A high-precision model identification method of a servo system

Abstract

The application belongs to the technical field of modeling of servo system, and discloses a high-precision model identification method of servo system, which comprises the following steps: obtaining linear operation data of servo system under low-speed working condition; constructing a second-order controlled autoregressive model; using a variable recursive interval multiple new information least square algorithm to solve to-be-identified parameters of the second-order controlled autoregressive model, obtaining a predicted output of the second-order controlled autoregressive model based on the to-be-identified parameters, and determining a dead zone range according to the predicted output and an actual output of the second-order controlled autoregressive model; designing a Hammerstein model with dead zone nonlinearity of the servo system according to the dead zone range; and using a linear auxiliary constraint particle swarm algorithm to estimate to-be-identified parameters of the Hammerstein model offline, so as to finally obtain the Hammerstein model with dead zone nonlinearity of the servo system. The application improves the precision of model identification, improves the control performance of the alternating current servo system, and obtains a system model with higher precision.

Description

Technical Field

[0001] This invention belongs to the field of servo system modeling technology, specifically relating to a high-precision model identification method for servo systems, particularly realizing model identification of servo systems under low-speed conditions, reducing the tracking error of the model under low-speed conditions, so as to more accurately describe the dynamic behavior of the servo system under both high-speed and low-speed conditions, and providing a solid foundation for subsequent servo system design and optimization. Background Technology

[0002] As modern industry becomes increasingly large-scale and complex, traditional control theories and strategies based on quantitative mathematical models are no longer sufficient to meet practical needs in order to ensure the stability and control accuracy of servo systems. Modern control strategies are receiving increasing attention due to their ease of online computation and adaptability to process and environmental uncertainties.

[0003] Servo system modeling plays a crucial role in modern control strategies. However, nonlinear components are prevalent in many complex control systems, and nonlinear phenomena in real-world systems (such as frictional creep, dead zone effect, and backlash) significantly impact the accuracy of controllers designed based on linear models, especially under low-speed motion conditions.

[0004] To address this problem, the Hammerstein model offers an efficient solution. This method requires no additional test sensors and can decouple and identify the linear and nonlinear components of a system using only a single input-output data set. The advantages of the Hammerstein model lie in its broad applicability to complex systems exhibiting nonlinear phenomena, particularly in scenarios with significant nonlinearity such as friction creep, dead zone effects, and backlash, effectively improving modeling accuracy. Furthermore, it possesses strong decoupling capabilities; by decomposing the system into linear and nonlinear components, the Hammerstein model clearly describes the impact of nonlinear characteristics on the overall system performance and provides a basis for optimizing different subsystems.

[0005] In existing technologies, the Hammerstein model is often used to describe the nonlinear characteristics of servo systems and assist in control design. However, in practical applications, it still suffers from problems such as insufficient low-speed performance, difficulty in balancing identification efficiency and accuracy, and insufficient controller adaptability. Summary of the Invention

[0006] The purpose of this invention is to provide a high-precision model identification method for servo systems, thereby improving the accuracy of model identification when the servo system is running at low speed, improving the control performance of AC servo systems, and obtaining a higher precision system model.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A high-precision model identification method for a servo system, the method comprising:

[0009] Acquire linear operating data of the servo system under low-speed conditions;

[0010] Construct a second-order controlled autoregressive model based on linear operating data;

[0011] The variable recursive interval multi-innovation least squares algorithm is used to solve for the parameters to be identified in the second-order controlled autoregressive model. Based on the parameters to be identified, the predicted output of the second-order controlled autoregressive model is obtained. The dead zone range is determined according to the predicted output and the actual output of the second-order controlled autoregressive model.

[0012] Design a Hammerstein model for a servo system with dead-zone nonlinearity based on the dead-zone range;

[0013] The objective function is to minimize the cumulative error between the predicted and actual outputs of the Hammerstein model. Based on the objective function, the parameters to be identified in the Hammerstein model are estimated offline using a linear auxiliary constrained particle swarm optimization algorithm, and finally, a Hammerstein model with dead-zone nonlinearity for the servo system is obtained.

[0014] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0015] Preferably, the step of constructing a second-order controlled autoregressive model based on linear operating data includes:

[0016] The transfer function from the output to the input of the servo system is obtained using Mason's formula:

[0017]

[0018] In the formula, Represents the transfer function of the servo system. It is the frequency domain input of the servo system. It is the frequency domain output of the servo system. It is the velocity loop gain. It is the current loop gain. It is the elasticity coefficient. It is the moment of inertia of the motor in the servo system. It is the moment of inertia of the load. It is the coefficient of viscous friction. Represent the complex variable in the Laplace transform domain;

[0019] The simplified transfer function of the servo system is as follows:

[0020]

[0021] In the formula, This represents the simplified frequency domain output of the servo system. It is a combination of proportional constants, including the velocity loop gain. Current loop gain and elasticity coefficient , It is a time constant;

[0022] The second-order controlled autoregressive model is constructed as follows:

[0023]

[0024] In the formula, and Let represent the discrete polynomials of the input characteristics and the output characteristics of the servo system, respectively. and They are The actual input and actual output of the time servo system , , and These are the four parameters to be identified in the second-order controlled autoregressive model. This represents a shift operator.

[0025] Preferably, the step of obtaining the predicted output of the second-order controlled autoregressive model based on the parameters to be identified, and determining the dead zone range based on the predicted output and actual output of the second-order controlled autoregressive model, includes:

[0026] The residuals of the second-order controlled autoregressive model are calculated as follows:

[0027]

[0028] In the formula, express The residuals of the second-order controlled autoregressive model at time step 1. yes The actual output of the time servo system yes The predicted output of the second-order controlled autoregressive model at time step;

[0029] Find the residual in the motor commutation region under low-speed operating conditions of the servo system. The largest critical point is marked as the dead zone critical point, thus the dead zone range from which the target dead zone parameters are extracted is... and , This is the minimum value within the first dead zone. This represents the maximum value within the first dead zone. This is the minimum value of the second dead zone range. This represents the maximum value of the second dead zone range.

[0030] Preferably, the step of designing a Hammerstein model for the servo system with dead-time nonlinearity based on the dead-time range includes:

[0031] The input-output model of the servo system with dead-zone nonlinearity is constructed as follows:

[0032]

[0033] In the formula, and They are The actual input and actual output of the time servo system This represents a dynamic model with dead-zone nonlinearity. As intermediate variables, representing the dynamic model The predicted output, This represents the transfer function of the linear part of the Hammerstein model, i.e., the second-order controlled autoregressive model. These are intermediate variables, representing the model. The predicted output, It is a shift operator. To measure noise, the mean is taken as zero and the variance is... Gaussian white signal, and These represent the discrete polynomials for the input characteristics and the output characteristics of the servo system, respectively.

[0034] The dynamic model includes a dead zone nonlinearity. For input The processing procedure is as follows:

[0035]

[0036] Among them, the second-order controlled autoregressive model For intermediate variables The processing procedure is as follows:

[0037]

[0038] This yields the Hammerstein model with dead-zone nonlinearity, as follows:

[0039]

[0040]

[0041] In the formula, and If the slope of the linear segment of a dynamic model with dead-zone nonlinearity is the parameter to be identified in the Hammerstein model, then... ,in , , , These are the parameters to be identified in the second-order controlled autoregressive model, which are known quantities in the Hammerstein model. and These are the unknown dead zone parameters within the dead zone range.

[0042] Preferably, the linearly assisted constrained particle swarm optimization algorithm outputs the optimal solution for the parameters to be identified in the Hammerstein model, including the dead zone parameters. and The results, calculated based on the optimal solution, are as follows: and , The parameters to be identified in the Hammerstein model The third item in the list, The parameters to be identified in the Hammerstein model The fourth item in the list, The parameters to be identified in the Hammerstein model Item 5 in The parameters to be identified in the Hammerstein model The 6th item in the list.

[0043] Preferably, the linear auxiliary constraint range of the linear auxiliary constraint particle swarm algorithm is the dead zone range.

[0044] Preferably, the offline estimation of the parameters to be identified in the Hammerstein model using a linearly assisted constrained particle swarm optimization algorithm based on the objective function includes:

[0045] Initialize particle position, particle velocity, and fitness function; set population size, maximum number of iterations, and learning factor.

[0046] During particle convergence, the particle position and particle velocity are updated, and it is determined whether the updated particle position exceeds the set linear auxiliary constraint range. If it does, it is forcibly projected to the boundary of the dead zone range; otherwise, the forced projection is not performed.

[0047] Repeatedly calculate the fitness function and update the particle position and particle velocity until the objective function converges or the maximum number of iterations is reached, to obtain the optimal solution for the parameters to be identified in the Hammerstein model.

[0048] Preferably, it is determined whether the updated particle position exceeds the set linear auxiliary constraint range. If it does, it is forcibly projected to the boundary of the dead zone range; otherwise, the forced projection is not performed, and the following is executed:

[0049] The dead zone parameter is calculated based on the updated particle position, and it is determined whether the dead zone parameter is within the dead zone range. If the dead zone parameter is less than the dead zone range, the dead zone parameter is projected to the minimum value of the dead zone range. If the dead zone parameter is greater than the dead zone range, the dead zone parameter is projected to the maximum value of the dead zone range. Then, the updated particle position after projection is obtained by reverse calculation based on the projected dead zone parameter. If the dead zone parameter is within the dead zone range, no forced projection is performed, and the updated particle position is directly accepted.

[0050] In existing technologies, the dead zone and friction caused by system commutation, among other nonlinear factors, affect the overall control performance of low-speed, high-precision servo systems. Therefore, this invention significantly improves the modeling accuracy of the Hammerstein model in the low-speed region by introducing a linear auxiliary model and combining it with a linear auxiliary constrained particle swarm optimization algorithm. This improves the low-speed tracking and dynamic response performance of the servo system, accelerates the parameter identification process, and enhances identification accuracy, especially when dead zone parameters are significant or the model is complex.

[0051] This invention provides a high-precision model identification method for servo systems. During the linear operation phase of the servo system, a second-order controlled autoregressive (CAR) linear parameter model is established. An interval-varying multi-innovation least squares (V-MILS) algorithm is used for identification in the low-speed linear phase, eliminating the impact of reduced identification accuracy caused by bad data and initially obtaining the range of dead-zone parameters. In the low-speed nonlinear operation phase, a Hammerstein model incorporating nonlinear characteristics is established, and a linearly assisted constrained particle swarm optimization (PSO) algorithm is proposed to identify the servo system model. By introducing the range of dead-zone parameters to define the search space of the PSO algorithm, the accuracy of local searches is enhanced, the convergence of the algorithm in complex search spaces is accelerated, and the accuracy of the final identification result is improved. This improves the accuracy of model identification, enhances the control performance of AC servo systems, and yields a higher-precision system model suitable for modern industrial servo systems. Attached Figure Description

[0052] Figure 1This is a flowchart of a high-precision model identification method for a servo system according to the present invention;

[0053] Figure 2 This is a control block diagram of the second-order controlled autoregressive model constructed in this invention;

[0054] Figure 3 This is a simplified control block diagram of the second-order controlled autoregressive model of the present invention;

[0055] Figure 4 A schematic diagram illustrating the use of variable periodicity sequences in the V-MLS algorithm;

[0056] Figure 5 A schematic diagram of an input-output Hammerstein model with dead-zone input nonlinearity;

[0057] Figure 6 This is a schematic diagram of the actual rotational speed and estimated rotational speed under the condition of low speed superimposed small amplitude sine curve in the present invention based on the linear auxiliary constraint particle swarm algorithm;

[0058] Figure 7 for Figure 6 A magnified view of the portion between 0 and 3.5 seconds. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0061] To comprehensively improve the control performance of AC servo systems and enhance system modeling accuracy, especially in low-speed and motion-commutation scenarios, this invention proposes a high-precision model identification method for servo systems. This method aims to improve modeling performance in low-speed regions by optimizing the model identification process, thereby effectively improving the control accuracy and dynamic response performance of the servo system.

[0062] like Figure 1 As shown, this embodiment provides a high-precision model identification method for a servo system, including the following steps:

[0063] Step 1: Obtain linear operating data of the servo system under low-speed conditions.

[0064] All the operational data used for parameter identification are values ​​obtained in real time on the platform at sampling period intervals. This embodiment takes the tractor motor servo system as an example for explanation. In the tractor motor servo system, the speed and torque of the motor are obtained through the host computer platform for control.

[0065] To obtain a linear low-speed auxiliary model, a suitable excitation signal needs to be designed. Here, the selected input is... The system controls and acquires speed (in rpm) input and position output data through a host computer platform. for The actual input to the time servo system, This represents the number of sine waves superimposed on the input signal; in this embodiment, the value is... , Indicates the first The amplitude of a sine wave, in this embodiment, is taken as... , Indicates the first The frequency of the sine wave, in this embodiment, is taken as... , Indicates time.

[0066] Step 2: Construct a second-order controlled autoregressive (CAR) model based on the linear running data.

[0067] Step 21: When configuring the servo driver to operate in speed mode, the overall block diagram of the single-axis servo system is as follows: Figure 2 As shown, the motor and mechanical parts are controlled by a speed loop and a current loop.

[0068] Step 22: The transfer function from the output to the input of the servo system can be calculated using Mason's formula:

[0069]

[0070] In the formula, Let represent the transfer function of a second-order controlled autoregressive model. It is the frequency domain input of the servo system. It is the frequency domain output of the servo system. It is the velocity loop gain. It is the current loop gain. It is the elasticity coefficient. It is the moment of inertia of the permanent magnet synchronous servo motor (motor). It is the moment of inertia of the load. It is the coefficient of viscous friction. This represents a complex variable in the Laplace transform domain.

[0071] Step 23: After analyzing the motion characteristics of the industrial mechatronics servo system, simplify the overall system structure as follows: Figure 3 As shown, its transfer function is:

[0072]

[0073] When the time constant When the value is small, the above formula can be approximated as:

[0074]

[0075] In the formula, This represents the simplified frequency domain output of the servo system. A series of proportionality constants, including It is the velocity loop gain. It is the current loop gain. It is the elasticity coefficient.

[0076] Step 24: Introduce the second-order controlled autoregressive model as shown in the following equation:

[0077]

[0078] In the formula, , These represent the discrete polynomials for the input characteristics and the output characteristics of the servo system, respectively. , They are The input discrete-time series and the corresponding output discrete-time series at each time step are thus... The actual input and actual output of the time servo system , , , There are four parameters to be identified. This represents the shift operator, also known as the time lag operator.

[0079] Step 3: Use the variable recursive interval multi-innovation least squares algorithm to solve for the parameters to be identified in the second-order controlled autoregressive model. , , and Based on the parameters to be identified, the predicted output of the second-order controlled autoregressive model is obtained. The dead zone range is determined according to the predicted output and the actual output, and used for subsequent linear auxiliary constrained particle swarm algorithm model identification.

[0080] Step 31: For the data consisting of excitation and output response, take... Time's up Moment From the set of data, we obtained:

[0081]

[0082]

[0083]

[0084] In the formula, Indicates by Actual output at time Before Actual output at time The output sequence is composed of; Indicates by Actual input at time Before Actual input at time The input sequence is composed of Indicates by Parameters to be identified in the second-order controlled autoregressive model at time step Before Parameters to be identified in the second-order controlled autoregressive model at time step The parameter sequence formed, express dimensional array, express A two-dimensional matrix.

[0085] Step 32, for the model to be identified: ,in Let the information vector of the model to be identified be a sequence of integers that satisfies the following conditions: ,in Representative from The time series corresponding to the valid data starting from a given time point represents the time series corresponding to the valid data obtained after removing obviously excessive or missing data from the collected operational data. Representative from The time series corresponding to the valid data starting at time [time]. Representing time series The length, using Replace the model to be identified The identification model for the variable recursive interval multi-information least squares algorithm can be obtained as follows:

[0086]

[0087] In the formula, This represents the output sequence after the replacement. This represents the input sequence after the replacement. This represents the sequence of parameters after the replacement. express The transpose of .

[0088] like Figure 4 The data shown, y(3) and y(14) are missing or unavailable, two missing output data, while y(9) is bad or unbelievable data because it is significantly off-limits to its surrounding data range. To handle these missing and unbelievable data situations, a valid data sequence is defined that satisfies the following conditions. ,have Therefore, for any , Both are usable. For example Figure 4 The valid data used are: y(0), y(1), y(2), y(4), y(5), y(6), y(7), y(8), y(10), y(11), y(12), y(13), y(15), y(16), y(17), y(18). Then we get... .

[0089] Step 33: Use the variable recursive interval multi-innovation least squares algorithm for identification to obtain the parameters to be identified in the second-order controlled autoregressive model, including... , , , The parameter vector is given by the following formula:

[0090]

[0091] In the formula, Indicates the time series corresponding to the use of valid data. The estimated values ​​of the unidentified parameters of the second-order controlled autoregressive model are obtained by updating the data using current observation data and historical data. Indicates the use of time series The obtained estimated values ​​of the parameters to be identified in the second-order controlled autoregressive model are used as the initial values ​​for the update. express Estimated values ​​of the unidentified parameters of the second-order autoregressive model at time step [time]. Indicates the use of time series The resulting gain matrix is ​​used to adjust the contribution of the current observation data to the model parameter updates. Indicates the use of time series The obtained covariance matrix, Indicates the use of time series The obtained covariance matrix, Represents the identity matrix. In time series The actual output of the servo system obtained below can be understood similarly for other cases. In time series The parameters to be identified in the second-order controlled autoregressive model obtained below can be understood similarly for others.

[0092] Step 34: Calculate the residuals based on the predicted and actual outputs of the second-order controlled autoregressive model, and preliminarily determine the dead zone range based on the residuals.

[0093] Step 341: Calculate the residuals of the second-order controlled autoregressive model. The residuals are defined as the difference between the predicted values ​​and the actual outputs of the second-order controlled autoregressive model, as follows:

[0094]

[0095] In the formula, express The residuals of the second-order controlled autoregressive model at time step 1. yes The actual output of the time servo system yes The predicted output of the second-order controlled autoregressive model at time step 2, if Significant deviations, especially in regions where the input is close to zero, may be caused by dead zones.

[0096] Step 342, Analysis Actual input of the time servo system and Relationship: In the dead zone region, the dead zone affects the output. The deviation from the predicted value. At this point, the residual... It exhibits a clear nonlinear trend, through the analysis of... exist Statistical analysis of the distribution across different intervals was performed to find the residuals in the motor commutation region. The largest critical point is marked as the dead zone critical point, thus extracting the target dead zone parameter range: and , This is the minimum value within the first dead zone. This represents the maximum value within the first dead zone. This is the minimum value of the second dead zone range. This represents the maximum value of the second dead zone range.

[0097] Step 4: Design a Hammerstein model of the servo system with dead-zone nonlinearity based on the dead-zone range.

[0098] Step 41: Assuming the servo system operates at low speeds, the following dynamic model with dead-zone nonlinearity in discrete time is provided: The input speed is, i.e. Actual input of the time servo system , This is a speed command, which can be understood as the target speed value.

[0099] ;

[0100] in It refers to the unknown dead zone parameters, and This is the parameter for the first dead zone, and its range is [missing information]. , This is the second dead zone parameter, and its dead zone range is... .

[0101] Step 42, according to Figure 5 The diagram shown illustrates an input-output model with dead-zone input nonlinearity, and the target velocity... and location These are the actual input command and the actual measured output, respectively. Therefore, the input-output model of the self-designed servo system for a driven motor with dead-zone input nonlinearity can be expressed as:

[0102]

[0103] In the formula, This represents a dynamic model with dead-zone nonlinearity. As intermediate variables, representing the model The predicted output, This represents a second-order controlled autoregressive model. These are intermediate variables, representing the model. The predicted output, It is a shift operator, with unknown measurement noise. Assume the mean is zero and the variance is... The Gaussian white signal. The existing linear part is used for modeling, with coprime polynomials. and The definition is as follows:

[0104]

[0105] coprime polynomials and It is a coprime polynomial characterizing the input and output features of the system. In a drag servo platform, based on the characteristics of the linear segment transfer function of the current loop, we have... ,but:

[0106]

[0107] Step 43: Based on the nonlinear dead zone model in step 42, input the output of the nonlinear module. The definition is as follows:

[0108]

[0109] In the formula, and It is the slope of the linear segment of the nonlinear input function. Therefore... It can also be expressed as follows:

[0110]

[0111] Among them It is the following function, For the function's input:

[0112]

[0113] Step 44: Rewrite using matrix polynomial multiplication get:

[0114]

[0115] intermediate variables and The possible values ​​are as follows:

[0116]

[0117]

[0118] in, , , and Since it is an intermediate variable, the Hammerstein model for the tractor servo system with dead-zone nonlinearity is:

[0119]

[0120]

[0121] Step 45: Based on the formulas in steps 42 and 44, we obtain:

[0122]

[0123] Step 46: The parameter vector for modeling the dead zone of the Hammerstein model. and information vector It can be defined as follows:

[0124]

[0125] in This represents the total number of dimensions, and In a servo system for a tractor motor, the parameter vector that the Hammerstein model needs to identify is... for:

[0126]

[0127] Get the actual output as follows:

[0128]

[0129] Step 47: If no noise term is added here, then... =0, the prediction output error can be calculated using the following formula:

[0130]

[0131] Step 5: The objective function is to minimize the cumulative error between the predicted output and the actual output of the Hammerstein model. Based on the objective function, the linear auxiliary constrained particle swarm optimization algorithm is used to estimate the parameters to be identified in the Hammerstein model offline, and finally the Hammerstein model of the servo system with dead zone nonlinearity is obtained.

[0132] Step 51: Introduce a linearly assisted constrained particle swarm optimization algorithm to estimate the system's model parameters offline. Consider the optimal fit as minimizing the cumulative error between the model's estimated output and the actual measured position output, given the objective function. as follows:

[0133]

[0134] In the formula, To obtain the actual measured time series data of the output signal, The output signal time series data of the Hammerstein model under the same input excitation signal. This can be understood as accumulating all errors to a minimum value, and is used here as a general error calculation formula.

[0135] Dead zone range using the dead zone parameters initially extracted in step 342 and Constrain the search space.

[0136] Step 52: Initialize particle position, velocity, and fitness function. Set the population size to 40, the maximum number of iterations to 1000, and the learning factor... = =1.49445, particle position Particle velocity , The maximum value corresponding to the inertia weight, The minimum value corresponding to the inertia weight.

[0137] Step 53: During the particle swarm convergence process, the velocity and position update formulas for the linearly assisted constrained particle swarm algorithm are as follows:

[0138]

[0139] In the formula, For the updated particle velocity, The particle velocity before the update. The particle positions before the update. For the updated particle positions, It is inertial weight. , It is a learning factor. , It is a random number. It is the particle's own historical optimal position. It is the globally optimal position.

[0140] Determine if the updated particle position exceeds the set linear auxiliary constraint range. If it does, force projection to the boundary of the dead zone; otherwise, do not perform forced projection. The specific execution is as follows:

[0141] The dead zone parameter is calculated based on the updated particle position, and it is determined whether the dead zone parameter is within the dead zone range. If the dead zone parameter is less than the dead zone range, the dead zone parameter is projected to the minimum value of the dead zone range. If the dead zone parameter is greater than the dead zone range, the dead zone parameter is projected to the maximum value of the dead zone range. Then, the updated particle position after projection is obtained by reverse calculation based on the projected dead zone parameter. If the dead zone parameter is within the dead zone range, no forced projection is performed, and the updated particle position is directly accepted.

[0142] Because the dead zone parameters include and Therefore, when determining whether the dead zone range has been exceeded, a check is performed for each dead zone parameter. The corrected result is obtained after projection. and The value is then multiplied by the corresponding parameter (including...). , , and ), to obtain the parameters to be identified in the Hammerstein model after projection update.

[0143] Step 54: Repeat fitness calculation and particle update. If the particle has the best fitness in all dimensions, update it to the historical best solution. Otherwise, repeat the above process until the objective function converges or the maximum number of iterations is reached. Obtain the global optimum and the optimal solution for the parameters to be identified in the Hammerstein model.

[0144] Taking a servo system for a tow motor as an example, the parameters of the Hammerstein model obtained from the optimal solution are... The dead zone parameters are then obtained by solving for them. and Thus, the Hammerstein model of the servo system was obtained. Because So here Represented by vectors The third item divided by the fourth item; Represented by vectors The 5th term divided by the 6th term.

[0145] The identification effect of the identification method designed in this embodiment can be found in [reference]. Figure 6 and Figure 7 The vertical axis in the figure The graph shows speed in rpm and time in seconds. Actual values ​​represent actual speeds, while estimated values ​​represent estimated speeds. The Hammerstein model identified using the method of this invention was tested on a tractor motor servo system platform. The actual speed values ​​of the tractor motor servo system and the estimated speed values ​​output by the Hammerstein model were obtained. The test results show that the tractor motor servo system exhibits high-precision tracking performance under low-speed conditions.

[0146] This invention utilizes the V-MLS method for identification in the low-speed linear phase of the servo system, removing the influence of bad data and initially obtaining the range of dead zone parameters. In the nonlinear phase, a linearly assisted constrained particle swarm optimization algorithm is used for identification. By introducing the range of dead zone parameters to define the search space, the accuracy of local searches is enhanced, the convergence of the algorithm in complex search spaces is accelerated, and the accuracy of the final identification result is improved. The identified model has higher accuracy and better represents the actual characteristics of the controlled system, making it suitable not only for this servo platform but also for wide application in modern industrial equipment.

[0147] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0148] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A high-precision model identification method of a servo system, characterized by, The high-precision model identification method of the servo system comprises the following steps: Obtain linear operation data of the servo system under low-speed working conditions; Construct a second-order controlled autoregressive model according to the linear operation data; Solve the to-be-identified parameters of the second-order controlled autoregressive model by using a variable recursive interval multiple new information least square algorithm, and obtain the predicted output of the second-order controlled autoregressive model based on the to-be-identified parameters, and determine the dead zone range according to the predicted output and the actual output of the second-order controlled autoregressive model; Design a Hammerstein model with dead zone nonlinearity of the servo system according to the dead zone range; Take the cumulative error of the predicted output and the actual output of the Hammerstein model as a target function, and estimate the to-be-identified parameters of the Hammerstein model by using a linear auxiliary constraint particle swarm optimization algorithm according to the target function, and finally obtain the Hammerstein model with dead zone nonlinearity of the servo system.

2. The high precision model identification method of a servo system according to claim 1, characterized by, The step of constructing a second-order controlled autoregressive model according to the linear operation data comprises the following steps: Obtain the transfer function from the output end to the input end of the servo system according to Mason's formula: ； wherein represents a transfer function of a servo system, is a frequency domain input of the servo system, is a frequency domain output of the servo system, is a speed loop gain, is a current loop gain, is a spring constant, is a moment of inertia of a motor in the servo system, is a load moment of inertia, is a viscous friction coefficient, represents a complex variable in a Laplace transform domain; Simplify the transfer function of the servo system as follows: ； wherein represents the frequency domain output of the simplified servo system, is a proportional constant combination including a speed loop gain , a current loop gain , and a spring coefficient , is a time constant; Then, the second-order controlled autoregressive model is constructed as follows: ； wherein and denote the discrete polynomial of the input characteristic and the discrete polynomial of the output characteristic of the servo system, respectively, and are the actual input and the actual output of the servo system at the time instant t, , , and are the four parameters to be identified of the second order controlled autoregressive model, denotes the shift operator.

3. The high precision model identification method of a servo system according to claim 1, characterized by, The step of obtaining the predicted output of the second-order controlled autoregressive model based on the to-be-identified parameters, and determining the dead zone range according to the predicted output and the actual output of the second-order controlled autoregressive model comprises the following steps: Calculate the residual error of the second-order controlled autoregressive model as follows: ； wherein denotes the residual of the second-order controlled autoregressive model at time instant is the actual output of the servo system at time instant is the predicted output of the second-order controlled autoregressive model at time instant Finding residual error in the commutation region of the motor in the low-speed working condition of the servo system The maximum critical point is marked as the dead zone critical point, and the dead zone range of the target dead zone parameter is extracted and , The minimum value of the first dead zone range is The maximum value of the first dead zone range is The minimum value of the second dead zone range is The maximum value of the second dead zone range is 4. The high precision model identification method of a servo system according to claim 1, characterized by, The step of designing a Hammerstein model with dead zone nonlinearity of the servo system according to the dead zone range comprises the following steps: Construct the input-output model of the servo system with dead zone nonlinearity as follows: ； where and are respectively the actual input and the actual output of the servo system, denotes the dynamics model with dead-zone nonlinearity, is an intermediate variable, denoting the predicted output of the dynamics model , denotes the transfer function of the linear part in the Hammerstein model, i.e. the second-order controlled autoregressive model, is an intermediate variable, denoting the predicted output of the model , is a shift operator, is the measurement noise, taken as a Gaussian white signal with zero mean and variance , and denote respectively the discrete polynomial of the input feature and the discrete polynomial of the output feature of the servo system; The dynamic model with dead-zone nonlinearity The processing procedure for the input is as follows: ； where the second order controlled autoregressive model for the intermediate variable The process is as follows: ； Then, the Hammerstein model with dead zone nonlinearity is obtained as follows: ； ； wherein and is the linear segment slope of the kinetic model with dead zone nonlinearity, then the Hammerstein model to be identified parameters wherein , , , are the to-be-identified parameters of the second-order controlled autoregressive model, which are known quantities in the Hammerstein model, and are the unknown dead zone parameters in the dead zone range.

5. The high precision model identification method of a servo system according to claim 4, characterized by, The linear auxiliary constraint particle swarm algorithm outputs the optimal solution of the to-be-identified parameters of the Hammerstein model, the dead zone parameters and According to the calculation of the optimal solution, the first term, the second term, the third term, the fourth term, the fifth term and the sixth term of the Hammerstein model are respectively and , represents the first term of the Hammerstein model , represents the fourth term of the Hammerstein model , represents the fifth term of the Hammerstein model , represents the sixth term of the Hammerstein model .

6. The high precision model identification method of a servo system according to claim 1, characterized by, The linear auxiliary constraint range of the linear auxiliary constraint particle swarm optimization algorithm is the dead zone range.

7. The high precision model identification method of a servo system according to claim 6, characterized by, The step of estimating the to-be-identified parameters of the Hammerstein model by using a linear auxiliary constraint particle swarm optimization algorithm according to the target function comprises the following steps: Initialize the particle position, particle velocity and fitness function, and set the population number, maximum iteration number and learning factor; In the particle convergence process, update the particle position and particle velocity, and judge whether the updated particle position exceeds the set linear auxiliary constraint range, if yes, forcibly project to the boundary of the dead zone range; otherwise, do not perform the forced projection; Repeat the calculation of the fitness function and the update of the particle position and particle velocity until the target function converges or the maximum iteration number is reached, and obtain the optimal solution of the to-be-identified parameters of the Hammerstein model.

8. The high precision model identification method of a servo system according to claim 7, characterized by, The step of judging whether the updated particle position exceeds the set linear auxiliary constraint range, if yes, forcibly project to the boundary of the dead zone range; otherwise, do not perform the forced projection, performs the following steps: According to the updated particle position, a dead zone parameter is calculated, and it is judged whether the dead zone parameter is within a dead zone range. If the dead zone parameter is less than the dead zone range, the dead zone parameter is projected as a minimum value of the dead zone range. If the dead zone parameter is greater than the dead zone range, the dead zone parameter is projected as a maximum value of the dead zone range. Then, according to the projected dead zone parameter, an updated particle position after projection is obtained by reverse solving. If the dead zone parameter is within the dead zone range, no forced projection is performed, and the updated particle position is directly accepted.

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