0 to k, respectively. The above data matrix satisfies the dynamics relation of discrete system: ； in, For the state matrix of a discrete system, Input matrix for discrete system; simultaneously construct data block matrix The data block matrix The conditions for sustained incentives must be met, namely It has full row order.

4. The magnetic levitation control method based on regularized data-driven strategy optimization according to claim 3, characterized in that, The sample covariance matrix constructed in S3 for: ； In the formula, The duration of data collection; simultaneously based on the input / output data matrix and the data block matrix. The covariance term is defined as follows: ； In the formula, For historical air gap state covariance term, For historical control input covariance terms, For the acceleration integral covariance term, This is the covariance term for the current air gap state.

5. The magnetic levitation control method based on regularized data-driven strategy optimization according to claim 4, characterized in that, The step in S3 of rewriting the dynamics of the suspension system through covariance parameterization is as follows: based on the data block matrix Given the full row rank characteristic, the sample covariance matrix Ψ is a positive definite matrix. The closed-loop control gain is correlated with the policy parameter matrix through covariance parameterization. ； In the formula, This is the closed-loop control gain matrix. for An identity matrix of order 1. Let be the strategy parameter matrix to be optimized; based on the covariance parameterization relationship, the discrete system dynamics of the maglev train are rewritten as: 。 6. The magnetic levitation control method based on regularized data-driven strategy optimization according to claim 5, characterized in that, In step S4, based on the deterministic equivalence principle, the unmeasurable noise term is ignored. At that time, the basic direct data-driven LQR optimization problem is: ; ； In the formula, Let cost function be This is the trace operation of a matrix; This is the state weight matrix; express Constraints To control the input weight matrix; The solution to the Lyapunov equation satisfies ； Closed-loop control gain satisfies 。 7. The magnetic levitation control method based on regularized data-driven strategy optimization according to claim 6, characterized in that, In S4, after introducing a regularization term into the cost function, the constructed regularized direct data-driven LQR optimization problem is: ； ； ； In the formula, This is a regularization parameter used to enhance the robust stability of the system against noise and disturbances; Describe the solutions to the Lyapunov equations The constraints.

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