Optimal tracking control method for protecting transient performance of magnetically levitated train

Abstract

The invention provides an optimal tracking control method for protecting transient performance of a magnetically levitated train, and relates to the technical field of magnetically levitated trains. Comprising the following steps: determining a magnetic suspension dynamic model according to the structure of a 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 according to the virtual controller; and controlling the suspension air gap of the magnetic suspension vehicle by using the real controller. According to the invention, the problems of inconsistent suspension gap output, high cost and low resource utilization rate of suspension magnetic suspension control in the prior art are solved.

Description

Technical Field

[0001] The invention relates to the technical field of maglev trains, in particular to an optimal tracking control method for protecting the transient performance of maglev trains. Background Art

[0002] At present, most medium and low-speed maglev trains adopt a four-suspension structure. Each suspension frame is independently controlled by four suspension controllers. However, each suspension point operates independently of each other. Under the influence of factors such as uneven load distribution in the train and random unevenness of the track, there will be problems such as inconsistent suspension gap output, and even overall resonance of the suspension, affecting the riding comfort of passengers. Therefore, it is particularly important to design a control algorithm to improve the transient performance of maglev trains. At the same time, in the actual environment, maglev trains will inevitably be affected by some random interference factors, which will reduce the normal operation of maglev trains. In order to avoid the influence of interference, control methods with anti-interference ability are worthy of further exploration. In addition, with the rapid development of science and technology today, resource waste and energy consumption are urgent problems to be solved in our development process. Designing a control algorithm to improve resource utilization has attracted widespread attention from researchers at home and abroad. If there are insufficient or limited resources, the traditional adaptive backstepping control strategy is no longer applicable. At the same time, excessive resource waste will bring high costs. Summary of the invention

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

[0004] To achieve the above object, the present invention provides the following solutions:

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

[0006] Determine the dynamic model of the suspended magnetic levitation according to the structure of the suspension frame;

[0007] Determining a suspended maglev train model according to the suspended maglev dynamic model;

[0008] Constructing a corresponding virtual controller according to the maglev train model;

[0009] constructing a real controller based on the virtual controller;

[0010] The real controller is used to control the suspension air gap of the suspended maglev vehicle.

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

[0012]

[0013] Where m represents the mass of the suspension, g is the gravitational acceleration, z(t) represents the distance between the magnetic pole surface and the reference surface, h(t) represents the trajectory irregularity, μ0 = 4π×10 -7 H / m represents the permeability of air, A is the area of ​​the magnetic 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, and f d represents external interference, R represents resistance, and t represents time.

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

[0015]

[0016] in, 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 derivative of x2 with respect to time t.

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

[0018] Determining the constraint boundary of the transient performance constraint scale function of the suspended maglev train model, wherein the constraint boundary includes an upper boundary function and a lower boundary function;

[0019] Determining an error conversion of the suspended maglev train model with the constraint boundary;

[0020] A corresponding virtual controller is constructed according to the error conversion.

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

[0022]

[0023] Among them, 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, and κ is a constrained 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))(κ-κ ∞ )+μ2κ.

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

[0029]

[0030] Among them, ρ1 is the parameter to be designed, For virtual controllers, is the first-order derivative of the reference signal, represents the error after transformation, ψ1 represents the fuzzy basis function, represents the estimate of the first Actor weight, σ1, σ2 represent the error The first function and the second function are obtained by derivation, and T represents the transpose of the matrix.

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

[0032] Construct performance index functions related to the error and the true controller;

[0033] The HJB equation is obtained according to the performance index function of the relevant error and the real controller;

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

[0035] The optimal real controller is obtained according to the virtual controller equation of the Actor-Critic structure and the HJB equation.

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

[0037]

[0038] in, is the optimal true controller, ο is a positive constant, represents the error related to the state x2 after transformation, ψ2 represents the fuzzy basis function, Represents an estimate of the second Actor's weight. Represents the output of the filter. represents the adaptive parameter, ρ2 represents the control gain, which is an adjustable parameter, and T represents the transpose of the matrix.

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

[0040] The present invention provides an optimal tracking control method for protecting the transient performance of a maglev train, comprising: determining a suspended maglev dynamic model according to the structure of a suspension frame; determining a suspended maglev train model according to the suspended maglev dynamic model; constructing a corresponding virtual controller according to the suspended maglev train model; constructing a real controller according to the virtual controller; and controlling the suspension air gap of the suspended maglev vehicle using the real controller. The present invention is directed to the mathematical model of the maglev train system, and considers how to design an adaptive transient performance constrained optimal controller to limit the suspension air gap of the maglev vehicle within a safe range while reducing the communication burden, thereby improving resource utilization, and enabling the suspended train to track the target trajectory within a certain period of time and ensure tracking stability. First, based on the maglev train model, it is accurately modeled to obtain a more practical system. Secondly, with the help of reinforcement learning strategy and stability theory in the sense of Lyapunov, using dynamic surface technology, approximation technology of fuzzy logic system, and scaling method of Young's inequality, transient performance boundary constraint function and adaptive transient performance constraint optimal controller are designed for the system under consideration. The designed controller can not only smoothly realize safe control when the system is disturbed and constrained, but also save communication resources and reduce communication burden; the designed optimization controller can not only smoothly realize safe control when the system is disturbed and constrained, but also save communication resources and reduce communication burden; the designed transient performance constraint optimal control algorithm enables the trajectory tracking error of the maglev train to be constrained in a predetermined area and ensure the tracking stability; the simplified structure of the maglev system can reduce economic costs. At the same time, the optimal control algorithm based on reinforcement learning strategy can improve the work efficiency of the system and achieve the desired tracking control target with the lowest cost, which has important practical application value for improving the control performance of maglev. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0042] Figure 1 A schematic flow chart of an optimal tracking control method for protecting the transient performance of a maglev train provided by an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of an optimal tracking control method strategy for protecting the transient performance of a maglev train provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work 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 Figure 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: determining a magnetic levitation dynamic model according to the structure of the suspension frame;

[0048] Step 200: determining 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 according to the virtual controller;

[0051] Step 500: Control the suspension air gap of the suspended 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 magnetic leakage and rail reluctance, the magnetic core and effective air gap reluctance 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 is the total magnetic flux, Φ T represents the main magnetic flux. The energy stored in the magnetic field is

[0059]

[0060] Where W represents the energy stored in the magnetic field. The controllable electromagnetic force F(i,c) is

[0061]

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

[0063]

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

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

[0066]

[0067] Where m represents the mass of the suspension, g is the gravitational acceleration, z(t) represents the distance between the magnetic pole surface and the reference surface, h(t) represents the trajectory irregularity, μ0 = 4π×10 -7 H / m represents the permeability of air, A is the area of ​​the magnetic 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, and f d represents external interference, R represents resistance, and t represents time.

[0068] Specifically, the expression of the suspended maglev train model is:

[0069]

[0070] in, 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 derivative of x2 with respect to time t.

[0071]

[0072] Furthermore, the step of constructing a corresponding virtual controller according to the maglev train model includes:

[0073] Determining the constraint boundary of the transient performance constraint scale function of the suspended maglev train model, wherein the constraint boundary includes an upper boundary function and a lower boundary function;

[0074] Determining an error conversion of the suspended maglev train model with the constraint boundary;

[0075] A corresponding virtual controller is constructed according to the error conversion.

[0076] Specifically, the constraint boundary of the transient performance constraint scale function is defined. Continuous constraint boundary function b The following conditions are met: and b They are all increasing functions, and for T0>0, they are strictly increasing in [0,T0].

[0077] For T0>0,

[0078] Where T0 is the residence time. 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] Among them, 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 constrained piecewise function, which is defined as follows:

[0082]

[0083] Where n represents the convergence rate of the output error and κ0 is 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] Among them, e(0) is the initial value of the tracking error, κ ∞ , μ1, μ2 are the designed parameters, sign(·) is the sign function, and:

[0087]

[0088] Where n represents the convergence rate of the output error and κ0 is the initial value of the preset boundary.

[0089] Define a fuzzy logic system that approximates nonlinear functions. A fuzzy logic system consists of a fuzzy rule base, fuzzification and defuzzification operators. The fuzzy rule base consists of inference rules. x1 is x2 is yes 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 is a fuzzy set on the real number field; combined with the theory of fuzzy logic system, the output of the fuzzy system is expressed as

[0090] in, is the point that maximizes the function By order ψ=[ψ 1 ,ψ 2 ,...,ψ m ] T and Available

[0091] y(x)=Γ T ψ+ε.

[0092] Define the error transformation for the maglev train system.

[0093]

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

[0095]

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

[0097] The derivative of the error is then solved.

[0098]

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

[0100] Using the definition of error conversion and filtering, we get:

[0101]

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

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

[0104]

[0105] Among them, ρ1 is the parameter to be designed, For virtual controllers, is the first-order derivative of the reference signal, represents the error after transformation, ψ1 represents the fuzzy basis function, represents the estimate of the first Actor weight, σ1, σ2 represent the error The first function and the second function are obtained by derivation, and T represents the transpose of the matrix.

[0106] At the same time, the actor-critic weight update rate and Adaptive Law Designed to:

[0107]

[0108] in are the parameters to be designed.

[0109] Furthermore, constructing a real controller according to the virtual controller includes:

[0110] Construct performance index functions related to the error and the true controller;

[0111] The HJB equation is obtained according to the performance index function of the relevant error and the real controller;

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

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

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

[0115]

[0116] in, and is the cost function. The HJB equation is to find the time derivative of the performance index function, so the HJB equation for each step is as follows:

[0117]

[0118] in, yes and The gradient involved.

[0119] First, construct the performance index function of the error and controller Then, the derivative of the performance index function with respect to time t is obtained to obtain the HJB equation:

[0120]

[0121] Using equations Get the controller The gradient Rewritten Bring it into the controller and get

[0122]

[0123] because is unknown, and we use the fuzzy logic system to approximate it and get

[0124]

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

[0126]

[0127] Substituting into the HJB equation we get So for

[0128]

[0129] According to the optimal control design, the optimal virtual controller To satisfy the approximation function of the HJB equation If the optimal virtual controller yes The only solution of , then it needs to satisfy,

[0130]

[0131] According to the fuzzy logic system By designing the weight update rate The reinforcement learning strategy was implemented and the actual optimal controller was successfully obtained. The actual optimal controller is:

[0132]

[0133] Among them, ρ2,ο>0 is a designed positive constant, is the optimal true controller, represents the error related to the state x2 after transformation, ψ2 represents the fuzzy basis function, Represents an estimate of the second Actor's weight. Represents the output of the filter. represents the adaptive parameter, and T represents the transpose of the matrix.

[0134] The various embodiments in this 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 referenced to each other.

[0135] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

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; The real controller is used to control the suspension air gap of the suspended maglev vehicle.

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 maglev dynamic model is: Where m represents the mass of the suspension, g is the gravitational acceleration, z(t) represents the distance between the magnetic pole surface and the reference surface, h(t) represents the trajectory irregularity, μ0 = 4π×10 -7 H / m represents the permeability of air, A is the area of ​​the magnetic 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, and f d represents external interference, R represents resistance, and t represents 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, is the control gain, g is the control input, d is the disturbance, 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 derivative of x2 with respect to time t.

4. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 3, characterized in that: The step of constructing a corresponding virtual controller according to the suspended maglev train model comprises: Determining the constraint boundary of the transient performance constraint scale function of the suspended maglev train model, wherein the constraint boundary includes an upper boundary function and a lower boundary function; Determining an error conversion of the suspended maglev train model with the constraint boundary; A corresponding virtual controller is constructed according to the error conversion.

5. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 4, characterized in that: The expression of the upper boundary function is: Among them, 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, and κ is a constrained piecewise function, which is defined as follows: Where n represents the convergence rate of the output error, κ0 is the initial value of the preset boundary, T0 represents the adjustment time, and csch represents the hyperbolic cosecant function.

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 lower boundary function is: b=sign(e(0))(k-k ∞ )+m2k.

7. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 6, characterized in that: The expression of the virtual controller is: Among them, ρ1 is the parameter to be designed, For virtual controllers, is the first-order derivative of the reference signal, represents the error after transformation, ψ1 represents the fuzzy basis function, represents the estimate of the first Actor weight, σ1, σ2 represent the error The first function and the second function are obtained by derivation, and T represents the transpose of the matrix.

8. 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 according to the virtual controller comprises: Construct performance index functions related to the error and the true controller; The HJB equation is obtained according to the performance index function of the relevant error and the real controller; Based on the reinforcement learning strategy, a virtual controller equation of an Actor-Critic structure is obtained according to the fuzzy logic system and the virtual controller; The optimal real controller is obtained according to the virtual controller equation of the Actor-Critic structure and the HJB equation.

9. The optimal tracking control method for protecting the transient performance of a maglev train according to claim 7, characterized in that: The expression of the optimal true controller is: in, is the optimal true controller, ο is a positive constant, represents the error related to the state x2 after transformation, ψ2 represents the fuzzy basis function, represents the estimate of the second Actor's weight, represents the output of the filter, represents the adaptive parameter, ρ2 represents the control gain, which is an adjustable parameter, and T represents the transpose of the matrix.

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