Direct current motor speed regulation identification method and system based on improved quasi-newton method

Abstract

This invention discloses a DC motor speed control identification method and system based on an improved quasi-Newton method, belonging to the technical field of DC motor speed control system modeling. First, a time-varying nonlinear DC motor speed control system is constructed, and an identification model of this system is obtained. Then, an identification method flow based on the quasi-Newton method under step-size line search is constructed. The optimal step size is obtained through step-size line search for parameter estimation, and a correction strategy is designed to ensure the positive definiteness of the approximation of the Hessian matrix inverse. This invention avoids the oscillation or slow convergence problems caused by a fixed step size by dynamically adjusting the step-size factor, and simultaneously introduces a correction strategy to forcibly guarantee the positive definiteness of the approximation of the Hessian matrix inverse, thereby obtaining more accurate motor model parameters.

Description

Technical Field

[0001] This invention relates to a DC motor speed control identification method and system, specifically to a DC motor speed control identification method and system based on an improved quasi-Newton method, belonging to the field of DC motor speed control system modeling technology. Background Technology

[0002] DC motor speed control systems are widely used in CNC machine tools, electric vehicle drives, and industrial automation due to their high control precision, fast dynamic response, and excellent adjustment performance. In these systems, parameters such as the motor's armature resistance, inductance, and flux linkage are not constant but are affected by factors such as temperature, magnetic circuit saturation, and load disturbances, exhibiting significant nonlinear and time-varying characteristics. To achieve high-precision speed control, establishing a mathematical model capable of accurately capturing these parameter changes in real time is a crucial prerequisite for controller design and online compensation.

[0003] Currently, modeling methods for DC motor speed control systems are mainly divided into two categories: linear modeling based on physical mechanisms and nonlinear modeling based on data-driven approaches. In mechanism modeling, the motor's transfer function model is derived based on Kirchhoff's voltage law and Newton's second law, and fixed parameters such as resistance, inductance, and moment of inertia are identified through offline experiments. However, this method is essentially based on the assumption of linear time invariance, neglecting resistance drift caused by temperature rise or inductance fluctuations caused by magnetic circuit saturation during actual operation. This leads to a significant decrease in model accuracy when parameters change over time. To address this issue, some researchers have turned to nonlinear modeling, introducing nonlinear autoregressive moving average models to capture the system's nonlinear dynamics and combining them with genetic algorithms for parameter optimization. While these black-box or gray-box models significantly improve the ability to approximate nonlinear characteristics, their complex model structures, numerous parameters to be identified, and heavy reliance on computationally demanding heuristic optimization algorithms result in slow convergence speeds, making it difficult to meet the requirements of DC motor speed control systems for online real-time parameter identification.

[0004] Traditional model identification and parameter estimation methods still have significant limitations when dealing with the nonlinear characteristics, colored noise interference, and time-varying parameters of DC motor systems. To overcome the slow convergence of traditional methods, quasi-Newton methods, represented by the quasi-Newton method, have gradually become mainstream. By iteratively updating the approximate Hessian matrix to utilize second-order curvature information, they can theoretically significantly improve optimization efficiency. However, the practical performance of quasi-Newton methods largely depends on the robustness of the line search strategy. The Wolfe line search condition, a standard in industry, has numerical defects when dealing with non-convex problems, which may lead to algorithm interruption. Although convergence can be improved by using projection-based correction methods, such mathematical corrections often come with complex additional computational overhead. In embedded motor control systems with limited computing power, such complex step-size correction strategies are difficult to meet the millisecond-level real-time control requirements and are easily affected by sensor noise interference.

[0005] In summary, in the field of modeling and identification of DC motor speed control systems, existing linear models cannot accurately describe the time-varying characteristics of parameters, while nonlinear models based on intelligent algorithms are computationally too complex. Furthermore, the standard quasi-Newton method and its conventional improvements face the dual challenges of numerical stability and computational efficiency in embedded applications. Therefore, there is an urgent need for a system identification scheme that combines a modeling method that reflects the dynamic changes in parameters with an improved quasi-Newton method. This scheme should accurately describe the time-varying characteristics of motor parameters while achieving online real-time parameter estimation with extremely high computational efficiency and numerical stability, thereby solving the technical challenge of simultaneously achieving model accuracy and identification speed in existing technologies. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing DC motor speed control system model identification methods, such as slow convergence speed, sensitivity to initial values, and easy trapping in local minima under noise or strong nonlinear conditions. This invention proposes an improved quasi-Newton method for DC motor speed control system identification based on step-length line search, in order to improve the accuracy of model parameter estimation, the stability of algorithm iteration, and the convergence efficiency of the identification process.

[0007] To achieve the above-mentioned objective, this invention provides a DC motor speed control identification method based on an improved quasi-Newton method, comprising the following steps:

[0008] Step 1: Construct a time-varying nonlinear DC motor speed control system and obtain the identification model of the nonlinear DC motor speed control system;

[0009] Step 2: Construct an identification process for the quasi-Newton method under step-size line search to identify time-varying parameters. Obtain the optimal step size through a dynamic step-size line search strategy for parameter estimation, and execute a correction strategy to ensure the positive definiteness of the approximation of the inverse matrix of the Hessian matrix.

[0010] Further, in step 1, the expression of the identification model is:

[0011] ,

[0012] in, It is the system output signal. To output the information vector, For the input information vector, To act on the output information vector The output coefficient matrix, To act on the input information vector The input coefficient matrix, Let be the perturbation vector. It is Gaussian white noise.

[0013] Furthermore, in step 2, the identification process includes the following steps:

[0014] Step 2-1: Initialize the parameters used in the identification process, including data length, maximum number of iterations, Armijo criterion judgment coefficient, Wolfe curvature criterion judgment coefficient, step expansion coefficient, and maximum number of attempts for step line search;

[0015] Step 2-2: Use the DC motor armature voltage data as input data, the motor speed data as output data, and select disturbance vector data;

[0016] Steps 2-3: Let the iteration number variable k=1, define the criterion function and calculate its gradient relative to the stacked vector estimate at the k-th iteration time;

[0017] Step 2-4: Based on the gradient from Step 2-3 and the approximate value of the inverse of the Hessian matrix, obtain the search direction and calculate the directional derivative;

[0018] Steps 2-5: Use a dynamic step-size line search strategy and iteratively update the parameters to determine the optimal step-size value;

[0019] Steps 2-6: Calculate the difference between the stacked vector estimates before and after the update iteration, and the difference between the gradient of the criterion function and the stacked vector estimates before and after the update iteration;

[0020] Steps 2-7: Update the approximate inverse of the Hessian matrix using a correction strategy to complete the matrix update for this iteration;

[0021] Steps 2-8: Increment the value of the iteration variable k by 1, repeat the above process until the maximum number of iterations is reached, then stop the iteration and output the parameter estimate and the rotation speed estimate.

[0022] Furthermore, the expression for the criterion function is:

[0023] ,

[0024] Where H is the data length. and Representing the coefficient matrix respectively and The estimated value at the k-th iteration, where ||.|| represents the modulo operation. The value is the criterion function value.

[0025] Furthermore, the specific process of the dynamic step-size line search strategy includes:

[0026] Set the step size line search loop variable m=1 and the step size value for the m-th line search;

[0027] The parameter estimates are updated based on the current step size, and the criterion function value, gradient, and directional derivative r(k+1) for the k+1th iteration are calculated.

[0028] Based on the Armijo criterion and the Wolfe curvature criterion, calculate the judgment coefficient q of the step size passing the Armijo criterion and the judgment coefficient e of the step size passing the Wolfe criterion;

[0029] If q > 0, then assign the current step size to the upper bound of the interval, and enter the next step size line search after calculating the m+1th line search step size;

[0030] If q≤0, then further determine e:

[0031] When e≤0, the current step size is considered the optimal step size, and the line search is terminated;

[0032] When e > 0, further determine r(k+1): if r(k+1) ≥ 0, assign the current step size to the upper bound of the interval, and calculate the m+1th line search step size before entering the next step size line search; if r(k+1) < 0, assign the current step size to the lower bound of the interval, and calculate the m+1th line search step size through the step expansion coefficient before entering the next step size line search.

[0033] Increment the step size loop variable by 1, repeat the above process until the maximum number of iterations is reached, then stop the line search and output the optimal step size value.

[0034] Furthermore, the process of updating the approximate inverse of the Hessian matrix using a correction strategy includes:

[0035] Based on the difference in the stacked vector estimates and the difference in the gradients from steps 2-6, an intermediate variable is defined;

[0036] If the intermediate variable is not positive, the difference in gradients is corrected to obtain the corrected gradient difference.

[0037] Based on the corrected gradient difference, the approximate value of the inverse of the Hessian matrix required for the k+1th iteration update of the stacked vector estimate is updated, thus completing the matrix update for this iteration.

[0038] Furthermore, the expression for correcting the gradient difference is as follows:

[0039] ,

[0040] in, The intermediate vector is used to help determine the positive definiteness of the approximate value of the inverse of the Hessian matrix. As an intermediate variable to help determine the positive definiteness of the approximate value of the inverse of the input Hessian matrix, This represents the gradient difference between the criterion function and the output stacked estimation vector in two consecutive iterations. This represents the gradient difference between the criterion function and the input stacked estimation vector in two consecutive iterations. This represents the gradient difference between the updated criterion function and the output stacked estimation vector. This represents the gradient difference between the updated criterion function and the input stacked estimation vector.

[0041] The present invention also provides a DC motor speed control identification system based on an improved quasi-Newton method, comprising:

[0042] A DC motor speed control system construction module is used to construct a nonlinear DC motor speed control system and its identification model.

[0043] The algorithm optimization module is used to construct the identification process of the quasi-Newton method under the step-size line search, and obtain the optimal step size for parameter estimation through the dynamic step-size line search strategy;

[0044] The correction strategy module is used to execute correction strategies to ensure the positive definiteness of the inverse matrix approximation of the Hessian matrix.

[0045] Meanwhile, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed, it implements the steps of the method described in the present invention.

[0046] Furthermore, the present invention provides a computer-readable storage medium having a computer program stored thereon, the computer program being configured to implement the steps of the method described in the present invention when invoked by a processor.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] (1) This invention adopts an iterative strategy based on the improved quasi-Newton method, using the second derivative information of the estimated parameters, i.e., the inverse of the Hessian matrix, to construct the search direction. Compared with the traditional first-order gradient descent method or least squares method, it has a superlinear convergence speed. At the same time, this invention introduces an adaptive step-size line search mechanism. By constructing a judgment logic based on the Armijo criterion and the Wolfe curvature criterion, the step-size factor is dynamically adjusted in each iteration, avoiding the oscillation or slow convergence caused by a fixed step-size. Thus, while ensuring the stable descent of the algorithm, the number of iterations required to reach the optimal parameters is significantly reduced, improving the real-time performance of DC motor speed control system identification.

[0049] (2) To address the susceptibility of DC motor speed control systems to load disturbances, electromagnetic noise, and time-varying parameter characteristics during operation, this invention introduces a correction strategy in the Hessian matrix inverse approximation update step. When the traditional quasi-Newton method update conditions are not met, the update vector is adjusted by introducing parameters and correction terms, thus forcibly ensuring the positive definiteness of the Hessian matrix inverse. This improvement overcomes the defect of the standard quasi-Newton method, which is prone to algorithm divergence due to matrix singularity or non-positive definiteness under noise interference. This allows the identification method to maintain high numerical stability even in environments with strong nonlinearity and low signal-to-noise ratio, thereby obtaining more accurate motor model parameters and providing a reliable model foundation for subsequent high-performance motor control. Attached Figure Description

[0050] Figure 1 This is a structural diagram of a DC motor speed control system;

[0051] Figure 2 This is a flowchart of the DC motor speed control system identification method proposed in this invention;

[0052] Figure 3 This is a voltage input curve of the DC motor armature in Example 1;

[0053] Figure 4 It is a curve of the excitation current in the measurable disturbance vector;

[0054] Figure 5 This is a curve showing the fit between the predicted output and the actual output of the motor speed in Example 1;

[0055] Figure 6 This is a graph showing how the parameters change as the number of iterations increases;

[0056] Figure 7 This is a graph showing the error between the predicted output and the actual output of the motor speed;

[0057] Figure 8 This is a voltage input curve of the DC motor armature in Example 2;

[0058] Figure 9 This is a curve showing the fitting of the predicted output and the actual output of the motor speed in Example 2. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0060] This invention provides a DC motor speed control identification method and system based on an improved quasi-Newton method. The proposed method is applied to the following DC motor system: the input variable of the DC motor is the armature voltage, the output variable is the motor speed, and process noise and measurement noise are system disturbances. The basic system structure is described below. Figure 1 The DC motor speed control system identification method proposed in this invention was simulated using MATLAB software.

[0061] In the simulation process, the basic structure of the DC motor speed control system was first established. Then, the quasi-Newton method under step-length search was used to identify the parameters of the DC motor speed control system. Finally, the estimated motor speed was compared with the actual results. It was determined that the method of the present invention can effectively estimate the DC motor speed when the inverse matrix of the Hessian matrix is ​​unknown or inaccurate, and the error is small.

[0062] Example 1:

[0063] The structural diagram of the DC motor speed control system in this embodiment is shown below. Figure 1 As shown, where μ (t) represents the voltage input to the armature of the DC motor, L f For the magnetizing inductance, R f For the magnetizing resistance, μ f (t) represents the excitation voltage, M is the symbol for the motor rotor, J is the system moment of inertia, and I... a (t) represents the armature current, R represents the circuit resistance, E0(t) represents the back electromotive force, and I f (t) represents the excitation current, L m The inductance of the armature circuit is generally negligible. According to the laws of electromagnetism, the following relationship can be obtained:

[0064] ,

[0065] Among them, the voltage input of the DC motor armature like Figure 3 As shown, the motor speed output like Figure 5 The actual curve shown in the figure represents the measurable disturbance vector. ,in, Represents the excitation current, such as Figure 4 As shown in Figure C. e represents the back electromotive force constant, which depends on the motor structure and air gap flux. Here, it is simplified to a proportionality constant, indicating that the faster the rotational speed, the greater the back electromotive force. J0 represents the moment of inertia. T represents the coefficient of viscous friction. e Indicates the load torque. C f C is the excitation flux coefficient, representing the amount of effective magnetic flux that can be generated per unit excitation current. l is the electromagnetic torque structure constant, representing the magnitude of the electromagnetic torque generated by the interaction energy of a unit magnetic flux and a unit armature current.

[0066] After discretizing the relation, it can be transformed into a DC motor speed control system model:

[0067] ,

[0068] Where T represents the transpose operation, and the information vector Parameter matrix and perturbation vector They are respectively

[0069] ,

[0070] T c Indicates the sampling period.

[0071] In the simulation, the quasi-Newton algorithm under step-size line search was used to identify the DC motor speed control system model. The basic parameters of the quasi-Newton algorithm in the initialization stage were set as follows: maximum number of iterations K=500, data length H=1000, Armijo criterion judgment coefficient c1=0.0001, Wolfe curvature criterion judgment coefficient c2=0.9, step expansion coefficient z=0.5, maximum number of attempts for step-size line search x=30, and the maximum value of the time-varying polynomial order of the output constant coefficients. The maximum order of the time-varying polynomial when inputting constant coefficients. The dimension of the measurable perturbation vector is p=2.

[0072] Figure 5 and Figure 7 The results show the fitting and error between the motor speed predicted by the quasi-Newton algorithm under step-length search and the actual output. Figure 6 The changes of each parameter as the number of iterations increases are shown.

[0073] Example 2:

[0074] In this embodiment, the voltage input data of the DC motor armature like Figure 8 As shown, the motor speed output data like Figure 9 The actual curve shown in the figure represents the measurable disturbance vector. .in, This indicates periodic fluctuations in the load. This indicates the change in resistance in the motor caused by temperature rise.

[0075] The model expression for the DC motor speed control system can be obtained as follows:

[0076] ,

[0077] in, The output constant coefficients are time-varying polynomials acting on the system output signal. The time-varying polynomial with input constant coefficients acting on the system input signal takes the following values:

[0078] ,

[0079] .

[0080] Where s is the unit shift operator, and R1(t) is the time-varying polynomial with constant output coefficients. The first output parameter to be identified, R2(t), is the time-varying polynomial with constant output coefficients. The second output parameter to be identified, R 11 It is the first constant output coefficient remaining after separating the disturbance vector from the output parameter R1(t) to be identified. 12 It is the second constant output coefficient remaining after separating the disturbance vector from the output parameter R1(t) to be identified. 13 It is the third constant output coefficient remaining after separating the disturbance vector from the output parameter R1(t) to be identified; R 21 It is the first constant output coefficient remaining after separating the disturbance vector from the output parameter R2(t) to be identified. 22 It is the second constant output coefficient remaining after separating the disturbance vector from the output parameter R2(t) to be identified. 23 L1(t) is the third constant output coefficient remaining after separating the perturbation vector from the output parameter R2(t) to be identified. L1(t) is the time-varying polynomial with constant input coefficients. The first input parameter to be identified, L2(t), is a time-varying polynomial with constant input coefficients. The second input parameter to be identified, L 11 It is the first constant input coefficient remaining after separating the perturbation vector from the input parameter L1(t) to be identified. 12 It is the second constant input coefficient remaining after separating the disturbance vector from the input parameter L1(t) to be identified. 13It is the third constant input coefficient remaining after separating the disturbance vector from the input parameter L1(t) to be identified; L 21 It is the first constant input coefficient remaining after separating the perturbation vector from the input parameter L2(t) to be identified. 22 It is the second constant input coefficient remaining after separating the disturbance vector from the input parameter L2(t) to be identified. 23 It is the third constant input coefficient remaining after separating the disturbance vector from the input parameter L2(t) to be identified.

[0081] The parameters that need to be identified are the output coefficient matrix acting on the output information vector. and the input coefficient matrix acting on the input information vector :

[0082] ,

[0083] .

[0084] The expression for a DC motor speed control system can be transformed into:

[0085]

[0086] in, , .

[0087] In the simulation, the quasi-Newton algorithm under step-size line search was used to identify the DC motor speed control system model. The basic parameters of the quasi-Newton algorithm in the initialization stage were set as follows: maximum number of iterations K=800, data length H=1000, Armijo criterion judgment coefficient c1=0.0001, Wolfe curvature criterion judgment coefficient c2=0.93, step expansion coefficient z=0.4, maximum number of attempts for step-size line search x=30, and the maximum value of the time-varying polynomial order of the output constant coefficients. The maximum order of the time-varying polynomial when inputting constant coefficients. The dimension of the measurable perturbation vector is p=3. Figure 9 The results show the fit between the motor speed predicted by the quasi-Newton algorithm under step-line search and the actual output.

[0088] One of the DC motor speed control identification methods based on the improved quasi-Newton method in Examples 1 and 2, such as... Figure 2 As shown, it includes the following steps:

[0089] A time-varying nonlinear DC motor speed control system model is constructed, and the specific steps are as follows:

[0090] Step 1: Construct the structure of a DC motor speed control system model;

[0091] Step 2: Based on this model, the expression for the DC motor speed control system model is as follows:

[0092] ,

[0093] Where t is the time variable, It is a system input signal. It is the system output signal. It is an unknown Gaussian white noise disturbance. s is the unit shift operator. , The time-varying polynomial acting on the output constant coefficients of the system output signal The time-varying polynomial with constant coefficients acting on the system input signal has the following definition:

[0094] ,

[0095] In the above formula, and They represent and The maximum polynomial order, It is a time-varying polynomial with constant coefficients. The various output parameters to be identified, It is a time-varying polynomial with constant input coefficients. The various input parameters to be identified, assuming and Known.

[0096] And define the output information vector. and input information vector :

[0097] ,

[0098] The DC motor speed control system model in equation (1) can be expressed as follows:

[0099] ,

[0100] in, It is an output parameter vector composed of the output parameters to be identified. It is an input parameter vector consisting of the input parameters to be identified, and their definition is:

[0101] ,

[0102] Based on the characteristics of generalized time-varying parameter systems, their time-varying parameters can be expressed as:

[0103] ,

[0104] in, It is a measurable perturbation vector. It is to identify the output parameters The remaining constant output coefficients after separating the perturbation vector. It is the input parameters to be identified The remaining constant input coefficients after separating the perturbation vector. It is a function of the measurable disturbance in the system. Assuming p is known, p represents... The dimension, defining intermediate variables Indicates constant output coefficient The column vectors formed by grouping based on i are defined with intermediate variables. Indicates input constant coefficient The column vector formed by grouping based on 'i' is expressed as follows:

[0105] ,

[0106] Using these two intermediate parameter vectors, a vector is formed that acts on the output information. The output coefficient matrix and acting on the input information vector Input coefficient matrix The specific expression is as follows:

[0107] ,

[0108] Time-varying parameter vector and It can be written as:

[0109] ,

[0110] Once the coefficient matrix is ​​estimated and This allows us to obtain the time-varying parameter vector. and The estimated value. Therefore, the coefficient matrix. and Arranged into two stacked vectors respectively and ,in, It is the output parameter vector The output vector is formed by arranging all elements in column order. It is the input parameter vector The input vector, formed by arranging all elements in column order, is specifically represented as:

[0111] ,

[0112] ,

[0113] Step 3: The identification model of the DC motor speed control system is obtained as follows:

[0114] ,

[0115] The process of constructing a DC motor speed control system identification method based on the quasi-Newton method under step-length line search is as follows:

[0116] Step 1: Initialize the step-size line search quasi-Newton method identification method: Select an appropriate data length H, maximum number of iterations K, Armijo criterion coefficient c1, Wolfe curvature criterion coefficient c2, step expansion coefficient z, and maximum number of attempts for the step-size line search x. The iteration variable k represents the current iteration number. and Representing the coefficient matrix respectively and The estimated value at the k-th iteration time, and Representing the coefficient matrix respectively and The estimated value of the stacked vector at time k-th iteration. and They represent and The approximate value of the inverse of the Hessian matrix required for the k-th iteration update, I R and I L Show two identity matrices of different dimensions; and Defined as:

[0117] ,

[0118] ,

[0119] Step 2: Collect the voltage of the DC motor armature. As input data, motor speed As output data, appropriate data is selected as measurable perturbation vector data. ;

[0120] Step 3: Let the iteration variable k=1, and calculate the gradient g. R (k) and g L (k) and criterion function value The criterion function is defined as follows:

[0121] ,

[0122] Where H is the data length. and Representing the coefficient matrix respectively and The estimated value at the k-th iteration, where ||.|| represents the modulus of the vector or matrix. R (k) and g L (k) represents the time at the k-th iteration. Compared to stacked vector estimation and The gradient.

[0123] g R (k) and g L The calculation method for (k) is as follows:

[0124] First, calculate the criterion function. Regarding parameters partial derivatives and criterion function Regarding parameters partial derivatives The specific calculations are as follows:

[0125] ,

[0126] It is a function of the measurable disturbance vector in the system, and then calculated separately. Compared to stacked vector estimation and gradient:

[0127] ,

[0128] ,

[0129] in, The operators representing the Kronecker product have the following rules of operation:

[0130] Known ,but

[0131] .

[0132] Step 4: Obtain the search direction d that acts on the system output parameters using equations (22)-(23). R (k) and the search direction d acting on the system input parameters L (k), calculate the directional derivative r(k) using equation (24), let the line search variable be m and set the initial step size. The upper bound of the step size search interval is h=10. 7 The lower bound of the step size search interval is l=0.

[0133] ,

[0134] Where, d R (k) and d L (k) represents the search direction at time k iterations. and They represent and The approximate value of the inverse of the Hessian matrix required for the k-th iteration update, where r(k) represents the directional derivative at the k-th iteration. This represents the value of the step size in the m-th line search. The upper bound of the step size search cannot be determined at the moment, so it is set to a very large, definite value of 10. 7 .

[0135] Step 5: Enter the step-size line search and update the parameters. Set the step-size line search loop variable m=1, and update the parameter estimates using equations (25)-(26). and ,get and .

[0136] ,

[0137] The criterion function for the (k+1)th iteration is calculated using equation (17). Equations (20)-(21) calculate the gradient g for the (k+1)th iteration. R (k+1) and g L (k+1), calculate the directional derivative r(k+1) of the k+1 iterations using equation (24). Then, calculate the two judgment coefficients q,e using equations (27)-(28) as follows:

[0138] ,

[0139] Where q represents the judgment coefficient that the step size passes the Armijo criterion (sufficient descent condition), e represents the judgment coefficient that the step size passes the Wolfe criterion (curvature condition), c1 is the judgment coefficient of the Armijo criterion, and c2 is the judgment coefficient of the Wolfe curvature criterion.

[0140] Next, determine the sign of q, as follows:

[0141] 1) If q > 0: This means that at this time Larger, at this time Assign a value to the upper bound h of the interval and calculate the (m+1)th linear search step size using equation (29). Then proceed to the next step-length search;

[0142] 2) If q≤0: First calculate r(k+1), then determine the sign of e.

[0143] 2-1) If e≤0: This means that at this time This is the optimal value; exit line search.

[0144] 2-2) If e > 0: First determine the sign of r(k+1),

[0145] 2-2-1) If r(k+1)≥0: This means that at this time... Larger, at this time Assign a value to the upper bound h of the interval and calculate using equation (29). Then proceed to the next step-length search;

[0146] 2-2-2) If r(k+1) < 0: This means that at this time... Smaller, at this time Assign a value to the lower bound l of the interval and calculate using equation (30). Then proceed to the next step-length search.

[0147] Increment the value of the step size line search loop variable m by 1, repeat the above process until the maximum number of iterations x is reached, then stop the line search and output the final step size value.

[0148] ,

[0149] Where h is the upper bound of the interval, l is the lower bound of the interval, and z is the expansion coefficient.

[0150] Step 6: Calculate the difference s between the estimated parameters. R (k) and s L (k) and the difference between the gradient and .

[0151] Among them, s R (k) represents the coefficient matrix The stacked estimation vector at the (k+1)th iteration With coefficient matrix The stacked estimation vector at the k-th iteration time The difference, s L (k) represents the coefficient matrix The stacked estimation vector at the (k+1)th iteration With coefficient matrix The stacked estimation vector at the k-th iteration time The difference, Represents the criterion function in two adjacent iterations Relative to the output stacked estimation vector gradient g R (k+1) and the criterion function Relative to the output stacked estimation vector gradient g R The difference of (k), Represents the criterion function in two adjacent iterations Relative to the input stacked estimation vector gradient g L (k+1) and the criterion function Relative to the input stacked estimation vector gradient g L The difference between (k) and s R (k), s L (k) and The definition is as follows:

[0152] ,

[0153] Step 7: Update the search direction d used to calculate the system output parameters R Approximate value of the inverse of the output Hessian matrix of (k) and the search direction d used to calculate the input parameters of the computing system L Approximate value of the inverse of the input Hessian matrix (k) To ensure the updated matrix maintains positive definiteness, a damping correction strategy is introduced. An auxiliary judgment output Hessian matrix is ​​defined. The intermediate vector of positive definiteness and auxiliary judgment input Hess matrix Positive definiteness is an intermediate variable :

[0154] ,

[0155] Before performing the standard quasi-Newton method update, first check the curvature condition: if or If it is not positive, then use equations (37)-(38) respectively to... and The correction is then performed to obtain the corrected gradient difference. This is the gradient difference between the updated criterion function and the output stacked estimation vector. The gradient difference between the updated criterion function and the input stacked estimation vector They are respectively

[0156] ,

[0157] Finally, update using equations (39)-(40) respectively. The approximate value of the inverse of the output Hessian matrix required for the (k+1)th iteration update. and The approximate value of the inverse of the input Hessian matrix required for the (k+1)th iteration update. This completes the matrix update for this iteration.

[0158] ,

[0159] Among them, I R and I L Represent two identity matrices of different dimensions.

[0160] Step 8: Increment the value of the iteration variable k by 1, and repeat the above process until the maximum number of iterations is reached and then stop iterating.

[0161] The identification effect of the step-size line search quasi-Newton method designed in this embodiment is shown in [reference]. Figure 5 , Figure 6 , Figure 7 as well as Figure 9 The specific explanation is as follows: Figure 6 This demonstrates how the parameters of the algorithm change with the number of iterations k during the identification process. Figure 6 It contains four subgraphs, each corresponding to a parameter matrix. Two components (Top left sub-image) (Top right subplot) shows how this changes with iteration number k, and Two components (Lower left sub-image) (Bottom right subplot) The changes with the number of iterations k. These four subplots show that in the early stages of iteration (k < 200), all four parameters can be rapidly and significantly adjusted, and then quickly stabilize as the iteration progresses, eventually converging to near the true value. This demonstrates that the quasi-Newton algorithm of this invention, combined with an improved line search strategy, can provide an effective search direction and step size for parameter updates, directly overcoming the technical problem of slow convergence in traditional gradient algorithms in complex nonlinear systems, and achieving efficient and high-precision parameter identification.

[0162] Figure 7 The curve showing the variation of the relative identification error with time t during the identification process is illustrated. The figure shows that the identification error fluctuates only in the very short period after the iteration begins, then rapidly decays to near zero, and remains at a very low level throughout the subsequent complex running cycle, without any divergence or significant oscillation. This performance demonstrates the high robustness of the step-size line search mechanism designed in this invention, effectively solving the technical problem of traditional algorithms experiencing update interruptions or instability near minimum points due to difficulties in step-size selection, thus ensuring the stability of the identification process and the accuracy of parameter estimation.

[0163] Figure 5 and Figure 9The figures show a comparison of the actual speed and the model-predicted speed of the DC motor system over time t under two different variable operating conditions, as presented in Examples 1 and 2. In these two figures, the actual speed curve (solid red line) includes complex dynamic processes such as rapid acceleration, deceleration, and multiple steady-state phases, while the speed points predicted by the model (blue asterisks) highly overlap with the actual speed curve over the entire time axis. This intuitively verifies that the time-varying parameter model identified using the algorithm of this invention can accurately reproduce the dynamic tracking performance of the actual physical system and precisely capture the nonlinear dynamic characteristics within the system.

[0164] In summary, the quasi-Newton identification algorithm proposed in this invention, which combines an improved line search strategy, can efficiently, accurately, and stably identify the time-varying parameters of a DC motor speed control system. It is fully applicable to the speed control requirements of DC motors with significant nonlinearity and time-varying parameter characteristics.

[0165] This embodiment also provides a DC motor speed control identification system based on an improved quasi-Newton method, including a DC motor speed control system construction module, an algorithm optimization module, and a correction strategy module;

[0166] In this embodiment, the DC motor speed control system construction module is used to construct a nonlinear DC motor speed control system and its identification model.

[0167] In this embodiment, the algorithm optimization module is used to construct the identification process of the quasi-Newton method under step-size line search, and obtain the optimal step size for parameter estimation through the dynamic step-size line search strategy.

[0168] In this embodiment, the correction strategy module is used to execute a correction strategy to ensure the positive definiteness of the inverse matrix approximation of the Hessian matrix.

[0169] The aforementioned system can implement the DC motor speed control identification method based on the improved quasi-Newton method described in this invention. However, the implementation device of the DC motor speed control identification method based on the improved quasi-Newton method described in this invention includes, but is not limited to, the DC motor speed control identification system based on the improved quasi-Newton method described in this invention.

[0170] This invention provides a DC motor speed control identification method and system based on an improved quasi-Newton method. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A DC motor speed regulation identification method based on an improved quasi-Newton method, characterized in that, Includes the following steps: Step 1: Construct a time-varying nonlinear DC motor speed control system and obtain the identification model of the nonlinear DC motor speed control system; Step 2: Construct an identification process for the quasi-Newton method under step-size line search to identify time-varying parameters. Obtain the optimal step size through a dynamic step-size line search strategy for parameter estimation, and execute a correction strategy to ensure the positive definiteness of the approximation of the inverse matrix of the Hessian matrix.

2. The DC motor speed control identification method based on the improved quasi-Newton method according to claim 1, characterized in that, In step 1, the expression of the identification model is: ， in, It is the system output signal. To output the information vector, For the input information vector, To act on the output information vector The output coefficient matrix, To act on the input information vector The input coefficient matrix, Let be the perturbation vector. It is Gaussian white noise.

3. The DC motor speed control identification method based on the improved quasi-Newton method according to claim 1, characterized in that, In step 2, the identification process includes the following steps: Step 2-1: Initialize the parameters used in the identification process, including data length, maximum number of iterations, Armijo criterion judgment coefficient, Wolfe curvature criterion judgment coefficient, step expansion coefficient, and maximum number of attempts for step line search; Step 2-2: Use the DC motor armature voltage data as input data, the motor speed data as output data, and select disturbance vector data; Steps 2-3: Let the iteration number variable k=1, define the criterion function and calculate its gradient relative to the stacked vector estimate at the k-th iteration time; Step 2-4: Based on the gradient from Step 2-3 and the approximate value of the inverse of the Hessian matrix, obtain the search direction and calculate the directional derivative; Steps 2-5: Use a dynamic step-size line search strategy and iteratively update the parameters to determine the optimal step-size value; Steps 2-6: Calculate the difference between the stacked vector estimates before and after the update iteration, and the difference between the gradient of the criterion function and the stacked vector estimates before and after the update iteration; Steps 2-7: Update the approximate inverse of the Hessian matrix using a correction strategy to complete the matrix update for this iteration; Steps 2-8: Increment the value of the iteration variable k by 1, repeat the above process until the maximum number of iterations is reached, then stop the iteration and output the parameter estimate and the rotation speed estimate.

4. The DC motor speed control identification method based on the improved quasi-Newton method according to claim 3, characterized in that, The expression for the criterion function is: ， Where H is the data length. and Representing the coefficient matrix respectively and The estimated value at the k-th iteration, where ||.|| represents the modulo operation. The value is the criterion function value.

5. The DC motor speed control identification method based on the improved quasi-Newton method according to claim 3, characterized in that, The specific process of the dynamic step-size line search strategy includes: Set the step size line search loop variable m=1 and the step size value for the m-th line search; The parameter estimates are updated based on the current step size, and the criterion function value, gradient, and directional derivative r(k+1) for the k+1th iteration are calculated. Based on the Armijo criterion and the Wolfe curvature criterion, calculate the judgment coefficient q of the step size passing the Armijo criterion and the judgment coefficient e of the step size passing the Wolfe criterion; If q > 0, then assign the current step size to the upper bound of the step size search interval, and enter the next step size line search after calculating the m+1th line search step size; If q≤0, then further determine e: When e≤0, the current step size is considered the optimal step size, and the line search is terminated; When e > 0, further determine r(k+1): if r(k+1) ≥ 0, assign the current step size to the upper bound of the interval, and calculate the m+1th line search step size before entering the next step size line search; if r(k+1) < 0, assign the current step size to the lower bound of the step size search interval, and calculate the m+1th line search step size through the step expansion coefficient before entering the next step size line search. Increment the step size loop variable by 1, repeat the above process until the maximum number of iterations is reached, then stop the line search and output the optimal step size value.

6. The DC motor speed control identification method based on the improved quasi-Newton method according to claim 3, characterized in that, The process of updating the approximate inverse of the Hessian matrix using a correction strategy includes: Based on the difference in the stacked vector estimates and the difference in the gradients from steps 2-6, an intermediate variable is defined; If the intermediate variable is not positive, the difference in gradients is corrected to obtain the corrected gradient difference. Based on the corrected gradient difference, the approximate value of the inverse of the Hessian matrix required for the k+1th iteration update of the stacked vector estimate is updated, thus completing the matrix update for this iteration.

7. The DC motor speed control identification method based on the improved quasi-Newton method according to claim 6, characterized in that, The expression for correcting the gradient difference is: ， in, The intermediate vector is used to help determine the positive definiteness of the approximate value of the inverse of the Hessian matrix. As an intermediate variable to help determine the positive definiteness of the approximate value of the inverse of the input Hessian matrix, This represents the gradient difference between the criterion function and the output stacked estimation vector in two consecutive iterations. This represents the gradient difference between the criterion function and the input stacked estimation vector in two consecutive iterations. This represents the gradient difference between the updated criterion function and the output stacked estimation vector. This represents the gradient difference between the updated criterion function and the input stacked estimation vector.

8. A DC motor speed control identification system based on an improved quasi-Newton method, characterized in that, The steps of applying the method according to any one of claims 1 to 7 include: A DC motor speed control system construction module is used to construct a nonlinear DC motor speed control system and its identification model. The algorithm optimization module is used to construct the identification process of the quasi-Newton method under the step-size line search, and obtain the optimal step size for parameter estimation through the dynamic step-size line search strategy; The correction strategy module is used to execute correction strategies to ensure the positive definiteness of the inverse matrix approximation of the Hessian matrix.

9. An electronic device, characterized in that, The method includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the DC motor speed control identification method based on the improved quasi-Newton method as described in any one of claims 1 to 7.

10. A storage medium, characterized in that, The device stores a computer program or instructions that, when executed on a computer, perform the steps of the DC motor speed control identification method based on the improved quasi-Newton method as described in any one of claims 1 to 7.

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