Finite time control method, device and storage medium for maglev train suspension system

Abstract

The present invention relates to a finite-time control method, device, and storage medium for a maglev train suspension system. First, a mathematical model of the maglev train suspension system is established; second, a finite-time state observer is introduced based on the mathematical model to estimate the unmeasurable state quantities of the system; then, the stability of the system is judged based on the approximate model, the changes in the disturbance in the dynamic equation are analyzed, and the constraints are designed in combination with the convergence time required by the system; finally, a maglev control system model based on terminal sliding mode control is established, and the suspension controller given by the control law that satisfies the constraints is used to dynamically adjust the current of the electromagnet. Compared with the prior art, the present invention introduces a finite-time control method into the suspension controller of the maglev train, so that the maglev train suspension system can achieve rapid convergence within a finite time under external disturbances. This effectively reduces the adverse effects of external continuous disturbances and improves the stability of the maglev train under special working conditions such as passing through bridges.

Description

Technical Field

[0001] The present invention relates to the technical field of suspension control systems, and in particular to a suspension control method for a magnetic levitation train based on finite-time sliding mode control. Background Art

[0002] The maglev transportation system has many excellent features such as low noise, strong climbing ability, small turning radius, no pollution, low overall cost, and energy saving. It has gradually become the forefront of the development of global rail transportation.

[0003] Suspension control technology is a core and key technology for maglev trains, fundamental to their proper operation. The suspension controller controls the current within the electromagnet coils so that, at a given suspension gap, the electromagnetic levitation force equals the train's weight, achieving stable suspension and precise control.

[0004] Because the suspension system of a maglev train exhibits nonlinearities and open-loop instabilities, active control techniques are required to achieve stable suspension. Commonly used suspension control methods include linear control methods such as PID control and quadratic optimal control. These methods optimize the suspension system's performance under certain system parameter conditions by adjusting the weighted coefficients of three state variables related to the suspension gap. However, these control methods have the following drawbacks: each set of weighted coefficients can only optimize the suspension system's performance under certain system parameter conditions, and fixed weighted coefficients cannot adapt to time-varying systems. Furthermore, linear controllers only perform well near the operating point; away from the operating point, the system may fail to achieve the desired control effect or even become unstable. The suspension system of a maglev train is a complex dynamic system. When the system encounters external disturbances, track irregularities, vehicle-track coupling vibrations, cornering, and vertical curves, the system model and parameters will change. Therefore, the suspension controller must overcome the effects of system parameter perturbations on control. For the suspension system of a maglev train, after encountering a disturbance, the suspension system should converge quickly to minimize the impact of the disturbance on subsequent dynamic processes. Summary of the Invention

[0005] The purpose of the present invention is to overcome the influence of system parameter perturbation on control when the suspension system encounters external disturbance, and to provide a finite time control method, device and storage medium for a maglev train suspension system.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] As a first aspect of the present invention, a finite time control method for a maglev train suspension system is provided, the control method comprising the following steps:

[0008] Construct a dynamic model of the maglev train suspension system;

[0009] Based on the dynamic model, a finite-time state observer is introduced to obtain the unmeasurable state quantities of the suspension system.

[0010] Construct a finite-time controller based on terminal sliding mode control and set constraints based on the convergence time required by the system;

[0011] A finite time controller based on terminal sliding mode control is used to dynamically adjust the current of the electromagnet to ensure stable suspension of the maglev train.

[0012] As a preferred technical method, the dynamic model of the maglev train suspension system is obtained based on the dynamic equation and electromagnetic equation of the suspension system:

[0013]

[0014] Where: m is the equivalent mass of the suspended electromagnet; z(t) is the distance from the magnetic pole surface to the reference plane; g is the acceleration due to gravity; F d (δ, t) is the external disturbance force at time t; F e (t) is the electromagnetic attraction at time t; k is the parameter of the suspension force formula; δ(t) is the suspension air gap; i(t) is the coil current.

[0015] As a preferred technical method, the suspension system control model with current as the control input is obtained according to the dynamic equation of the suspension system:

[0016]

[0017] Where: x1 and x2 are two state variables of the system, namely the air gap and the air gap change rate; g is the acceleration of gravity; b(x) is the input coefficient under the corresponding state; u is the input quantity; d is the disturbance.

[0018] As a preferred technical method, the finite-time state observer is expressed as follows:

[0019]

[0020] Where: z1, z2, z3 are the observed values ​​of the system state variables air gap x1, air gap change rate x2, and disturbance d respectively; 1>α>0, β1>0, β2>0, β3>0 are positive constants; the sig function is specifically expressed as:

[0021] sig α (x)=|x| α sign(x).

[0022] As a preferred technical method, the finite-time state observer parameters β1, β2, β3 and α are set to make the magnetic levitation system complete the finite-time stability. At the same time, the first convergence time t s satisfy:

[0023]

[0024] In the formula: C is;

[0025] V(η(t))=η(t) T Pη(t)

[0026] η(t)=[sig (α+1) / 2 (e1(t)), e2(t), e3(t)] T ;

[0027] Where: e1, e2, and e3 are the observation errors of x1, x2, and d respectively.

[0028] As a preferred technical method, the finite time controller designs the control law based on the second-order nonlinear dynamic system and the terminal sliding surface:

[0029]

[0030] Where: η>0 and satisfies sgn is the sign function:

[0031]

[0032] The second-order uncertain nonlinear dynamic system of the suspension system is expressed as follows:

[0033]

[0034] Where: x = [x1, x2] T is the system state vector; f(x) and b(x)≠0 are smooth nonlinear functions of x; g(x) satisfies ‖g(x)||≤l g Uncertain disturbance, where l g >0; u is the scalar control input;

[0035] The terminal sliding surface TSM described by the second-order uncertain nonlinear dynamic system is expressed as follows:

[0036]

[0037] Where: β, p, q are control parameters, satisfying β>0, q and p are both positive odd numbers, and

[0038] As a preferred technical method, the finite time controller adjusts the control parameters according to the design target so that the second convergence time of the system meets the requirements. The second convergence time is expressed as follows:

[0039] t=t s +t r

[0040] Where: t r is the time to converge to the sliding surface s = 0; t s It is the time when x1 converges to 0 after the system reaches the sliding surface.

[0041] As a preferred technical method, the algorithm for dynamically adjusting the electromagnet current using a finite time controller is:

[0042]

[0043] Where: i is the control current; g is the acceleration due to gravity; β, p, q, and η are control parameters.

[0044] As a second aspect of the present invention, a finite time control device for a maglev train suspension system is provided, comprising:

[0045] one or more processors;

[0046] a memory for storing one or more programs;

[0047] When the one or more programs are executed by the one or more processors, the one or more processors implement the finite time control method for the magnetic levitation train suspension system as described above.

[0048] As a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and wherein when the computer program is executed by a processor, the finite-time control method of the magnetic levitation train suspension system as described above is implemented.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1) This invention introduces a finite-time control method for the suspension controller of a maglev train for the first time. Utilizing a finite-time observer and a finite-time controller, this method allows for timely intervention in response to continuous disturbances in the suspension system. This allows the maglev system to achieve rapid convergence within a finite time under external disturbances, effectively mitigating the adverse effects of continuous external disturbances and improving the stability of the maglev train under special operating conditions, such as when crossing bridges. This method effectively meets the high stability and anti-interference performance requirements of the maglev system during operation and has promising application prospects in engineering practice.

[0051] 2) This invention designs a finite-time extended disturbance observer for the suspension system of a maglev train. This finite-time observer offers advantages such as rapidity, robustness, and accuracy. Compared to observers based on Lyapunov stability, the finite-time observer focuses more on the transient reconstruction of the system. It enables a given system to meet certain requirements within a finite time, thereby achieving rapid stabilization to an equilibrium position. For fast-changing systems such as the maglev suspension system, the finite-time observer can track state variables in a timely manner.

[0052] 3) By utilizing the design methods for the finite-time sliding surface and finite-time sliding mode controller for second-order systems provided herein, the present invention is able to obtain a variety of finite-time sliding surface and corresponding finite-time sliding mode controller forms. Finite-time control based on the terminal sliding surface is an effective control strategy. Compared with traditional control methods, finite-time control avoids the drawback of traditional control methods, which require a long time to reach a stable state. In addition, because the terminal sliding surface is attractive, it can effectively resist external interference and system uncertainty, thereby improving the robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flow chart of a finite time control method for a maglev train suspension system according to the present invention;

[0054] Figure 2 Schematic diagram of the electromagnet suspension system;

[0055] Figure 3 A structural diagram of a single electromagnet suspension system relative to a reference model in one embodiment of the present invention;

[0056] Figure 4 This is a waveform diagram of the simulation result of the finite time observer suspension gap in one embodiment of the present invention;

[0057] Figure 5 This is a waveform diagram of the simulation result of the finite time observer suspension gap after adding interference in one embodiment of the present invention;

[0058] Figure 6 This is a waveform diagram of the simulation results of the suspension gap of a finite time controller based on the terminal sliding surface in one embodiment of the present invention;

[0059] Figure 7 This is a waveform diagram of the simulation results of the suspension gap of a finite-time controller based on a non-singular terminal sliding surface in one embodiment of the present invention;

[0060] Figure 8 This is a waveform diagram of the simulation results of the finite-time observer and the finite-time controller combined with the suspension gap in one embodiment of the present invention. DETAILED DESCRIPTION

[0061] The concept behind the finite-time control method for a maglev train suspension system is to observe the maglev train suspension system using a finite-time observer. Based on the homogeneous properties of the terminal sliding surface, design criteria for the finite-time sliding surface are proposed, resulting in the finite-time sliding surface of the maglev train suspension system. Based on Lyapunov's stability theory, a finite-time sliding mode controller for the maglev train suspension system is designed.

[0062] Sliding mode control is a nonlinear control method with remarkable flexibility. This is because the system's dynamic performance is determined by the pre-designed sliding surface within which it operates. The design of the sliding surface directly affects the system's dynamic performance. As long as the accessibility and stability of the sliding mode are guaranteed, appropriate control can be achieved.

[0063] Finite-time control methods based on terminal sliding surfaces design the sliding surface as a nonlinear function, allowing the system state to converge to an equilibrium point within a finite time. This sliding surface is called a terminal sliding surface. The convergence performance of a terminal sliding surface is better than asymptotic convergence. Stability analysis can be performed using the Lyapunov method, which simplifies the design of the control law and has been successfully applied to complex nonlinear systems such as robots and motors. For dynamic systems, by appropriately adjusting the control law parameters, the phased convergence speed can be achieved to meet convergence within a finite time and stability requirements. Finite-time control methods based on terminal sliding surfaces have the advantages of fast dynamic response, no overshoot, and strong robustness. Furthermore, the control structure is simple and easy to implement in engineering.

[0064] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0065] Example 1

[0066] As one of the implementation methods of the present invention, this embodiment provides a method for controlling the suspension system of a maglev train based on finite-time control. First, a mathematical model of the suspension system is established based on the suspension system of the maglev train; secondly, a finite-time state observer is introduced based on the mathematical model to estimate the unmeasurable state quantities of the system; then, the stability of the system is judged based on the approximate model, the changes in the disturbances in the dynamic equations are analyzed, and the constraints are designed in combination with the convergence time required by the system; finally, the basic principle of finite-time control is used to establish a maglev control system model based on terminal sliding mode control (TSM), and the design structure of the suspension controller is given by adopting the control law that meets the constraints. Figure 1 As shown, the method specifically includes the following steps:

[0067] Step S1: Construct the dynamic equation of the maglev train suspension system:

[0068] Step S11: performing a force analysis on the suspension system of the maglev train to obtain a dynamic equation of the suspension system.

[0069] Assuming that the magnetic permeability in the magnetic pole is infinite and the magnetic potential is evenly distributed on the air gap, and the winding leakage flux is ignored, the electromagnetic force F at time t is e (t) is:

[0070]

[0071] Where t is time; δ(t) is the suspension air gap; i(t) is the coil current; and k is the parameter in the suspension force formula. Clearly, the relationship between the electromagnetic force and the air gap is nonlinear, indicating the instability of the maglev train's suspension system, which requires control.

[0072] The mechanical equilibrium equation of the suspension system in the vertical direction is:

[0073]

[0074] Where: m is the equivalent mass of the suspension system, with a reference size of 750 kg; z(t) is the distance from the magnetic pole surface to the reference plane; g is the acceleration due to gravity; F d (δ,t) is the magnitude of external disturbance. Figure 3 The single electromagnet suspension system model considers the changes in the guide rail action surface and has the following relationship:

[0075] z(t)=h(t)+δ(t)

[0076] Where: h(t) is the distance from the suspension track plane to the reference plane.

[0077] In summary, the dynamic equation of the maglev train suspension system is obtained based on the dynamic equation and electromagnetic equation of the suspension system:

[0078]

[0079] Step S12: Perform force analysis on the suspension system of the maglev train to obtain the dynamic equation of the suspension system. According to the dynamic equation of the suspension system, a suspension system control model with current as the control input is obtained:

[0080]

[0081] Where: x1 and x2 are the two state variables of the system, air gap and air gap change rate; g is the acceleration of gravity; u is the input quantity; b(x) is the input coefficient under the corresponding state; d is the disturbance.

[0082] Where:

[0083] Step S2: Design a finite-time state observer to obtain the displacement of the suspension system and its rate of change:

[0084] Since the change speed of the maglev gap and the unknown disturbance are unmeasurable, a state observer is designed to obtain them. At the same time, considering the finite time problem, a finite time extended state observer is set as:

[0085]

[0086] Where: z1, z2, z3 are the observed values ​​of x1, x2, and d respectively; 1>α>0, β1>0, β2>0, β3>0 are the designed positive constants. Here, the sig function is specifically expressed as:

[0087] sig α (x)=|x| α sign(x)

[0088] The observer error equation can be obtained by taking the difference between the state equation and the observer equation:

[0089]

[0090] Where: e1, e2, and e3 are the observation errors of x1, x2, and d respectively.

[0091] According to the error equation above, the Lyapunov function can be constructed:

[0092] V(η(t))=η(t) T Pη(t)

[0093] η(t)=[sig (α+1) / 2 (e1(t)), e2(t), e3(t)] T

[0094] According to the above Lyapunov function and error equation, d is continuously differentiable and bounded; 1>α>0, β1>0, β2>0, β3>0; and they are all positive numbers; and at the same time, α1=α2=(α+1) / 2, α3=α, then the system is finite-time stable.

[0095] Therefore, it is only necessary to select appropriate β1, β2, β3 and α to make the magnetic levitation system stable in finite time, and the first convergence time also satisfies:

[0096]

[0097] Where: t0 is the initial time of the system; C is a constant determined by the above parameters and the disturbance boundary.

[0098] Step S3: Design a finite-time controller based on the terminal sliding surface:

[0099] Step S31: Consider the second-order uncertain nonlinear dynamic system of the suspension system:

[0100]

[0101] Where: x = [x1, x2] T is the system state vector, f(x) and b(x)≠0 are smooth nonlinear functions of x, and g(x) satisfies ‖g(x)||≤l g Uncertain disturbance, where l g >0, and u is a scalar control input.

[0102] Step S32: Design the terminal sliding surface TSM according to the second-order nonlinear dynamic system:

[0103]

[0104] Where: β, p, q are control parameters, and they satisfy β>0, q and p are both positive odd numbers, and

[0105] Step S33: Design a control law based on the second-order nonlinear dynamic system and the terminal sliding surface:

[0106]

[0107] Where: η>0.

[0108] Where: sgn is the sign function and

[0109]

[0110] Combined with the terminal sliding surface, we can take the Lyapunov equation:

[0111]

[0112] Considering the second-order nonlinear dynamic system of the maglev train suspension system, the derivative of the Lyapunov equation and scaling it yields:

[0113]

[0114] The second convergence time can be determined based on the Lyapunov equation and the terminal sliding surface:

[0115] t=t s +t r

[0116] Where: t r is the time to converge to the sliding surface s = 0, t sIt is the time when x1 converges to 0 after the system reaches the sliding surface.

[0117] Therefore, the parameters are adjusted according to the design objectives so that the second convergence time of the system meets the requirements.

[0118] Step S4: Use a finite time controller to dynamically adjust the current of the electromagnet to ensure stable suspension of the maglev train. The algorithm for controlling the current is:

[0119]

[0120] Where: i is the control current; g is the acceleration due to gravity; β, p, q, and η are control parameters.

[0121] Solution Verification

[0122] The suspension system was modeled and numerically simulated using the Simulink toolbox in Matlab. The model consists of an observer and a suspension control system. The initial position of the maglev train's suspension electromagnets is set approximately 10 mm off the equilibrium point, with a stable suspension gap of 9 mm. The control system calculates the required control current based on the observed air gap value and its variation. This current generates an electromagnetic force that influences the suspension system's motion. The suspension system calculates the new vehicle state as output based on parameters such as the input current and track displacement.

[0123] First, a finite time observer for the suspension system is built to observe the performance of the suspension observer and build a control model with PID as the control law. The parameters of the finite time observer for the magnetic suspension system are selected as β1=10000, β2=100, β3=0.01, α=0.4. From the simulation results Figure 4 The tracking effect of the finite time observer of the suspension system is good and the convergence is fast. After adding the disturbance, the simulation results are as follows Figure 5 ,The finite-time observer has good tracking effect, and it converges quickly and has good robustness when encountering noise.

[0124] Next, build a finite time controller for the suspension system. Select the magnetic suspension system control parameter β = 2, η+l g =100. From the simulation results, the finite time controller of the suspension system has good control effect and fast convergence. After adding the disturbance, the simulation results are as follows Figure 6 The overall response time is fast, the adjustment time is 0.058s, and the system steady-state error is very small. Compared with the control law based on PID, the system has good response speed, anti-interference ability, and strong robustness. At the same time, in order to avoid the singular phenomenon of the terminal sliding mode surface, a non-singular terminal sliding mode surface (NTSM) is adopted for simulation. The results are as follows Figure 7 shown.

[0125] Finally, the finite time observer is combined with the finite time controller and simulation is performed according to the above parameters. The simulation results are as follows: Figure 8 , it can be seen that the overall convergence speed of this method is fast and the error is small. The chattering phenomenon of the observer is the inevitable result of the influence of the switching function used in the sliding surface.

[0126] In summary, this maglev train suspension system control method based on finite time control has good response speed, anti-interference ability, and strong robustness, and is a control method with broad application prospects.

[0127] Example 2

[0128] As a second aspect of the present invention, the present application further provides an electronic device comprising: one or more processors; a memory for storing one or more programs; and when the one or more programs are executed by the one or more processors, the one or more processors implement the above-described method for controlling a maglev train suspension system based on finite time control. In addition to the aforementioned processor, memory, and interface, any device with data processing capabilities in which the apparatus in the embodiments is located may also include other hardware, typically based on the actual functionality of the device, which will not be described in detail.

[0129] Example 3

[0130] As a third aspect of the present invention, the present application also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-mentioned method for controlling the suspension system of a maglev train based on finite time control. The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities as described in any of the aforementioned embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0131] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A finite time control method for a maglev train suspension system, characterized in that: The control method comprises the following steps: Construct a dynamic model of the maglev train suspension system; Based on the dynamic model, a finite-time state observer is introduced to obtain the unmeasurable state of the suspension system. The finite-time state observer sets the finite-time state observer parameters to make the magnetic levitation system complete finite-time stability. At the same time, the first convergence time satisfy: Where: is a constant determined by the finite-time state observer parameters and the disturbance bounds; Representatives in t Error variables of the moment system; is the moment of the initial state; represents the Lyapunov function, which is used to quantify the degree to which the system state deviates from the equilibrium point; ； Where: P is a symmetric positive definite matrix; 、 、 are the observation errors of air gap, air gap change rate and disturbance respectively; is the finite-time state observer parameter; The function is specifically expressed as: A finite-time controller based on terminal sliding mode control is constructed. The finite-time controller adjusts the control parameters according to the design objectives so that the second convergence time of the system meets the requirements. The second convergence time is expressed as follows: Where: is the time to converge to the sliding surface; is the time when the air gap converges to 0 after the system reaches the sliding surface; A finite time controller based on terminal sliding mode control is used to dynamically adjust the current of the electromagnet to ensure stable suspension of the maglev train.

2. The finite time control method for a maglev train suspension system according to claim 1, characterized in that: The dynamic model of the maglev train suspension system is obtained based on the dynamic equation and electromagnetic equation of the suspension system: Where: is the equivalent mass of the suspended electromagnet; is the distance from the magnetic pole surface to the reference plane; is the acceleration due to gravity; for t External disturbance force at any moment; is the electromagnetic attraction at time t; is the suspension force formula parameter; is the suspended air gap; is the coil current.

3. The finite time control method for a maglev train suspension system according to claim 1, characterized in that: The finite-time state observer is expressed as follows: Where: 、 、 are the state variables of the system, air gap , air gap change rate and disturbances Observed values ​​of is a positive constant; is the input coefficient under the corresponding state; The function is specifically expressed as: 。 4. The finite time control method for a maglev train suspension system according to claim 1, characterized in that: The finite time controller is designed based on the second-order nonlinear dynamic system and the terminal sliding surface control law: Where: and satisfy ; is a symbolic function: The second-order uncertain nonlinear dynamic system of the suspension system is expressed as follows: Where: is the system state vector, are the two state variables of the system, namely the air gap and the air gap change rate; is the input coefficient under the corresponding state; is the acceleration due to gravity; Express satisfaction The uncertainty disturbance is the upper limit of the uncertainty disturbance and ; is the scalar control input; The terminal sliding surface TSM described by the second-order uncertain nonlinear dynamic system is expressed as follows: Where: is the control parameter, satisfying 0, q and p are all positive odd numbers, and .

5. The finite time control method for a maglev train suspension system according to claim 1, characterized in that: The algorithm for dynamically adjusting the electromagnet current using a finite time controller is: Where: is the control current; m is the equivalent mass of the suspension system; , represents the vacuum permeability, is the number of turns of the electromagnetic coil, is the effective magnetic pole area; is the acceleration due to gravity; is the control parameter; is the upper limit of the uncertainty disturbance; represents the terminal sliding surface.

6. A finite time control device for a maglev train suspension system, characterized in that: include: one or more processors; a memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the finite time control method for the magnetic levitation train suspension system as described in any one of claims 1 to 5.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the finite time control method for a magnetic levitation train suspension system according to any one of claims 1 to 5 is implemented.

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