An optimal tracking control method for protecting transient performance of maglev train

Abstract

The application provides an optimal tracking control method for protecting transient performance of a magnetic levitation train and relates to the technical field of the magnetic levitation train. The method comprises the following steps: determining a magnetic suspension dynamic model according to the structure of a suspension frame; determining a magnetic suspension train model according to the magnetic suspension dynamic model; constructing a corresponding virtual controller according to the magnetic suspension train model; constructing a real controller according to the virtual controller; and controlling the suspension air gap of the magnetic suspension vehicle by using the real controller. The application solves the problems of inconsistent suspension gap output, high cost and low resource utilization in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of magnetic levitation train, in particular to an optimal tracking control method for protecting transient performance of a magnetic levitation train. BACKGROUND

[0002] At present, most of the medium and low speed magnetic levitation trains adopt four suspension structures. Each suspension frame is independently controlled by four suspension controllers. However, under the action of factors such as uneven load distribution in the train, random irregularity of the track, etc., the suspension gap outputs are inconsistent, and even the whole suspension resonates, which affects the passenger comfort. Therefore, it is particularly important to design a control algorithm for improving the transient performance of the magnetic levitation train. At the same time, in the actual environment, the magnetic levitation train will inevitably be affected by some random interference factors, which will reduce the normal operation of the magnetic levitation train. In order to avoid the influence of interference, a control method with anti-interference ability is worth further exploring. In addition, in today's rapid development of science and technology, resource waste and energy consumption are problems that need to be solved in our development process, and a control algorithm that improves the utilization rate of resources has attracted extensive attention of researchers at home and abroad. If there is a lack of resources or limited resources, the traditional adaptive backstepping control strategy is no longer applicable. At the same time, excessive resource waste will bring high cost. SUMMARY

[0003] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide an optimal tracking control method for protecting the transient performance of a magnetic levitation train, which solves the problems of inconsistent suspension gap output, high cost and low resource utilization rate in the prior art.

[0004] To achieve the above purpose, the present application provides the following solutions:

[0005] An optimal tracking control method for protecting the transient performance of a magnetic levitation train, comprising:

[0006] determining a magnetic suspension dynamic model according to the structure of the suspension frame;

[0007] determining a magnetic suspension train model according to the magnetic suspension dynamic model;

[0008] constructing a corresponding virtual controller according to the magnetic suspension train model;

[0009] constructing a real controller according to the virtual controller;

[0010] controlling the suspension air gap of the magnetic suspension vehicle by using the real controller.

[0011] Preferably, the expression of the magnetic suspension dynamic model is:

[0012]

[0013] where m represents the mass of the levitation body, g is the acceleration of gravity, z(t) represents the distance between the pole face and the reference surface, h(t) represents the track irregularity, μ0=4π×10 -7 H / m represents the permeability of air, A is the area of the core pole, c(t) represents the air gap between the magnetic pole and the guide rail, N represents the number of turns of the electromagnet winding, i(t) represents the control coil current, F(i,c) is the controllable electromagnetic force, f d represents external interference, R represents resistance, and t represents time.

[0014] Preferably, the expression of the maglev train model is:

[0015]

[0016] where, is the control gain, g is the control input, d is the disturbance, and x1 represents the output of the system. represents the first-order derivative of x1 with respect to time t. x2 represents the state of the system, represents the first-order derivative of x2 with respect to time t.

[0017] Preferably, the constructing a corresponding virtual controller according to the maglev train model comprises:

[0018] determining the constraint boundary of the transient performance constraint dimension function of the maglev train model, the constraint boundary comprising an upper boundary function and a lower boundary function;

[0019] determining the error conversion of the maglev train model according to the constraint boundary;

[0020] constructing a corresponding virtual controller according to the error conversion.

[0021] Preferably, the expression of the upper boundary function is:

[0022]

[0023] where e(0) is the initial value of the tracking error, κ ∞ , μ1, μ2 are the first design parameter, the second design parameter and the third design parameter respectively, sign(·) is the sign function, κ is a constraint piecewise function, which is defined as follows:

[0024]

[0025] where n represents the convergence rate of the output error, and κ0 is the initial value of the preset boundary.

[0026] Preferably, the expression of the lower boundary function is:

[0027] b = sign (e (0)) (K - K ∞ )+ μ2K.

[0028] Preferably, the expression of the virtual controller is:

[0029]

[0030] wherein ρ1 is a parameter to be designed, is a virtual controller, is a first derivative of a reference signal, represents a transformed error, ψ1 represents a fuzzy base function, represents an estimation of a first Actor weight, σ1 and σ2 respectively represent a first function and a second function obtained by derivation on the error T represents a transpose of a matrix.

[0031] Preferably, the constructing a real controller according to the virtual controller comprises:

[0032] constructing a performance index function related to the error and the real controller;

[0033] obtaining a HJB equation according to the performance index function related to the error and the real controller;

[0034] obtaining a virtual controller equation of an Actor-Critic structure according to a fuzzy logic system and the virtual controller based on a reinforcement learning strategy;

[0035] obtaining an optimal real controller according to the virtual controller equation of the Actor-Critic structure and the HJB equation.

[0036] Preferably, the expression of the optimal real controller is:

[0037]

[0038] wherein, is an optimal real controller, and represents a transformed error related to a state x2, ψ2 represents a fuzzy base function, represents an estimation of a second Actor weight. represents an output of a filter. represents an adaptive parameter, and ρ2 represents a control gain, which is an adjustable parameter. T represents a transpose of a matrix.

[0039] The present application discloses the following technical effects:

[0040] The application provides an optimal tracking control method for protecting transient performance of a magnetic levitation train, and comprises the following steps: determining a magnetic suspension dynamic model according to the structure of a suspension frame; determining a magnetic suspension train model according to the magnetic suspension dynamic model; constructing a corresponding virtual controller according to the magnetic suspension train model; constructing a real controller according to the virtual controller; and controlling the suspension air gap of the magnetic suspension train by using the real controller. The application considers how to design an adaptive transient performance constraint optimal controller for the mathematical model of the magnetic suspension train system, limits the suspension air gap of the magnetic suspension train in a safe range, reduces the communication burden, improves the resource utilization rate, and enables the magnetic suspension train to track the target trajectory within a certain time and ensure the stability of the tracking. Firstly, the magnetic suspension train model is accurately modeled to obtain a more practical system. Secondly, by means of the reinforcement learning strategy and the stability theory in the Lyapunov sense, the dynamic surface technology, the approximation technology of the fuzzy logic system, and the scaling method of the Young inequality, a transient performance boundary constraint function and an adaptive transient performance constraint optimal controller are designed for the system. The designed controller can not only successfully realize safe control under the condition that the system is disturbed and constrained, but also save communication resources and reduce the communication burden. The designed optimal controller can not only successfully realize safe control under the condition that the system is disturbed and constrained, but also save communication resources and reduce the communication burden. The designed transient performance constraint optimal control algorithm enables the tracking error of the magnetic suspension train to be constrained in a predetermined area and ensures the stability of the tracking. The simplified structure of the magnetic suspension system can reduce the economic cost. Meanwhile, the optimal control algorithm based on the reinforcement learning strategy can improve the working efficiency of the system and realize the expected tracking control target with the least cost, and has important practical application value for improving the control performance of the magnetic suspension. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0042] Fig. 1 A flowchart of an optimal tracking control method for protecting transient performance of a magnetic suspension train is provided for the embodiments of the present application.

[0043] Fig. 2 A strategy diagram of an optimal tracking control method for protecting transient performance of a magnetic suspension train is provided for the embodiments of the present application. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] like Figs. 1-2 As shown, the present invention provides an optimal tracking control method for protecting the transient performance of a maglev train, comprising:

[0047] Step 100: Determine a dynamic model of the magnetic levitation system according to the structure of the suspension frame;

[0048] Step 200: Determine a suspended maglev train model according to the suspended maglev dynamic model;

[0049] Step 300: constructing a corresponding virtual controller according to the maglev train model;

[0050] Step 400: constructing a real controller based on the virtual controller;

[0051] Step 500: Control the suspension air gap of the maglev vehicle using the real controller.

[0052] Furthermore, due to the structural decoupling function of the suspension frame, the design of the suspension controller can be simplified to a single electromagnet suspension problem within a certain range. Ignoring the magnetic leakage and the magnetic resistance of the guide rail, the magnetic core and the effective air gap magnetic resistance R T It can be expressed as:

[0053]

[0054] Where μ0 = 4π × 10 -7 H / m represents the permeability of air, A is the area of ​​the core pole, and c(t) represents the air gap between the pole and the rail. The winding inductance of the electromagnet is

[0055]

[0056] Where L is the inductance, Ψ is the breathing flux, N is the number of turns of the electromagnet winding, i(t) is the control coil current, and the air gap flux density is then defined as

[0057]

[0058] Where B represents the air gap flux density, Φm Φ is total magnetic flux T Φ represents main magnetic flux. Energy stored in magnetic field is

[0059]

[0060] wherein W represents energy stored in magnetic field. Controllable electromagnetic force F(i,c) is

[0061]

[0062] The voltage equation of electromagnet winding circuit can be obtained as follows:

[0063]

[0064] wherein u(t) represents voltage of electromagnet winding.

[0065] According to vertical force of electromagnet, the equation of suspension system can be derived. d f represents external disturbance. Considering irregular track surface, then z(t) = h(t) + c(t). According to the above, the dynamic model can be obtained as follows:

[0066]

[0067] wherein m represents mass of suspended body, g is acceleration of gravity, z(t) represents distance between magnetic pole surface and reference surface, h(t) represents irregularity of track, μ0 = 4π × 10 -7 H / m represents permeability of air, A is area of magnetic core pole, c(t) represents air gap between magnetic pole and guide rail, N represents turns of electromagnet winding, i(t) represents control coil current, F(i,c) is controllable electromagnetic force, f d represents external disturbance, R represents resistance, and t represents time.

[0068] Specifically, the expression of suspended magnetic levitation train model is as follows:

[0069]

[0070] wherein, is control gain, g is control input, d is disturbance, and x1 represents output of system. represents first order derivative of x1 with respect to time t. x2 represents state of system, represents first order derivative of x2 with respect to time t.

[0071]

[0072] Further, the constructing corresponding virtual controller according to the suspended magnetic levitation train model comprises:

[0073] determining a constraint boundary of a transient performance constrained scaling function of the maglev train model, the constraint boundary comprising an upper boundary function and a lower boundary function;

[0074] determining an error transformation of the maglev train model with the constraint boundary;

[0075] constructing a corresponding virtual controller according to the error transformation.

[0076] Specifically, a constraint boundary of a transient performance constrained scaling function is defined. The continuous constraint boundary function b satisfies the following conditions: and b are increasing functions, and for T0>0, are strictly increasing on [0, T0].

[0077] for T0>0,

[0078] where T0is the dwell time. By using the properties of the hyperbolic cosecant function, we provide a pair of feasible boundary functions as follows:

[0079] The expression of the upper boundary function is:

[0080]

[0081] where e(0) is the initial value of the tracking error, κ ∞ , μ1, μ2 are the first, second and third design parameters respectively, sign(·) is the sign function, and κ is a constraint piecewise function, which is defined as follows:

[0082]

[0083] where n represents the convergence rate of the output error, and κ0is the initial value of the preset boundary.

[0084] The expression of the lower boundary function is:

[0085] b = sign(e(0))(κ- κ ∞ )+ μ2κ.

[0086] where e(0) is the initial value of the tracking error, κ ∞ , μ1, μ2 are the design parameters, sign(·) is the sign function, and:

[0087]

[0088] where n represents the convergence rate of the output error, and K0 is the initial value of the preset boundary.

[0089] A fuzzy logic system is defined to approximate the nonlinear function. The fuzzy logic system is composed of a fuzzy rule base, fuzzification and defuzzification operators. The fuzzy rule base is composed of inference rules, which are defined as x1 is x2 is is then y is x = [x1, x2,..., x n ] ∈ R n and y ∈ R are the input and output of the fuzzy logic system, respectively, and are fuzzy sets on the real number field; according to the theory of fuzzy logic system, the output of the fuzzy system is represented as

[0090] where, is the point that maximizes the function By letting ψ = [ψ 1 , ψ 2 ,..., ψ m ] T and , we have

[0091] y(x) = Γ T ψ + ε.

[0092] An error transformation of the maglev train system is defined.

[0093]

[0094] A first-order low-pass filter is designed as

[0095]

[0096] where θ1 is the input of the filter, l is the filtered error, is the output of the filter.

[0097] Then the derivative of the error is solved.

[0098]

[0099] where, is a constant, is the first derivative of the reference signal.

[0100] Using the error transformation and the definition of the filter, we have:

[0101]

[0102] Subsequently, a virtual controller is constructed. In the design process of the controller, a candidate Lyapunov function is selected at each step to construct a virtual controller, until the last step to construct a real controller.

[0103] Further, the expression of the virtual controller is:

[0104]

[0105] wherein ρ1 is a parameter to be designed, is a virtual controller, is a first-order derivative of a reference signal, represents a converted error, and ψ1 represents a fuzzy basis function, represents an estimation of a first Actor weight, and σ1 and σ2 respectively represent a first function and a second function obtained by derivation on an error , and T represents a transpose of a matrix.

[0106] Meanwhile, an Actor-Critic weight update rate and an adaptive law are designed as:

[0107]

[0108] wherein is a parameter to be designed.

[0109] Further, the real controller is constructed according to the virtual controller, comprising:

[0110] a performance index function related to an error and the real controller is constructed;

[0111] an HJB equation is obtained according to the performance index function related to the error and the real controller;

[0112] a virtual controller equation of an Actor-Critic structure is obtained according to a fuzzy logic system and the virtual controller based on a reinforcement learning strategy;

[0113] an optimal real controller is obtained according to the virtual controller equation of the Actor-Critic structure and the HJB equation.

[0114] Further, the actual optimal controller is solved. The performance index function is also called a value function, and is related to an error and a controller:

[0115]

[0116] wherein, and is the cost function. The HJB equation is the derivative of the performance index function with respect to time, then the HJB equation of each step is shown as follows,

[0117]

[0118] where, is the gradient related to .

[0119] Firstly, the performance index function related to the error and the controller is constructed Then the derivative of the performance index function with respect to time t is taken to obtain the HJB equation,

[0120]

[0121] The controller is obtained by using the equation where the gradient is rewritten as and is brought into the controller to obtain

[0122]

[0123] Since is unknown, it is approximated using a fuzzy logic system to obtain

[0124]

[0125] where, Γ1 is the ideal weight, ψ1 is the fuzzy basis function, and ε1 is the residual error of the fuzzy logic system. In order to achieve optimal control based on the reinforcement learning strategy, an Actor-Critic structure is designed,

[0126]

[0127] is brought into the HJB equation to obtain then is

[0128]

[0129] According to the optimal control design, the optimal virtual controller is obtained by satisfying the approximation function of the HJB equation If the optimal virtual controller is the unique solution of , then it needs to satisfy

[0130]

[0131] According to the fuzzy logic system the weight update rate is designed to make ​The reinforcement learning strategy is implemented and a practical optimal controller is successfully obtained, which is

[0132]

[0133] where ρ2,0>0 is a designed normal number, is the optimal real controller, represents the converted error related to state x2, and ψ2 represents a fuzzy base function, represents the estimation of the second Actor weight. represents the output of the filter. represents an adaptive parameter, and T represents the transpose of a matrix.

[0134] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0135] The principles and implementation modes of the present application are described by applying specific examples in this paper. The above description of the embodiments is only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation modes and application ranges will be changed according to the idea of the present application. In conclusion, the content of the specification should not be understood as a limitation of the present application.

Claims

1. An optimal tracking control method for protecting the transient performance of a maglev train, characterized in that: include: Determine the dynamic model of the suspended magnetic levitation according to the structure of the suspension frame; Determining a suspended maglev train model according to the suspended maglev dynamic model; Constructing a corresponding virtual controller according to the maglev train model; constructing a real controller based on the virtual controller; controlling the suspension air gap of the suspended maglev vehicle using the real controller; The step of constructing a corresponding virtual controller according to the maglev train model includes: Determining the constraint boundaries of the transient performance constraint scaling function of the suspended maglev train model, wherein the constraint boundaries include an upper boundary function and a lower boundary function; determining an error conversion of the suspended maglev train model according to the constraint boundary; constructing a corresponding virtual controller according to the error conversion; The expression of the upper boundary function is: ； The expression of the lower boundary function is: ； in, is the initial value of the tracking error, are the first design parameter, the second design parameter and the third design parameter respectively, is a sign function, is a constrained piecewise function, which is defined as follows: ； in, represents the convergence rate of the output error, is the initial value of the preset boundary, Indicates adjustment time. Represents the hyperbolic cosecant function.

2. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 1, characterized in that: The expression of the suspended magnetic levitation dynamic model is: ； in, represents the mass of the suspension, is the acceleration due to gravity, represents the distance between the magnetic pole face and the reference surface, Indicates the irregularity of the trajectory, Indicates the air permeability, is the area of ​​the core pole, represents the air gap between the magnetic poles and the guide rail, Indicates the number of turns of the electromagnet winding, Indicates the control coil current, is a controllable electromagnetic force, Indicates external interference, represents resistance, Indicates time.

3. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 2, characterized in that: The expression of the suspended maglev train model is: ； in, To control the gain, For control input, For disturbance, represents the output of the system, express About Time The first derivative of Indicates the status of the system, express About Time The first derivative of .

4. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 1, characterized in that: The expression of the virtual controller is: ； in, are the parameters to be designed, For virtual controllers, is the first-order derivative of the reference signal, represents the error after transformation, represents the fuzzy basis function, Indicates the first The weight estimate, Respectively represent the error The first and second functions obtained by derivation.

5. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 1, characterized in that: The step of constructing a real controller based on the virtual controller includes: Construct the performance index function related to the error and the true controller; The HJB equation is obtained based on the performance index function of the relevant error and the real controller; Based on the reinforcement learning strategy, the fuzzy logic system and the virtual controller are obtained Structured virtual controller equations; According to the The optimal real controller is obtained by combining the virtual controller equation and HJB equation of the structure.

6. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 5, characterized in that: The expression of the optimal true controller is: ； in, is the optimal true controller, is a positive constant, Indicates the status after conversion The relevant errors, represents the fuzzy basis function, Indicates the second The weight estimate, represents the output of the filter, represents the adaptive parameter, Represents the control gain, which is an adjustable parameter.

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