Motor system identification method based on neural network fitting model mechanism form conversion

Abstract

The application discloses a motor system identification method based on a neural network fitting model mechanism form conversion, and realizes a method for identifying mechanical characteristic parameters of a permanent magnet synchronous motor (hereinafter, motors refer to the motor). The neural network is used to learn the evolution law of the state of the motor system under the controlled action, and the motor mechanical characteristics are fitted. Through dynamic linearization and local linearization and other approximate conversion approaches, the neural network model is converted into a mechanism / mechanism model of the motor mechanical characteristics in the form of state transition. The dynamic learning of the neural network realizes real-time, accurate and continuous self-learning identification and tracking of part parameters of the motor. The method can solve the problems of real-time and accurate modeling and mathematical expression of unknown, time-varying, strongly coupled and highly nonlinear motor systems on the basis of lacking prior knowledge and mechanism analysis, provides a mathematical model for the design of a classical, modern and advanced control system controller, provides a qualitative and quantitative analysis basis for motor control based on the neural network, and can be widely applied to various types of motor control technologies.

Description

TECHNICAL FIELD

[0001] The application is a permanent magnet synchronous motor system identification method, which can be widely applied to motor control scheme design with inaccurate motor system modeling and complex environmental disturbance, and improves the motor control performance. BACKGROUND

[0002] Permanent magnet synchronous motor has the characteristics of time-varying, nonlinearity and strong coupling. It is widely used in high-precision position servo systems due to its high power density, low loss, small torque fluctuation and easy maintenance. Under various tasks and load conditions, the permanent magnet synchronous motor is required to have the control quality of timely response, small control overshoot, short control stable time, small control static error, and strong torque disturbance and load robustness.

[0003] The existing various control methods have a relatively mature control concept and qualitative and quantitative analysis design method. The construction of the control law needs to start from the analysis of the physical, chemical, electromagnetic and other kinematics and dynamics mechanism of the system, adopt the form of mathematical equation, establish and represent the balance relationship between the system input, external disturbance and system state, system output and the evolution law of the system with time. Through system stability analysis, the control law is designed around the control performance and cost constraints. For time-varying, nonlinear, strong coupling, multi-input, multi-output complex systems, there has always been a problem of accurate modeling of the system in the design of the controller.

[0004] The present application starts from the modeling design of motor mechanical characteristics, uses neural network to train the data generated by motor system, and converts the trained neural network into an equivalent isomorphic mechanism model. Similar motor system modeling technology has not been reported. SUMMARY

[0005] The technical problem to be solved by the present application is to correct the motor mechanical characteristic neural network non-mechanism model according to the input control parameters and state parameters, and the output state parameters. The motor system model is calculated by a mechanism form conversion method. This method has the advantages of good real-time coefficient identification, high accuracy and good generalization.

[0006] The technical scheme of the present application is: a motor system identification method based on neural network fitting model mechanism form conversion, comprising the following steps:

[0007] Considering the motor control needs and motor state measurement capability, the neural network input and output state quantities are determined, the motor mechanical characteristic equation is established in the continuous time system, and the discretized state transition matrix is obtained;

[0008] The neural network structure is constructed, and the neural network structure is converted into a mechanism state transition matrix which is isomorphic with the discretized state transition matrix obtained in step one;

[0009] According to the measurement or simulation data of the state quantity and the control quantity formed in the actual or simulation of the motor control, the neural network is trained and converted to obtain a final mechanism-like state transition matrix;

[0010] According to the measured data in the motor control, the mechanism-like state transition matrix is combined to obtain the output of the motor system in real time.

[0011] Preferably, the constructed neural network structure is a neural network structure conforming to the general paradigm of the motor system, specifically a neural network with a full connection structure, an input layer, an output layer, and a hidden layer.

[0012] Preferably, the conversion of the neural network structure into the mechanism-like state transition matrix isomorphic to the discretized state transition matrix obtained in step one includes:

[0013] According to the forward propagation process of the neural network, the input and output of the neurons in the hidden layer of the constructed neural network structure are unfolded to obtain an input and output unfolding expression of each neuron in the output layer;

[0014] The activation function of the neurons in the hidden layer of the neural network structure is approximated into a linear function expression form, the approximate expression is brought into the input and output unfolding expression of each neuron in the output layer, and the neural network input parameters and constant terms are arranged and simplified to obtain a simplified expression;

[0015] The input and output in the simplified expression are replaced by the fitting model expression obtained by the system state and the control action to obtain the mechanism-like state transition matrix.

[0016] Preferably, the approximation of the activation function of the neurons in the hidden layer of the neural network structure into a linear function expression form is:

[0017] f(x)≈a0+a1x

[0018] Wherein, a0, a1 vary with different activation functions and input values.

[0019] Preferably, the approximate expression is brought into the input and output unfolding expression of each neuron in the output layer to obtain an expression form:

[0020]

[0021] In the formula: A 01 is the constant approximation matrix of the hidden layer activation function, A 11 is the first-order approximation matrix of the hidden layer activation function, A 02 is the constant approximation matrix of the output layer activation function, A 12Φ1W1W2+B1B2+D

[0022] Φ1W1W2+B1B2+D

[0023] Y=ΦX+D

[0024] Φ1W1W2+B1B2+D

[0025] Φ1W1W2+B1B2+D

[0026] Φ1W1W2+B1B2+D k+1 Φ1W1W2+B1B2+D k+1,k Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D k+1,k Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D Φ1W1W2+B1B2+D

[0027] Φ1W1W2+B1B2+D k+1,k Φ1W1W2+B1B2+D k+1,k Φ1W1W2+B1B2+D k+1,k Φ1W1W2+B1B2+D k+1,k Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D k+1 Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D k+1 Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D k Φ1W1W2+B1B2+D Φ1W1W2+B1B2+D

[0028] Φ1W1W2+B1B2+D m Φ1W1W2+B1B2+D m Φ1W1W2+B1B2+D Φ1W1W2+B1B2+D

[0029] Φ1W1W2+B1B2+D Φ1W1W2+B1B2+D

[0030] The advantage of the present application is that a method for realizing permanent magnet synchronous motor (hereinafter referred to as motor) mechanical characteristic parameter identification by neural network fitting model class mechanism form conversion is disclosed. The evolution law of the motor system state under the controlled action is learned by using the neural network, and the motor mechanical characteristic is fitted. Through dynamic linearization and local linearization approximation conversion, the neural network model is converted into a state transition form of the motor mechanical characteristic mechanism / class mechanism model. The dynamic learning of the neural network is used to realize the real-time, accurate and continuous self-learning identification and tracking of the motor parameters. This method can solve the problems of real-time accurate modeling and mathematical expression of unknown, time-varying, strongly coupled and highly nonlinear motor systems without prior knowledge and mechanism analysis, and can provide a mathematical model for the design of classical, modern and advanced control system controllers, and can provide a qualitative and quantitative analysis basis for motor control based on neural networks, and can be widely applied to various types of motor control technology BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 BP neural network model diagram

[0032] Figure 2 Motor system identification block diagram based on neural network fitting model class mechanism form conversion. DETAILED DESCRIPTION

[0033] The present application will be further described below in combination with the drawings and examples.

[0034] The present application establishes a motor mechanical characteristic equation and obtains a discretized state transition matrix; a neural network structure is constructed, the neural network structure is converted into a class mechanism state transition matrix in the same expression form as the discretized state transition matrix; the influence mechanism of the control action on the system state is obtained, and the different control actions and system states are used as the input and output of the neural network to train the neural network, and the isomorphic equivalent form of the mechanism model is obtained according to the trained weight and bias, and high-precision modeling of the motor system is realized. The neural network structure of the present application conforms to the general paradigm of the motor system, so that the neural network non-mechanism fitting model of the motor system has the basis for conversion to the motor mechanism model, and the isomorphic form is established between the neural network fitting model and the motor mechanism model. The present application utilizes the continuous self-learning capability, and the neural network non-mechanism model can be continuously corrected, and the neural network continuously approximates the motor system, and the corresponding parameters in the class mechanism model converted by the neural network and the actual parameters in the isomorphic mechanism model will have consistent and equivalent convergence. The present application can correct the neural network non-mechanism model of the motor system in real time according to the measured data in the motor control, and realize real-time dynamic tracking and online identification of the motor parameters.

[0035] The neural network non-mechanism modeling of a certain motor mechanical characteristic model is introduced as follows:

[0036] Step one, considering the motor control needs and motor state measurement capabilities, determine the neural network input, output state quantity, in continuous time system, establish the motor mechanical property equation, and get the discrete state transition matrix;

[0037] In the d-q coordinate system, the motor mechanical property equation is

[0038] T e =1.5p[λi q +(L d -L q )i d i q ] (1)

[0039]

[0040]

[0041] In the formula, L d , L q is the d, q axis inductance, i d , i q is the d, q axis current, λ is the rotor permanent magnet on the stator side of the magnetic flux amplitude, p is the pole pair number, θ m is the rotor angle position, T e is the electromagnetic torque, J is the rotor moment of inertia, B is the viscous friction coefficient, T1 is the load torque, ω m is the rotor mechanical angular velocity.

[0042] For the hidden pole type permanent magnet synchronous motor, using i d =0 vector control strategy (same as maximum torque current ratio control) has:

[0043] T e =1.5pλi q (4)

[0044] According to formula (1), (2), (3), the state space form can be obtained by arranging:

[0045]

[0046] Among them, the state variable is X = [θ m ω m ] T , the control input is U2 = [i q ], the load Q = [T l ],

[0047] The state transition equation of the motor mechanical property is obtained by solving formula (5) and using power series approximation:

[0048] X(k+1)=A d2 X(k)+B d2 U2(k)+H d Q(k) (6)

[0049]

[0050] τ is the control period. High power terms can be reasonably selected based on accuracy requirements and computing power. It is easy to see that the system state is completely controllable.

[0051] Step 2: Construct a neural network structure and convert it into a mechanistic state transition matrix that is consistent with the discretized state transition matrix expression obtained in Step 1.

[0052] Introducing neural networks for non-mechanistic modeling of dynamic models without sacrificing generality. For example... Figure 1 The training data for the neural network shown is as follows. The neural network has an input layer of n neurons, a hidden layer of p neurons, and an output layer of q neurons.

[0053] Input layer vector X = [x1, x2, ..., x n ] T Hidden layer input vector H in =[h in,1 ,h in,2 ,…,h in,p ] T Hidden layer output vector H out =[h out,1 ,h out,2 ,…,h out,p ] T The input vector Y of the output layer in =(y in,1 ,y in,2 ,…,y in,q ) T The output layer vector is Y = (y1, y2, ..., y3). q ) T The connection weights w between the input layer and the hidden layer 1,ji (i = 1, 2, ..., n; j = 1, 2, ..., p), the connection weights w between the hidden layer and the output layer 2,kj (j=1,2,…,p;k=1,2,…,q), the activation functions of the hidden layer and the output layer are f(·), and the hidden layer bias B1=[b 11 ,b 12 ,…b 1p ] T Output layer bias B2 = [b 21 ,b 22 ,…b2q ] T .

[0054] The neural network forward propagation process, which is respectively for the input, output of neurons in the hidden layer:

[0055]

[0056] h out,j = f(h in,j + b 1j ),j = 1,2,…,p (11)

[0057] The specific expansion of it is as follows:

[0058]

[0059]

[0060] In the formula: W1 is the connection weight matrix of input layer and hidden layer; B1 is the hidden layer bias matrix.

[0061] Similarly, the input and output expression of each neuron in the output layer is as follows:

[0062]

[0063] y k = f(y in,k + b 2k ),k = 1,2,…,q (15)

[0064] The specific expansion of it is as follows:

[0065]

[0066]

[0067] In the formula: W2 is the connection weight matrix of hidden layer and input layer; B2 is the output layer bias matrix.

[0068] There are many different expressions of the activation function of the hidden layer neurons of the neural network, and here we take the most commonly used activation function Sigmoid function as an example to illustrate, the specific form is as follows:

[0069]

[0070] In order to realize the fitting of the state space form of the neural network, the Sigmoid is approximated as follows:

[0071] f(x)≈a0+a1x(19)

[0072] In the formula, a0 is a constant approximation term; a1 is a first-order approximation term, and a0 and a1 change with the activation function and the input value.

[0073] Substituting the obtained approximate expression (19) into the forward propagation process of the neural network, we get the following equation:

[0074]

[0075]

[0076] In the formula: A 01 Let A be the constant approximation matrix of the hidden layer activation function. 11 Let A be the first-order approximation matrix of the hidden layer activation function. 02 Let A be the constant approximation matrix of the output layer activation function. 12 is the first-order approximation matrix of the activation function of the output layer.

[0077] The simplified form of the above expression is obtained as follows:

[0078] Y=ΦX+D (22)

[0079] In the formula, Φ is the coefficient of the neural network input X, and D is a constant term.

[0080] Replace the input X and output Y of equation (22) with the system state X. k X k+1 With control U k The resulting fitted model expression is as follows:

[0081] X k+1 =Φ′ k+1,k X k +Q′ k+1,k U k +D k (twenty three)

[0082] In the formula Φ′ k+1,k To fit the system state matrix, Q′ k+1,k D is the control action coefficient matrix obtained by fitting. k The constant matrix is ​​usually the disturbance. The above method is used to transform the model into a mechanism-like state transition matrix similar to Equation (6).

[0083] Step 3: Based on the measurement or simulation data of the state variables and control variables formed in the actual or simulated motor control, train and transform the neural network in Step 2 to obtain an approximate result of the state transition matrix described in Step 1.

[0084] The time series data (basic data) of the state quantity and the control quantity are obtained by using the electromechanical characteristic model shown in formula (6), the BP neural network designed above is trained, the neural network calculates the state estimation quantity θ m (k+1), ω(k+1) according to the state quantity position θ m (k) and the speed ω(k) and the control quantity U(k) in the basic data at the k time, and the state estimation quantity θ m (k+1), ω(k+1) at the k+1 time is taken as the input of the neural network, and the state estimation quantity θ m (k+1), ω(k+1) at the k+1 time is taken as the output of the neural network, and the neural network is trained, in order to accelerate the training speed and effect of the neural network, the input and output of the neural network are normalized. The weights and biases of the BP neural network are trained by using the LM training algorithm, the training of the neural network is stopped when the gradient obtained by continuous 6 times of calculation is no longer reduced, and the training is stopped when the gradient value is lower than 10 -7 , the mapping relationship between the current motor state and the next state is obtained, and the state transition matrix approximation value and the control matrix approximation value

[0085] The conversion structure of the specific example is shown in Figure 2 , under the actual motor system, the system state at the k+1 time is obtained according to the control acting on the system state at the k time at the k time, the neural network is trained by taking the data as the training set, the trained weights and biases are obtained, and the system model isomorphic and equivalent to the mechanism model is obtained by substituting the weights and biases and the input into the conversion equation.

[0086] The idea of the application is that the neural network training has unexplainability, the model obtained by training is inconsistent with the configuration of the actual dynamic system model, and cannot be used in some control methods, based on this problem, the model obtained by training is converted into a form isomorphic and equivalent to the mechanism model, in the conversion process, the nonlinear activation function is replaced by the derivative and the bias, and the relationship between the original input and output is decoupled, so that the model isomorphic and equivalent to the mechanism model is obtained.

[0087] Although the application has been disclosed as above with preferred examples, it is not intended to limit the application, any person skilled in the art can make possible changes and modifications to the technical solutions of the application by using the disclosed methods and technical contents without departing from the spirit and scope of the application, therefore, any simple modification, equivalent change and modification made to the above examples according to the technical essence of the application, which does not depart from the content of the technical solutions of the application, belongs to the protection scope of the technical solutions of the application.

Claims

1. A motor system identification method based on neural network fitting model class mechanism form conversion, characterized in that The method comprises the following steps: determining the input and output state quantities of the neural network according to the motor control requirements and the motor state measurement capabilities, establishing the mechanical characteristic equation of the motor in the continuous time system, and obtaining the discretized state transition matrix; constructing the neural network structure and converting the neural network structure into a mechanism-like state transition matrix isomorphic to the discretized state transition matrix obtained in step one; training and converting the neural network according to the measurement or simulation data of the state quantities and control quantities formed in the actual or simulation motor control to obtain the final mechanism-like state transition matrix; obtaining the output of the motor system in real time according to the measured data in the motor control and the final mechanism-like state transition matrix; the constructed neural network structure is a neural network structure conforming to the general paradigm of the motor system, specifically a neural network with a full connection structure, an input layer, an output layer, and a hidden layer; the conversion of the neural network structure into a mechanism-like state transition matrix isomorphic to the discretized state transition matrix obtained in step one comprises: expanding the input and output of the neurons in the hidden layer of the constructed neural network structure according to the forward propagation process of the neural network, and then obtaining the input and output expansion expression of each neuron in the output layer; approximating the activation function of the neurons in the hidden layer of the neural network structure into a linear function expression form, substituting the approximate expression into the input and output expansion expression of each neuron in the output layer, and arranging and simplifying according to the neural network input parameters and constant terms to obtain a simplified expression; substituting the input and output in the simplified expression with the fitting model expression obtained by the system state and control action to obtain the mechanism-like state transition matrix.

2. The method of claim 1, wherein: the approximation of the activation function of the neurons in the hidden layer of the neural network structure into a linear function expression form is: f(x)≈a0+a1x where a0 is a constant approximation term, and a1 is a first-order approximation term, and a0 and a1 change with different activation functions and input values.

3. The method of claim 2, wherein: the expression obtained by substituting the approximate expression into the input and output expansion expression of each neuron in the output layer is: wherein: A 01 is the activation function constant approximation matrix for the hidden layer, A 11 is the activation function first order approximation matrix for the hidden layer, A 02 is the activation function constant approximation matrix for the output layer, A 12 is the activation function first order approximation matrix for the output layer, W1 is the input to hidden layer connection weight matrix, W2 is the hidden to output layer connection weight matrix, B1 is the hidden layer bias matrix, B2 is the output layer bias matrix, Y is the neural network output, and X is the neural network input.

4. The method of claim 3, wherein: the simplified expression is: Y=ΦX+D where Φ is the coefficient of the neural network input X, and D is a constant term.

5. The method of claim 4, wherein: the expression form of the mechanism-like state transition matrix isomorphic to the discretized state transition matrix is: X k+1 = Φ' k+1,k X k + Q' k+1,k U k + D k In the formula, Φ′ k+1,k Q′ k+1,k Let Φ' be the matrix obtained by expanding Φ. k+1,k To fit the system state matrix, Q′ k+1,k D is the control action coefficient matrix obtained by fitting. k Let X be a constant matrix. k X k+1 For the system states at two moments, U k For control purposes, X k+1 As the output Y, X of the neural network k with U k Input X to the neural network.

6. The method of claim 5, wherein: The input and output of the neural network are determined based on basic data, which are measurement or simulation data of state variables and control variables formed in actual or simulation of motor control; the position θ m (k) and the speed ω(k) of the state variables in the basic data at time k and the control variable U(k) are taken as the input of the neural network, and the estimated state variables θ m (k+1) and ω(k+1) at time k+1 are taken as the output of the neural network.

7. The method of claim 1, wherein: the training and conversion of the neural network is to obtain a weight matrix by training the neural network, substitute the input and output and the weight matrix into the expression form of the mechanism-like state transition matrix isomorphic to the discretized state transition matrix, and obtain the isomorphic equivalent form of the mechanism model according to the trained weight and bias, i.e., the final mechanism-like state transition matrix.

Images