A BP neural network-based self-disturbance control method for a maglev train suspension system

Abstract

The application relates to a BP neural network-based self-disturbance control method for a maglev train suspension system. The method comprises the following steps: approximating the maglev train suspension system at an equilibrium point as a second-order system by using linearization processing technology, adopting a third-order extended state observer to estimate the gap signal and the speed signal of the system output and realizing compensation on the disturbance; obtaining the tracking signal and the differential signal of the target signal by a tracking differentiator, and forming corresponding error signals with the obtained signals; inputting the obtained error signals into a PD controller, feeding back and compensating the output of the controller by the extended state observer, and obtaining the input signal of the system; applying the input signal of the system to the suspension system, suspending the vehicle body on the track and obtaining the output signal of the system; transmitting the error signal and the output signal of the system to a BP neural network to optimize the parameters of the extended state observer; and repeating the above steps. The application realizes the control of the maglev train suspension system with strong anti-disturbance and real-time and accurate estimation of the disturbance.

Description

Technical Field

[0001] This invention relates to the field of maglev train suspension control technology, specifically to a method for active disturbance rejection control of maglev train suspension system based on BP neural network. Background Technology

[0002] Maglev trains are a new type of rail transit that uses electromagnetic levitation technology to achieve contactless levitation between the vehicle and the track. They offer advantages such as high speed, low noise, and low maintenance costs. The core subsystem of a maglev train is the levitation system, which controls the levitation gap between the vehicle and the track in real time to maintain a stable levitation state. The key is to adjust the levitation force of the train through a levitation controller to achieve balance with gravity (this state is called the equilibrium point).

[0003] The levitation system is a strongly coupled, non-minimum phase system, inherently exhibiting strong nonlinearity. Furthermore, in actual operation, maglev trains are susceptible to multi-source disturbances. These disturbances may originate from weather conditions, track unevenness, vehicle load variations, and other factors, adversely affecting the levitation system and leading to changes in the levitation gap and instability. Controllers designed based on an equilibrium point only exhibit good control performance near that point; their performance deteriorates when the system operates far from the equilibrium point. Their fixed parameter characteristics prevent them from demonstrating good control quality in environments with varying disturbances.

[0004] Therefore, designing a control method for maglev train suspension systems that has strong anti-disturbance capabilities and accurate real-time estimation of disturbances has become an urgent problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies in the levitation control of maglev trains and to provide an active disturbance rejection control method for maglev train levitation systems based on BP neural networks. Compared with traditional active disturbance rejection control methods, this method embeds BP neural networks into an extended state observer, thereby improving the estimation accuracy of disturbances and further enhancing the controller's disturbance rejection capability.

[0006] To achieve the above objectives, the technical solution of this invention is: a method for active disturbance rejection control of a maglev train levitation system based on a BP neural network. This method uses an active disturbance rejection controller as a framework and employs a BP neural network to adjust the parameters of an extended state observer in real time online, thereby achieving stable control of the maglev train levitation system. The method includes the following steps:

[0007] Step 1: Using linearization technology, the maglev train suspension system is approximated as a second-order system at the equilibrium point. An extended state observer is used to estimate the gap signal and speed signal output by the system and to compensate for disturbances.

[0008] Step 2: Obtain the tracking signal and the differential signal of the target signal through the tracking differentiator, and form a corresponding error signal with the signal obtained in Step 1;

[0009] Step 3: Input the error signal obtained in Step 2 into the PD controller. The extended state observer performs feedback compensation on the controller's output to obtain the system's input signal.

[0010] Step 4: Apply the system input signal to the maglev train levitation system, and the train body levitates on the track and obtains the system output signal;

[0011] Step 5: Pass the error signal from Step 2 and the system output signal from Step 4 to the BP neural network. Optimize the extended state observer parameters through the learning ability of the BP neural network to improve the estimation accuracy of the total disturbance.

[0012] Step 6: Repeat steps 1 to 5.

[0013] In one embodiment of the present invention, step 1 specifically includes:

[0014] This invention studies the levitation system of a maglev train. Each carriage contains multiple levitation points, each located below the edge of the carriage body and equipped with a gap sensor, an acceleration sensor, and a levitation electromagnet. Each levitation point has the same structure and is not coupled to others; therefore, this invention studies and analyzes the single-point levitation system as the controlled object. Combining principles of electrical engineering and dynamics, the single-point levitation system model can be represented as:

[0015]

[0016] Where s is the gap between the levitation electromagnet and the track; g is the acceleration due to gravity; m represents the mass of the train body at a single point; i is the current in the electromagnet coil; f is the total disturbance acting on the system; R is the equivalent resistance of the electromagnet coil; the parameter k can be expressed as:

[0017]

[0018] Where μ0 is the free permeability; N is the number of turns of the coil; A m This represents the effective pole area of ​​the electromagnetic coil.

[0019] This invention utilizes an Active Disturbance Rejection Controller (ADRC) as a levitating controller, which possesses advantages such as independence from mathematical models, strong disturbance rejection, and small overshoot. The ADRC primarily consists of a tracking differentiator (TD), an extended state observer (ESO), and a PD controller. Furthermore, this invention incorporates a backpropagation (BP) neural network as part of the ADRC. The BP neural network's role in the ADRC is parameter optimization. By learning real-time system response and error information, the neural network adaptively adjusts the ESO parameters to better adapt to the system's dynamic characteristics and changing operating conditions.

[0020] For a single-point levitation system, due to the high frequency characteristics of the current loop, it can be divided into two parts: a current loop and a gap loop. The current loop can be considered as a proportional element through loop correction. After linearization, a Taylor expansion of the nonlinear dynamic equations of the gap loop yields a second-order system:

[0021]

[0022] Where y1 and y2 are the system's gap signal and velocity signal, respectively; s0 in the above equation can be expressed as:

[0023]

[0024] Where i0 and u0 are the current and voltage at the equilibrium point, respectively; u is the system input signal; R k This is the proportionality coefficient between voltage and current.

[0025] For this second-order system, an extended state observer can be constructed:

[0026]

[0027] Where h is the step size; y is the system output signal; z1 is the estimated value of y; and z2 is... The estimated value of z3 is the total disturbance input; u is the system input signal; β is the estimated value of z3. 01 ,β 02 ,β 03 The design parameters for extended state observation are: b is the external input variable; the fal function expression is:

[0028]

[0029] Where x is the error between the expected value and the estimated value; a and δ are user-defined parameters; sign(x) is the sign function, which returns 0 when x = 0, 1 when x > 0, and -1 when x < 0.

[0030] In one embodiment of the present invention, step 2 specifically includes:

[0031] The tracking differentiator can be expressed as:

[0032]

[0033] Where v is the input signal; x1 is the tracking signal of v; x2 is the derivative of x1; r is the velocity factor; h is the integration time; c0 is the filter factor; and fhan is the fastest synthesis function, the specific expression of which is as follows:

[0034]

[0035] Therefore, the following error signal can be obtained:

[0036]

[0037] In one embodiment of the present invention, step 3 specifically includes:

[0038] For a single-point suspension system, a PD controller can be used for control:

[0039] u0 = k p e1+k d e2(10)

[0040] Where, k p and k d For proportional gain and derivative gain. Introduce controller bandwidth w. c The results were obtained through pole configuration. k d =2w c The system input signal is obtained by feedback compensation of the controller's output signal u0:

[0041]

[0042] Where b is the control gain of the maglev train's levitation system;

[0043] In one embodiment of the present invention, step 4 specifically includes:

[0044] The signal u from step 3 is input into the single-point suspension system, the vehicle body is suspended on the track and the system output signal is obtained.

[0045] In one embodiment of the present invention, step 5 specifically includes:

[0046] A BP network is constructed to achieve parameter adjustment of the extended state observer. This BP neural network contains 4 input layer nodes, 5 hidden layer nodes and 3 output layer nodes.

[0047] The input layer consists of the error signals e1 and e2 from step 2, the system output signal yout from step 4, and a bias term:

[0048] I i =[e1,e2,yout,1](12)

[0049] The input S of the hidden layer k and output z k Represented as:

[0050]

[0051] z k =f(S) k (14)

[0052] Where i is the i-th input layer node; k is the k-th hidden layer node; v ki The weights between the input layer and the hidden layer are: The activation function f(·) of the hidden layer is:

[0053] The input S of the output layer j and output y j Represented as:

[0054]

[0055] y j =g(S j (16)

[0056] Where j is the j-th output layer node; q is the number of hidden layer nodes; ω jk The weights between the hidden layer and the output layer are: The activation function of the output layer is:

[0057] The three parameters β of the extended state observer 01 ,β 02 ,β 03 It can be represented as:

[0058]

[0059] Among them, gain 1,2,3 This is the gain term.

[0060] Construct the loss function E:

[0061]

[0062] Where m is the number of output layer nodes; t j The target value;

[0063] Gradient descent is used to backpropagate the BP neural network to update the network's weights and biases, thereby gradually reducing the network's error. This is expressed as:

[0064]

[0065] Where η is the learning rate; f'(S j ) is the derivative of the activation function of the hidden layer; g'(S) j Let be the derivative of the output layer activation function; the weight update formula is:

[0066]

[0067] Where n is the time; Δω(n) can be represented by any weight; and α is the momentum factor.

[0068] In one embodiment of the present invention, step 6 specifically includes:

[0069] Repeat steps 1 to 5 above, use a BP neural network to optimize the extended state observer, adjust parameters in real time to improve estimation accuracy, and thus improve the performance of the active disturbance rejection controller.

[0070] Compared to existing technologies, this invention offers the following advantages: This invention provides an active disturbance rejection control method for a maglev train levitation system based on a BP neural network. Compared to traditional active disturbance rejection control methods, this method embeds a BP neural network into an extended state observer, thereby improving the estimation accuracy of disturbances and further enhancing the controller's disturbance rejection capability. This invention achieves maglev train levitation system control with strong disturbance rejection and accurate real-time disturbance estimation. Attached Figure Description

[0071] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0072] Figure 1 Block diagram of active disturbance rejection control for maglev train suspension system based on BP neural network.

[0073] Figure 2 BP neural network structure diagram.

[0074] Figure 3 Comparison of system output response curves.

[0075] Figure 4 Comparison of system output response curves under disturbance.

[0076] Figure 5 Extended state observer adaptive parameters. Detailed Implementation

[0077] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0078] like Figure 1 As shown, this invention provides an active disturbance rejection control method for a maglev train levitation system based on a BP neural network. This method uses an active disturbance rejection controller as a framework and employs a BP neural network to adjust the parameters of an extended state observer in real time online, thereby achieving stable control of the maglev train levitation system. The method includes the following steps:

[0079] Step 1: The research content of this invention is the levitation system of a maglev train. Each carriage of the train contains multiple levitation points, each located below the edge of the carriage body and equipped with a gap sensor, an acceleration sensor, and a levitation electromagnet. Each levitation point has the same structure and is not coupled to each other. Therefore, this invention studies and analyzes the single-point levitation system as the controlled object. Combining the principles of electrical engineering and dynamics, the single-point levitation system model can be represented as:

[0080]

[0081] Where s is the gap between the levitation electromagnet and the track; g is the acceleration due to gravity; m represents the mass of the train body at a single point; i is the current in the electromagnet coil; f is the total disturbance acting on the system; R is the equivalent resistance of the electromagnet coil; the parameter k can be expressed as:

[0082]

[0083] Where μ0 is the free permeability; N is the number of turns of the coil; A m This represents the effective pole area of ​​the electromagnetic coil.

[0084] This invention utilizes an Active Disturbance Rejection Controller (ADRC) as a levitating controller, which possesses advantages such as independence from mathematical models, strong disturbance rejection, and small overshoot. The ADRC primarily consists of a tracking differentiator (TD), an extended state observer (ESO), and a PD controller. Furthermore, this invention incorporates a backpropagation (BP) neural network as part of the ADRC. The BP neural network's role in the ADRC is parameter optimization. By learning real-time system response and error information, the neural network adaptively adjusts the ESO parameters to better adapt to the system's dynamic characteristics and changing operating conditions.

[0085] Step 2: For a single-point levitation system, due to the high frequency characteristics of the current loop, it can be divided into two parts: a current loop and a gap loop. The current loop can be considered as a proportional element through loop correction. After linearization, the nonlinear dynamic equations of the gap loop are Taylor-expanded to obtain a second-order system:

[0086]

[0087] Where y1 and y2 are the system's gap signal and velocity signal, respectively; s0 in the above equation can be expressed as:

[0088]

[0089] Where i0 and u0 are the current and voltage at the equilibrium point, respectively; u is the system input signal; R k This is the proportionality coefficient between voltage and current.

[0090] For this second-order system, an extended state observer can be constructed:

[0091]

[0092] Where h is the step size; y is the system output signal; z1 is the estimated value of y; and z2 is... The estimated value of z3 is the total disturbance input; u is the system input signal; β is the estimated value of z3. 01 ,β 02 ,β 03 The design parameters for extended state observation are: b is the external input variable; the fal function expression is:

[0093]

[0094] Where x is the error between the expected value and the estimated value; a and δ are user-defined parameters; sign(x) is the sign function, which returns 0 when x = 0, 1 when x > 0, and -1 when x < 0.

[0095] Step 3: The form of the tracking differentiator can be expressed as:

[0096]

[0097] Where v is the input signal; x1 is the tracking signal of v; x2 is the derivative of x1; r is the velocity factor; h is the integration time; c0 is the filter factor; and fhan is the fastest synthesis function, the specific expression of which is as follows:

[0098]

[0099] Therefore, the following error signal can be obtained:

[0100]

[0101] Step 4: For a single-point suspension system, a PD controller can be used for control.

[0102] u0 = k p e1+k de2(10)

[0103] Where, k p and k d For proportional gain and derivative gain. Introduce controller bandwidth w. c The results were obtained through pole configuration. k d =2w c The system input signal is obtained by feedback compensation of the controller's output signal u0:

[0104]

[0105] Where b is the control gain of the maglev train's levitation system;

[0106] Step 5: Input the signal u from step 4 into the single-point suspension system, and the vehicle body will be suspended on the track and the system output signal will be obtained.

[0107] Step 6: Construct a BP network to adjust the parameters of the extended state observer. (See [link]) Figure 2 This BP neural network contains 4 input layer nodes, 5 hidden layer nodes, and 3 output layer nodes.

[0108] The input layer consists of the error signals e1 and e2 from step 3, the system output signal yout from step 5, and a bias term:

[0109] I i =[e1,e2,yout,1](12)

[0110] The input S of the hidden layer k and output z k Represented as:

[0111]

[0112] z k =f(S) k (14)

[0113] Where i is the i-th input layer node; k is the k-th hidden layer node; v ki The weights between the input layer and the hidden layer are: The activation function f(·) of the hidden layer is:

[0114] The input S of the output layer j and output y j Represented as:

[0115]

[0116] y j =g(S j (16)

[0117] Where j is the j-th output layer node; q is the number of hidden layer nodes; ω jk The weights between the hidden layer and the output layer are: The activation function of the output layer is:

[0118] The three parameters β of the extended state observer 01 ,β 02 ,β 03 It can be represented as:

[0119]

[0120] Among them, gain 1,2,3 This is the gain term.

[0121] Construct the loss function E:

[0122]

[0123] Where m is the number of output layer nodes; t j This is the target value.

[0124] Gradient descent is used to backpropagate the BP neural network to update the network's weights and biases, thereby gradually reducing the network's error. This is expressed as:

[0125]

[0126] Where η is the learning rate; f'(S j ) is the derivative of the activation function of the hidden layer; g'(S) j Let be the derivative of the output layer activation function; the weight update formula is:

[0127]

[0128] Where n is the time; Δω(n) can be represented by any weight; and α is the momentum factor.

[0129] Step 7: Repeat steps 2 to 6 above, use a BP neural network to optimize the extended state observer, adjust parameters in real time to improve estimation accuracy, thereby improving the performance of the active disturbance rejection controller.

[0130] Simulation and Experiment Description

[0131] To verify the effectiveness of the active disturbance rejection control of the maglev train suspension system based on BP neural network proposed in this invention, including the anti-interference effect of the extended state observer based on BP neural network, the following maglev train suspension control experiment is used to illustrate this.

[0132] In the control effect experiment of the active disturbance rejection controller algorithm based on BP neural network, the bandwidth ω of the PD controller is taken as... c =144, with a step size h=0.0002, the parameters of the expanded state observer are... In designing the BP neural network, the learning rate η = 0.2 and the momentum factor α = 0.02 are chosen. The algorithm is compared with the classic active disturbance rejection controller algorithm, and the system output response curve is shown below. Figure 3 As shown. Simultaneously, a disturbance test was conducted, increasing the load on the maglev train between 0.4s and 0.8s. The system output response curve is shown below. Figure 4 As shown. Figure 5 As shown, the three parameters of the extended state observer can be adjusted in real time according to the disturbance, verifying the feasibility of using a BP neural network to adjust the parameters of the ESO and the superiority of the control effect.

[0133] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A BP neural network-based self-disturbance control method for a magnetic levitation train suspension system, characterized in that, This method uses an active disturbance rejection controller as a framework and employs a BP neural network to adjust the parameters of the extended state observer in real time to achieve stable control of the maglev train's levitation system. The method includes the following steps: Step 1: Using linearization technology, the maglev train suspension system is approximated as a second-order system at the equilibrium point. An extended state observer is used to estimate the gap signal and speed signal output by the system and to compensate for disturbances. Step 2: Obtain the tracking signal and the differential signal of the target signal through the tracking differentiator, and form a corresponding error signal with the signal obtained in Step 1; Step 3: Input the error signal obtained in Step 2 into the PD controller. The extended state observer performs feedback compensation on the controller's output to obtain the system's input signal. Step 4: Apply the system input signal to the maglev train levitation system, and the train body levitates on the track and obtains the system output signal; Step 5: Pass the error signal from Step 2 and the system output signal from Step 4 to the BP neural network. Optimize the extended state observer parameters through the learning ability of the BP neural network to improve the estimation accuracy of the total disturbance. Step 6: Repeat steps 1 through 5; The specific implementation method for step 1 is as follows: In the levitation system of a maglev train, each carriage contains multiple levitation points. Each levitation point is located below the edge of the carriage and is equipped with a gap sensor, an acceleration sensor, and a levitation electromagnet. Each levitation point has the same structure and is not coupled to each other. Taking the single-point levitation system as the controlled object, the single-point levitation system model is represented as follows: wherein, is the gap between the levitation electromagnet and the track; is the acceleration due to gravity; denotes the mass of the maglev car body at a single point; is the current in the levitation electromagnet coil; is the total disturbance acting on the system; is the equivalent resistance of the electromagnet coil; parameter is denoted as: in, Permeability of free space; This represents the number of turns in the coil. The effective pole area of ​​the electromagnetic coil; For a single-point levitation system, it is divided into two parts: a current loop and a gap loop. The current loop is treated as a proportional element through loop correction. After linearization, the nonlinear dynamic equations of the gap loop are Taylor expanded to obtain a second-order system. in , These are the system's gap signal and velocity signal, respectively; in the above formula... Represented as: in , These are the current and voltage at the equilibrium point, respectively; The input signal of the system; The proportionality coefficient between voltage and current; For a second-order system, construct an extended state observer: in, Step size; This is the system's output signal; for The estimated value; for The estimated value; This is an estimate of the total disturbance input. The input signal of the system; , , Design parameters for the extended state observer; For external input variables; The function expression is: in, The error between the expected value and the estimated value; and For custom parameters; For a sign function, when When, the function returns 0; when When, the function returns 1; when When the time is right, the function returns -1.

2. The active disturbance rejection control method for a maglev train levitation system based on a BP neural network according to claim 1, characterized in that, The specific implementation method for step 2 is as follows: The tracking differentiator is represented in the following form: in, For input signals; for The tracking signal for The differential, For velocity factor, For integration time, For the filter factor, The fastest synthesis function is expressed as follows: Therefore, the following error signal is obtained: 。 3. The active disturbance rejection control method for a maglev train levitation system based on a BP neural network according to claim 2, characterized in that, The specific implementation method for step 3 is as follows: For a single-point suspension system, a PD controller can be used for control: in, and To account for the proportional gain and derivative gain, a controller bandwidth is introduced. The results were obtained through pole configuration. , By controlling the output signal of the PD controller The system input signal is obtained by performing feedback compensation: in This refers to the control gain of the maglev train's levitation system.

4. The active disturbance rejection control method for a maglev train levitation system based on a BP neural network according to claim 3, characterized in that, Step 5 is implemented as follows: A BP neural network is constructed to achieve parameter adjustment of the extended state observer. The BP neural network includes 4 input layer nodes, 5 hidden layer nodes, and 3 output layer nodes. The input layer consists of the error signal from step 2. and The system output signal in step 4 And a bias term: Input of hidden layer and output Represented as: in, For the first One input layer node; This represents the number of nodes in the input layer. For the first One hidden layer node; The weights between the input layer and the hidden layer; the activation function of the hidden layer. for: ; Input of the output layer and output Represented as: in, For the first Each output layer node; This represents the number of hidden layer nodes. The weights between the hidden layer and the output layer are: The activation function of the output layer is: ; Three parameters of the extended state observer , , Represented as: in, For gain terms; Constructing the loss function : in, This represents the number of nodes in the output layer. The target value; Gradient descent is used to backpropagate the BP neural network to update the network's weights and biases, thereby gradually reducing the network's error. This is expressed as: in, The learning rate; The derivative of the activation function in the hidden layer; The derivative of the output layer activation function is given; the weight update formula is: in, For a specific moment; Represented as any weight; This is the momentum factor.

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