Non-inductive direct-current brushless servo motor control method based on neural network improved extended state observer

Abstract

The invention discloses a non-inductive direct-current brushless servo motor control method for improving an extended state observer based on a neural network, and aims to solve the technical problems that the low-speed signal-to-noise ratio of traditional sensorless control is low, and mismatch of the extended state observer is easily caused by high-speed parameter perturbation. According to the method, an active-disturbance-rejection controller comprising a tracking differentiator, an expansion state observer and a state error feedback control law is constructed, and the state observation smoothness is improved by adopting an improved three-region segmentation fal function; motor flux linkage is observed on line through a back electromotive force method, and flux linkage disturbance feed-forward compensation quantity and total disturbance of the extended state observer are subjected to weighted fusion according to the rotating speed; adopting a voltage signal injection method and a sliding-mode observer to obtain the position of the rotor in a segmented manner; and constructing a radial basis function neural network, taking the target rotating speed and the actual rotating speed as input, and adaptively adjusting the correction gain of the extended state observer on line under the constraint of a loss function embedded into a Riccati equation residual term.

Description

Technical Field

[0001] This invention relates to a sensorless brushless DC servo motor control method based on an improved extended state observer using a neural network. Background Technology

[0002] Brushless DC servo motors are widely used in high-precision motion control fields such as precision CNC machine tools, industrial robots, and aerospace due to their high efficiency, high torque density, and fast dynamic response. However, the control performance of brushless DC servo motors is significantly affected by multiple sources of uncertainty, including time-varying motor parameters, sudden load changes and nonlinear frictional disturbances, and inverter nonlinear characteristics. Traditional PID control relies on linearized models, making it difficult to reconcile the trade-off between response speed and disturbance rejection.

[0003] Active disturbance rejection control (ADRC) estimates and dynamically compensates for the total system disturbance in real time using an extended state observer. Compared to PID control, it has stronger robustness and anti-interference ability, lower requirements for model accuracy, and is suitable for nonlinear systems. However, ADRC suffers from difficulties in parameter tuning and complex debugging. Traditional FAL nonlinear functions have inherent defects: fixed power-law parameters are difficult to adapt to the nonlinear dynamic characteristics of motors under different operating conditions; parameter tuning relies on experience and lacks an adaptive adjustment mechanism.

[0004] Traditional control schemes for brushless DC servo motors rely on hardware such as photoelectric encoders, Hall effect sensors, and resolvers to obtain rotor position information. Sensors increase system hardware cost and size; they are susceptible to environmental influences, reducing system reliability; and in extreme environments, sensors struggle to operate stably for extended periods. Sensorless technology, on the other hand, obtains the motor rotor position through algorithms, improving system reliability and reducing costs.

[0005] Existing sensorless active disturbance rejection control (ADRC) schemes combine voltage signal injection or back EMF methods, but face the following challenges: low signal-to-noise ratio in the low-speed domain; parameter perturbations in the high-speed domain easily lead to mismatch in the extended state observer; and neural network parameter tuning is prone to divergence. These shortcomings limit the application of sensorless ADRC in wide-speed-domain, high-precision scenarios. Summary of the Invention

[0006] The present invention provides a sensorless brushless DC servo motor control method based on an improved extended state observer using neural networks to address the problems existing in the prior art.

[0007] The technical solutions adopted in this invention are as follows:

[0008] A sensorless brushless DC servo motor control method based on an improved extended state observer using neural networks includes the following steps:

[0009] Establish a mathematical model for a sensorless brushless DC servo motor;

[0010] Design an active disturbance rejection controller that uses an extended state observer to estimate the total disturbance of a sensorless brushless DC servo motor and generate a feedforward compensation control quantity.

[0011] A segmented rotor position observation strategy is adopted to obtain the rotor position and speed of the sensorless brushless DC servo motor and input it to the active disturbance rejection controller as a feedback signal. The segmented observation is achieved by voltage signal injection when the absolute value of the speed of the sensorless brushless DC servo motor is less than or equal to the first preset threshold, and by sliding mode observer when the absolute value of the speed of the sensorless brushless DC servo motor is greater than or equal to the second preset threshold.

[0012] A radial basis function neural network is constructed. The radial basis function neural network takes the target speed and the actual speed of the sensorless brushless DC servo motor as inputs and outputs the correction gain adjustment of the extended state observer. The residual term of the Riccati equation is embedded in the loss function and the network output is mapped to the feasible region that satisfies the stability constraint of the Riccati equation. The correction gain of the extended state observer is adaptively adjusted through online training.

[0013] The active disturbance rejection controller is used as a speed controller to adjust the speed of the sensorless brushless DC servo motor in real time.

[0014] Furthermore, the active disturbance rejection controller includes a tracking differentiator, an extended state observer, and a state error feedback control law. The tracking differentiator uses an improved FAL nonlinear function to smoothly track the target speed. The extended state observer uses an improved FAL nonlinear function to observe the system state and total disturbance. The state error feedback control law combines the control quantity generated by the extended state observer with the total disturbance estimate for feedforward compensation, and together generate the final control quantity.

[0015] Furthermore, the improved fal nonlinear function is a three-region piecewise function:

[0016] ,

[0017] Where e is the error signal, α is the tracking factor, δ is the filtering factor, λ is the limiting factor, sgn(·) is the sign function, and the coefficients k1 and k3 are determined by the condition that the function is continuous and differentiable at the point where the absolute value of the error equals the filtering factor:

[0018] .

[0019] Furthermore, the total disturbance of the sensorless brushless DC servo motor estimated by the active disturbance rejection controller includes a flux linkage disturbance component. This flux linkage disturbance component is obtained by online observation of the flux linkage of the sensorless brushless DC servo motor using the back electromotive force method. The flux linkage estimate is as follows:

[0020] ,

[0021] in, This is the q-axis voltage. For stator windings, For q-axis current, The electric angular velocity of the motor;

[0022] Convert the flux estimation error into a torque disturbance feedforward compensation:

[0023] ,

[0024] in, The nominal flux linkage value, For flux linkage estimation bias, This represents the number of pole pairs of the motor. For the moment of inertia of the motor, For torque current;

[0025] The torque disturbance feedforward compensation and the total disturbance observed by the extended state observer are weighted and fused according to the rotational speed. ,in, The weighting coefficients represent the total perturbation observations of the extended state observer. The value is 0 when the absolute value of the motor speed is less than or equal to the first preset threshold, 1-α when the absolute value of the motor speed is greater than or equal to the second preset threshold, and linear interpolation when it is in between. α is a weighting parameter.

[0026] Furthermore, the first preset threshold and the second preset threshold are 5% and 15% of the rated speed of the sensorless brushless DC servo motor, respectively, and the weight parameter α ranges from 0.7 to 0.9.

[0027] Furthermore, the voltage signal injection method extracts the q-axis current response by injecting a voltage signal and DC bias voltage into the d-axis of the sensorless brushless DC servo motor, while the voltage injected into the q-axis is zero.

[0028] ,

[0029] in, For the injected voltage amplitude, This is the inductance difference caused by magnetic saturation. To inject the signal angular frequency, and For the d-axis and q-axis inductance, This represents the position estimation error;

[0030] Rotor position information is extracted from the current response using a phase-locked loop; a sliding mode observer establishes a current observation model in the α-β stationary coordinate system of a sensorless brushless DC servo motor, extracts the back electromotive force by switching control signals, and obtains the rotor position through arctangent calculation.

[0031] Furthermore, the radial basis function neural network has an input layer containing two neurons, a hidden layer containing five neurons, and an output layer containing two neurons, with the output layer corresponding to the extended state observer. and Correction gain adjustment amount.

[0032] Furthermore, the loss function of the radial basis function neural network is:

[0033]

[0034] in, The expected output of the network, This is the actual output of the network. For stability weights, For Riccati residuals, and These are the Riccati weights.

[0035] Furthermore, the radial basis function neural network uses the driven gradient descent method to update the network weights, center, and width, and constrains the updated correction gain using the feasible region projection method.

[0036] ,

[0037] in, and This is the adjustment amount for the correction gain of the network output. and The gain is adjusted at time k.

[0038] Furthermore, the stability weight λ in the loss function ranges from 0.1 to 0.5, and the Riccati weight coefficients q1 and q2 are tuned according to the bandwidth requirements of the extended state observer.

[0039] The present invention has the following beneficial effects:

[0040] This invention achieves the following beneficial effects in sensorless brushless DC servo motor control by using a speed-domain adaptive fusion voltage signal injection method, a sliding mode observer, an improved FAL nonlinear function, and adaptive parameter tuning with radial basis neural network embedded with Riccati stability constraints:

[0041] Position errors in both low-speed and high-speed domains are effectively suppressed, significantly reducing cost and size compared to position sensor solutions, and significantly enhancing system reliability.

[0042] The radial basis neural network output is forcibly projected onto the feasible region of the Riccati polyhedron, which avoids the divergence of the parameters of the extended state observer. It recovers quickly and without overshoot when the load changes abruptly, and its disturbance rejection capability is greatly improved compared with the fixed parameter active disturbance rejection controller.

[0043] The improved FAL nonlinear function achieves fast convergence under large disturbances and maintains high gain characteristics under small errors, effectively suppressing chattering and improving tracking accuracy, with comprehensive performance optimization compared to the traditional FAL nonlinear function;

[0044] The algorithm has low computational cost, strong real-time performance, requires no external iterative solution, is compatible with mainstream embedded controllers, and enables efficient deployment.

[0045] Radial basis neural networks learn online to automatically optimize the gain of the extended state observer, maintaining control accuracy under a wide range of parameter perturbations and the full speed domain, and reducing debugging complexity. Attached Figure Description

[0046] Figure 1 This is a system block diagram for sensorless brushless DC servo motor control based on an improved extended state observer using a neural network, as per the present invention.

[0047] Figure 2 This is a structural diagram of an active disturbance rejection controller.

[0048] Figure 3 A schematic diagram of the structure for improving the extended state observer.

[0049] Figure 4 This is a schematic diagram of a radial basis neural network structure for an improved extended state observer based on a neural network.

[0050] Figure 5 Simulation comparison of the speed response of a sensorless brushless DC servo motor under different control strategies. Detailed Implementation

[0051] The invention will now be further described with reference to the accompanying drawings.

[0052] like Figure 1 A sensorless brushless DC servo motor control method based on an improved extended state observer using neural networks includes the following steps:

[0053] S1: In the speed loop, the active disturbance rejection controller adjusts the speed according to the target rotational speed. The error between the reference current and the actual speed of the sensorless brushless DC servo motor generates a current loop reference current. In the current loop, the reference current is compared with the actual feedback d and q axis currents, and the PI controller generates d and q axis voltage reference values. Then, Park inverse transformation and SVPWM modulation are performed in sequence to generate three-phase inverter switching signals to drive the sensorless brushless DC servo motor.

[0054] Based on the dynamic balance relationship between the motor's electromagnetic torque and mechanical load, the motor's motion equation (i.e., the mathematical model of a sensorless brushless DC servo motor) is derived. The formula for the motor's motion equation is as follows:

[0055] ,

[0056] In the formula: Indicates electromagnetic torque. Indicates the load torque. This represents the viscous friction coefficient of the motor. Represents the moment of inertia. This indicates the electric angular velocity of the motor.

[0057] S2: The tracking differentiator receives the target rotational speed and uses an improved fal nonlinear function to smoothly track the target rotational speed. Its discrete implementation is as follows:

[0058] ,

[0059] In the formula: It is the output signal of TD. It is a given input signal. It is the velocity factor. It is the filter factor. It is a tracking factor;

[0060] An improvement to the fal function of the extended state observer, the traditional fal nonlinear function in At that time, a sudden change in the derivative can lead to a deterioration in system performance, thus affecting... The function is improved, and its formula is as follows:

[0061] ,

[0062] let For a function to be continuous and differentiable at a given point, its value must be the same as its derivative. The formulas for k1, k2, and k3 are as follows:

[0063] ,

[0064] The extended state observer is used to observe the internal state and external disturbances of the system in real time. The extended state observer is improved based on the modified fal function, and its formula is as follows:

[0065] ,

[0066] In the formula: , It is a correction gain. It is the system's output signal. It refers to the state observation values ​​output by the system. These are the observed disturbance values ​​of the system.

[0067] The back electromotive force method is used to observe whether the motor flux linkage decays, thereby improving system stability and accuracy. Therefore, the estimated flux linkage value is:

[0068] ,

[0069] In the formula, To estimate the motor flux linkage, This is the q-axis voltage. For stator windings, For q-axis current, This is the electric angular velocity of the motor.

[0070] Convert the flux estimation error into a torque disturbance feedforward compensation:

[0071] ,

[0072] In the formula, The nominal flux linkage value, For flux linkage estimation bias, This represents the number of pole pairs of the motor. For the moment of inertia of the motor, This refers to the torque current.

[0073] The flux linkage deviation and the total system disturbance are modeled as an extended state, and the disturbance is estimated through a speed adaptive weighted fusion mechanism: when the speed of the sensorless brushless DC servo motor is lower than the first preset threshold (preferably 5% of the rated speed), the total system disturbance is observed entirely by the extended state observer; when the speed is higher than the second preset threshold (preferably 15% of the rated speed), the flux linkage change feedforward control is combined; and linear interpolation is used to achieve smooth fusion in the transition region between the two.

[0074] ,

[0075] In the formula, For speed adaptive weighting, This is a physical disturbance.

[0076] ,

[0077] In the formula, The first preset threshold is preferably 5% of the rated speed of the sensorless brushless DC servo motor, used to divide the low-speed range and the transition zone. The second preset threshold, preferably 15% of the rated speed of the sensorless brushless DC servo motor, is used to divide the transition zone and the high-speed domain. α is a weighting coefficient, ranging from 0.7 to 0.9, used to adjust the weight ratio of feedforward compensation in the high-speed domain.

[0078] The state error feedback control law compares the output signal of the tracking differentiator with the state observation value of the system output by the extended state observer to obtain the state error, and performs nonlinear processing on the state error based on the improved fal function. The active disturbance rejection controller (ADRC) weights and fuses the flux disturbance feedforward compensation amount with the total disturbance estimated by the extended state observer according to the rotational speed, and then performs disturbance feedforward compensation through the state error feedback control law to generate the final control quantity. The formula is as follows:

[0079] ,

[0080] In the formula: It is the output signal of TD. It refers to the state observation values ​​output by the system. It's about adjusting the gain. It is a compensation factor. To integrate the disturbances.

[0081] The system block diagram of the improved extended state observer is as follows: Figure 3 As shown. This improvement, under large error conditions, The parameters can be adjusted to change trends, speed up the system's response to errors, and enable the system to converge to a steady state more quickly.

[0082] S3: The segmented rotor position observation strategy combines voltage signal injection with a sliding mode observer to obtain the rotor position and speed of a sensorless brushless DC servo motor. When the absolute value of the speed of the sensorless brushless DC servo motor is less than or equal to a first preset threshold, the voltage signal injection method, based on the magnetic saturation salient pole effect, injects a voltage signal and DC bias voltage along the d-axis, and the injected voltage along the q-axis is zero. The rotor position information is extracted by detecting the q-axis current response. When the absolute value of the speed of the sensorless brushless DC servo motor is greater than or equal to a second preset threshold, the sliding mode observer establishes a current observation model in the α-β stationary coordinate system of the sensorless brushless DC servo motor. The back electromotive force is extracted by switching control signals and the rotor position is obtained through arctangent calculation.

[0083] ,

[0084] In the formula, For high-frequency injection amplitude, Because of poor saturation inductance, This represents the position estimation error.

[0085] The rotor position information of the motor is obtained by adjusting the PLL:

[0086] ,

[0087] In the formula: This is the PLL error signal. To estimate the electrical angle, , For PLL proportional-integral gain, This is the integral of the error.

[0088] Under high-speed operation, this invention switches to The coordinate system and the current observer are:

[0089] ,

[0090] In the formula, , Stator current estimated for the observer Quantity, This is the switching control signal for the sliding mode observer.

[0091] The sliding mode control rate is:

[0092] ,

[0093] In the formula, k is the sliding mode gain. This represents the amplitude of the back electromotive force.

[0094] Extracting the back electromotive force of the motor:

[0095] ,

[0096] In the formula, This is the cutoff angular frequency of the low-pass filter. The back electromotive force estimate extracted by the sliding mode observer.

[0097] Finally, the rotor position information of the motor is obtained:

[0098]

[0099] In S4, such as Figure 4 The radial basis function neural network has two neurons in the input layer, five neurons in the hidden layer, and two neurons in the output layer. The output layer corresponds to the extended state observer. and Correction gain adjustment amount.

[0100] The formula for obtaining the output of the neural network is as follows:

[0101] ,

[0102] The formula for the hidden layer is as follows:

[0103]

[0104] In the formula: Let be the basis width vector of the function. It is a Euclidean norm. The data center is a radial basis function.

[0105] Radial basis function (RBF) neural networks employ the momentum projection gradient descent method. By minimizing the loss function of the embedded Riccati equation residuals, they online optimize the center vector, basis width vector, and output layer weights of the radial basis functions. The loss function of the RBF neural network is:

[0106] ,

[0107] In the formula, For Riccati residuals, and For Riccati weights, For stability weights.

[0108] The optimization method employs gradient descent and projection methods, and the algorithm formulas are as follows:

[0109] ,

[0110] In the formula, To output weights, For hidden layer output, As the center vector, For optimal weights, For the weight projection margin, This is the width parameter. Here, is the learning rate, and proj is the projection function. This is a limiting function;

[0111] like Figure 2 The radial basis function neural network (RBN) is combined with an active disturbance rejection controller (ADRC). By using the kinetic projection gradient descent method to minimize the loss function embedded in the Riccati equation residuals, the center vector, basis width vector, and output layer weights of the RBN are optimized in real time. The network output is mapped to a feasible region satisfying the stability constraints of the Riccati equation, and the correction gains β1 and β2 of the extended state observer are adaptively adjusted online.

[0112] ,

[0113] in, and This is the adjustment amount for the correction gain of the network output. and The gain is adjusted at time k.

[0114] S5: Use the neural network active disturbance rejection controller designed above as a speed controller to adjust the system in real time.

[0115] The MATLAB simulation analysis of this invention is as follows:

[0116] For MATLAB simulations, based on the aforementioned control strategy, the feasibility and effectiveness of the control strategy mentioned in this patent were verified by adding corresponding component modules. The PI control strategy and the traditional ADRC were used for comparative analysis. The output waveforms of the comparative simulations are shown below. Figure 5 As shown, a 10 N·m load is suddenly applied at 0.1 s, and a 5 N·m load is subtracted at 0.3 s. The black line represents the traditional ADRC control strategy, the blue line represents the PI control strategy, and the red line represents the control strategy mentioned in this patent. In the load-resistance speed fluctuation graph, it can be observed that among the three control methods, the PI control exhibits the largest fluctuation, with the speed dropping to 990 r / min and taking 0.03 s to stabilize at the target speed. The traditional ADRC and RBF-ADRC show similar speed decreases under the sudden 10 N·m load, but the RBF-ADRC responds faster. Within 0.01 s after the load is applied, the RBF-ADRC speed recovers to 994 r / min, while the traditional ADRC speed is only 991 r / min. At the 0.3 s load reduction, the graph shows that the PI control exhibits the largest fluctuation and the longest recovery time, followed by the traditional ADRC, with the speed suddenly increasing to 1003 r / min, while the RBF-ADRC only reaches 1002 r / min.

[0117] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for controlling a non-inductive direct-current brushless servo motor based on a neural network improved extended state observer, characterized in that: The method comprises the following steps: a mathematical model of the non-inductive DC brushless servo motor is established; a disturbance observer is designed, which estimates the total disturbance of the non-inductive DC brushless servo motor and generates a feedforward compensation control amount by using an extended state observer; a segmented rotor position observation strategy is adopted to obtain the rotor position and speed of the non-inductive DC brushless servo motor and input to the disturbance observer as a feedback signal, the segmented observation is realized by a voltage signal injection method when the absolute value of the speed of the non-inductive DC brushless servo motor is less than or equal to a first preset threshold, and is realized by a sliding mode observer when the absolute value of the speed of the non-inductive DC brushless servo motor is greater than or equal to a second preset threshold; a radial basis neural network is constructed, the radial basis neural network takes the target speed and the actual speed of the non-inductive DC brushless servo motor as inputs, and outputs a correction gain adjustment amount of the extended state observer; a Riccati equation residual term is embedded in a loss function, and the network output is mapped to a feasible region that satisfies the stability constraint of the Riccati equation, and the correction gain of the extended state observer is adaptively adjusted through online training; the disturbance observer is used as a speed controller to adjust the speed of the non-inductive DC brushless servo motor in real time. 2.The method of claim 1, wherein the neural network improved extended state observer based control method of the non-inductive direct current brushless servo motor is characterized in that: The disturbance observer comprises a tracking differentiator, an extended state observer and a state error feedback control law, the tracking differentiator uses an improved fal nonlinear function to smoothly track the target speed, the extended state observer uses an improved fal nonlinear function to observe the system state and the total disturbance, and the state error feedback control law combines the control amount generated by the extended state observer and the total disturbance estimate value to generate a final control amount. 3.The method of claim 2, wherein the neural network improved extended state observer based sensorless direct current brushless servo motor control method is characterized in that: The improved fal nonlinear function is a three-region segmented function: ， wherein e is an error signal, α is a tracking factor, δ is a filtering factor, λ is a limiting quantity, sgn(·) is a sign function, and coefficients k1 and k3 are determined by the continuous and derivable conditions of the function at the error absolute value equal to the filtering factor. 。 4. The non-inductive DC brushless servo motor control method based on the neural network improved extended state observer according to claim 1, wherein: The total disturbance of the non-inductive DC brushless servo motor estimated by the disturbance observer includes a flux disturbance component, which is obtained by observing the flux of the non-inductive DC brushless servo motor online through a back electromotive force method, and the flux estimation value is: ， wherein, is the q-axis voltage, is the stator winding, is the q-axis current, is the electrical angular velocity of the motor; The flux estimation error is converted into a torque disturbance feedforward compensation amount: ， wherein, is a nominal flux linkage value, is a flux linkage estimation bias, is a number of motor pole pairs, is a motor moment of inertia, is a torque current; The torque disturbance feedforward compensation amount and the total disturbance observed by the extended state observer are weighted and fused according to the rotation speed, and the fused disturbance wherein, is the total disturbance observed value of the extended state observer, and the weighting coefficient is 0 when the absolute value of the motor speed is less than or equal to a first preset threshold, is 1-α when the absolute value of the motor speed is greater than or equal to a second preset threshold, and is linearly interpolated between the two, and α is a weight parameter.

5. The neural network based improved extended state observer control method for sensorless direct current brushless servo motor according to claim 4, wherein: The first preset threshold and the second preset threshold are 5% and 15% of the rated speed of the non-inductive DC brushless servo motor, respectively, and the weight parameter α has a value range of 0.7 to 0.

9.

6. The non-inductive DC brushless servo motor control method based on the neural network improved extended state observer according to claim 1, wherein: The voltage signal injection method injects a voltage signal and a direct current bias voltage on the d-axis of the non-inductive DC brushless servo motor and injects zero voltage on the q-axis, and extracts the q-axis current response: ， wherein, is the injected voltage amplitude, is the inductance difference caused by magnetic saturation, is the injected signal angular frequency, and are the d-axis and q-axis inductances, is the position estimation error; The phase-locked loop extracts the rotor position information from the current response; the sliding mode observer establishes a current observation model in the α-β stationary coordinate system of the non-inductive DC brushless servo motor, extracts the back electromotive force through a switching control signal, and obtains the rotor position through an inverse tangent operation. 7.The method of claim 1, wherein the neural network improved extended state observer based sensorless direct current brushless servo motor control method is characterized by: The input layer of the radial basis neural network contains two neurons, the hidden layer contains five neurons, and the output layer contains two neurons. The output layer corresponds to the With correction gain adjustment amount. 8.The method of claim 7, wherein the neural network improved extended state observer based sensorless direct current brushless servo motor control method is characterized in that: The loss function of the radial basis neural network is: wherein, is the network expected output, is the network actual output, is the stability weight, is the Riccati residual, and is the Riccati weight. 9.The method of claim 8, wherein the neural network improved extended state observer based sensorless direct current brushless servo motor control method is characterized by: The radial basis neural network uses a momentum projection gradient descent method to update the network weights, centers, and widths, and the updated correction gain is constrained by the feasible region projection method: ， wherein, with is the correction gain adjustment amount for the network output, with is the correction gain at time k.

10. The neural network based improved extended state observer control method for sensorless direct current brushless servo motor according to claim 1, wherein: The stability weight λ in the loss function is in the range of 0.1 to 0.5.

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