Servo system speed loop parameter self-tuning method based on digital-analog linkage

Abstract

The invention discloses a servo system speed loop parameter self-tuning method based on digital-analog linkage. The method comprises the following steps: establishing an open-loop transfer function of a speed loop of a servo system; parameters of a speed ring are initialized, a same-frequency and same-amplitude speed instruction is sent to a motor to drive a load to operate, and the total rotation inertia of the motor is calculated; a mapping relation equation is determined, and parameters of a speed PI controller are obtained; discretizing the parameters of the speed PI controller by adopting a bilinear method to obtain a discrete proportional gain and a discrete integral gain; determining constraint conditions of the servo system and calculating an evaluation function value according to the ITAE performance evaluation function; obtaining optimal control parameters by adopting a coordinate rotation method; corresponding discrete proportional gain and discrete integral gain are calculated according to the optimal control parameters to serve as parameters of a speed PI controller to complete parameter setting, and load operation is achieved according to a speed instruction. According to the method, the setting process is more efficient, the calculation parameters are more accurate, the manual debugging time can be greatly shortened, and the universality is good.

Description

Technical Field

[0001] The invention belongs to the technical field of motion control, and in particular relates to a servo system speed loop parameter self-tuning method based on digital-analog linkage. Background Art

[0002] Permanent magnet synchronous servo motors have the remarkable characteristics of high power density, no copper loss, low failure rate, simple structure and excellent control performance. They are widely used in many fields such as industrial robotic arms, electric vehicles, and robot systems. Permanent magnet synchronous motor vector control technology is favored because of its good steady-state and dynamic response characteristics. Self-tuning technology is of great significance for balancing the ease of use and motion performance during the use of servo. Through self-tuning technology, the difficulty of servo debugging can be reduced, the performance of the servo system can be improved, the service cost of servo manufacturers can be reduced, and the product can be made more competitive. Compared with manual tuning, the parameter self-tuning method is more time-saving and labor-saving, and can better adapt to the condition of variable load. Therefore, research on self-tuning technology is of great significance for the mass application of permanent magnet synchronous servo motor drivers.

[0003] Traditional self-tuning technologies are mainly divided into two categories: rule-based and model-based methods. Model-based self-tuning methods mainly include ZN tuning method, relay tuning method and tuning method based on frequency domain characteristics. Rule-based self-tuning methods mainly include tuning method based on genetic algorithm, tuning method based on iterative learning, tuning method based on fuzzy theory and tuning method based on pattern recognition.

[0004] However, these two types of self-tuning methods each have different defects. The rule-based method has problems such as complex rule establishment, the final performance of the system depends on the objective function, and if the objective function is inappropriate, the final tuning result will be unreliable. The model-based method has problems such as over-reliance on model accuracy, the result is a single optimal solution, and the tuning parameters are not realistic enough. Summary of the invention

[0005] The purpose of the present invention is to address the above-mentioned problems and propose a servo system speed loop parameter self-tuning method based on digital-analog linkage, which solves the problem that the tuning results of the existing model-based self-tuning technology are overly dependent on model accuracy and are easily interfered by external factors, resulting in inaccurate tuning parameters and failure to achieve optimal motion control performance.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] The servo system speed loop parameter self-tuning method based on digital-analog linkage proposed by the present invention comprises the following steps:

[0008] S1. Establish the open-loop transfer function of the speed loop of the servo system ;

[0009] S2, initialize the speed loop parameters and send the same frequency and amplitude speed command to the motor to drive the load to run, and adjust the total inertia of the motor. Perform real-time calculations;

[0010] S3. Determine the speed loop and open loop cut-off frequency and phase margin The mapping relationship equation between them is based on the total inertia of the motor Through the open loop cut-off frequency and phase margin Calculate the parameters of the speed PI controller, which include the speed proportional gain. and speed integral gain ;

[0011] S4. Use the bilinear method to discretize the parameters of the speed PI controller to obtain discrete proportional gain and discrete integral gain ;

[0012] S5, determining the constraint conditions of the servo system and calculating the evaluation function value according to the ITAE performance evaluation function;

[0013] S6. Based on the constraint conditions, the coordinate rotation method is used to obtain the optimal control parameters of the servo system. The optimal control parameters are the open-loop cutoff frequency corresponding to the minimum evaluation function value. and phase margin ;

[0014] S7, open-loop cutoff frequency corresponding to the minimum evaluation function value and phase margin , calculate the corresponding discrete proportional gain and discrete integral gain As the parameters of the speed PI controller, the parameters are set and the load operation is realized according to the speed command.

[0015] Preferably, the open-loop transfer function of the velocity loop of the servo system is established ,in:

[0016] The speed loop is used to perform the following operations:

[0017] The speed command is sequentially passed through the speed PI controller and the current loop to output the electromagnetic torque of the motor, and the load is driven to operate according to the electromagnetic torque of the motor and the external interference torque. The current loop is used to sequentially pass the current command output by the speed PI controller through the current PI controller and the inverter and then send it to the motor to obtain the electromagnetic torque output by the motor and to feed back to the input end of the current PI controller through the current sensor;

[0018] The actual speed of the load is passed through the speed integration, encoder, speed conversion and filter in sequence to obtain the feedback speed, which is then transmitted to the input end of the speed PI controller;

[0019] Open loop transfer function The formula is as follows:

[0020] (1);

[0021] In the formula, s is a complex variable, is the motor rotor inertia, is the motor load inertia, and the total motor rotation inertia , is the delay time of the inverter, is the filter time constant, is the encoder delay time, is the speed loop update time, is the motor torque coefficient, is the speed proportional gain, is the speed integral gain.

[0022] Preferably, the speed integral is used to convert the actual speed into the actual displacement within the sampling period, the encoder is used to convert the actual displacement into a displacement in digital form, the speed conversion is used to convert the displacement in digital form into a speed in digital form, and the filter is used to low-pass filter the speed in digital form and then output the feedback speed.

[0023] Preferably, the total moment of inertia of the motor Perform real-time calculations as follows:

[0024] S21. Assuming that the motor friction torque is ignored and the motor load torque is zero, the mechanical motion equation is:

[0025] (2);

[0026] In the formula, Represents the electromagnetic torque of the motor, Represents the motor load torque, Indicates the motor speed Perform differentiation with respect to time t;

[0027] S22. Assuming that the motor load torque remains unchanged during the acceleration time period and the deceleration time period, then:

[0028] (3);

[0029] In the formula, Indicates the change in motor speed during the acceleration or deceleration period;

[0030] S23. Calculate the total moment of inertia of the motor :

[0031] (4);

[0032] In the formula, Represents the electromagnetic torque of the motor during the acceleration period, Indicates the electromagnetic torque of the motor during the deceleration period, Indicates the change in motor speed during the acceleration period. Indicates the change in motor speed during the deceleration period.

[0033] Preferably, determine the speed loop and open loop cutoff frequency and phase margin The mapping relationship equation between them is based on the total inertia of the motor Through the open loop cut-off frequency and phase margin The parameters of the speed PI controller are calculated as follows:

[0034] Define the open loop cutoff frequency is the frequency corresponding to the point where the amplitude of the open-loop frequency response function is 1, and the phase margin is the angle between the vector from the origin of the polar coordinate system of the open-loop frequency response function to the point where the amplitude of the open-loop frequency response function is 1 and the negative real axis. Perform frequency response analysis. Substituting into formula (1), we get the following mapping equation:

[0035] (5);

[0036] In the formula, represents the open-loop frequency response function The amplitude of represents the open-loop frequency response function The phase angle, represents the imaginary unit, Represents the inverse tangent function arctan;

[0037] The parameter expression of the speed PI controller is as follows:

[0038] (6).

[0039] Preferably, a bilinear method is used to discretize the parameters of the speed PI controller to obtain a discrete proportional gain and discrete integral gain , as follows:

[0040] Transfer function for speed PI controller Perform Z domain transformation, the formula is as follows:

[0041] (7);

[0042] Where Z represents the Z domain transformation, Indicates the q-axis current of the motor in the dq coordinate system at the current speed loop update time n, Indicates the difference between the speed command and the feedback speed at the current speed loop update time n;

[0043] Will Substituting into formula (7), we can get:

[0044] (8);

[0045] In the formula, Indicates the difference between the q-axis current at the current speed loop update time n and the q-axis current at the previous speed loop update time n-1. It represents the difference between the speed command and the feedback speed at the last speed loop update time n-1, and z represents a complex variable in the digital domain;

[0046] The discrete form of the speed PI controller is expressed as:

[0047] (9);

[0048] In the formula, It represents the output of the speed PI controller at the current speed loop update time n. represents the discrete proportional gain, represents the discrete integral gain;

[0049] Rearranging formula (9) yields:

[0050] (10);

[0051] because , comparing formula (8) and formula (10), we can get:

[0052] (11).

[0053] Preferably, the constraints of the servo system are determined and the evaluation function value is calculated according to the ITAE performance evaluation function, wherein:

[0054] Constraints, the formula is as follows:

[0055] (12);

[0056] In the formula, Indicates the open-loop cutoff frequency and phase margin The proportional gain function, that is, the speed proportional gain in formula (6) The corresponding formula is, Indicates the open-loop cutoff frequency and phase margin The integral gain function, that is, the speed integral gain in formula (6) The corresponding formula is, Indicates the maximum open-loop cutoff frequency;

[0057] ITAE performance evaluation function, the formula is as follows:

[0058] (13);

[0059] In the formula, represents the evaluation function value, represents the speed command at time t, Indicates the feedback speed at time t, t=0~ , Indicates the preset time.

[0060] Preferably, based on the constraint conditions, the coordinate rotation method is used to obtain the optimal control parameters of the servo system, and the optimal control parameters are the open-loop cutoff frequency corresponding to the minimum evaluation function value. and phase margin , as follows:

[0061] The update formulas for S61, open-loop cutoff frequency and phase margin are as follows:

[0062] (14);

[0063] In the formula, represents the open-loop cutoff frequency of the a-th iteration; is the iteration step size of the open-loop cutoff frequency, represents the phase margin of the b-th iteration, represents the iteration step size of the phase margin;

[0064] S62, compare the evaluation function value of the current iteration with the evaluation function value saved in the previous iteration, and save the smaller evaluation function value and the corresponding open-loop cutoff frequency and phase margin The loop is iterated until all constraints are traversed to obtain the minimum evaluation function value and the corresponding open-loop cutoff frequency and phase margin .

[0065] Preferably, the motor is a permanent magnet synchronous motor, and the speed PI controller is an incremental PI controller.

[0066] Preferably, the speed command is a triangular wave speed command, and the update frequency of the speed command is the same as the update frequency of the speed loop.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] The servo system speed loop parameter self-tuning method based on digital-analog linkage provided in the present application combines the theoretical control model with actual data to perform self-tuning of the servo system speed loop parameters. Specifically: an open-loop transfer function of the servo system speed loop is established and the total motor rotation inertia is calculated, a mapping relationship equation between the speed loop and the open-loop cutoff frequency phase margin is determined, and the parameters of the speed PI controller are obtained based on the total motor rotation inertia through the open-loop cutoff frequency and phase margin calculation, the parameters of the speed PI controller are discretized and analyzed to optimize the calculation parameters, and gain parameters (discrete proportional gain and discrete integral gain) that are more in line with reality are obtained; and frequency domain indicators and gain parameters of the servo system are constructed. The mathematical relationship between them is used to transform the optimization problem of gain parameters into the optimization problem of frequency domain parameters. The ITAE performance evaluation function is introduced into the self-tuning process to evaluate the operating performance of the servo system in real time, not just relying on the model to calculate the gain parameters of the servo system. Through the constraints in the frequency domain, the evaluation function value is used as the evaluation index, and the coordinate rotation method is used to explore the optimal evaluation function value and its corresponding open-loop cutoff frequency and phase margin, and the corresponding discrete proportional gain and discrete integral gain are obtained as the parameters of the speed PI controller to complete the parameter tuning and realize the load operation according to the speed instruction. The calculation results of the rolling optimization model are used to improve the accuracy of self-tuning. This method combines the model and real-time data, and has an evaluation system in both the time domain and the frequency domain to reflect the control performance. Its self-tuning parameters can better combine the actual performance, the tuning process is more efficient, and the calculation parameters are more accurate. It can greatly reduce the manual debugging time, improve the automation and intelligence level of the equipment, and has good versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of the method for self-tuning the speed loop parameters of a servo system based on digital-analog linkage of the present invention;

[0070] Figure 2 A schematic diagram of a model of an open-loop transfer function of the present invention;

[0071] Figure 3 A schematic diagram showing the change of the total rotational inertia of the motor of the present invention;

[0072] Figure 4 It is a schematic diagram of the change of the evaluation function value of the present invention;

[0073] Figure 5Schematic diagram of parameter changes of the speed PI controller of the present invention. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0075] It should be noted that, unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art in the technical field of this application. The terms used herein in the specification of this application are only for the purpose of describing specific embodiments and are not intended to limit this application.

[0076] In order to overcome the many problems existing in the traditional model-based self-tuning method, such as the dependence on the modeling accuracy of the servo system model, the irrationality of the assumptions, and the inaccuracy of the final tuning parameters, the present application provides a servo system speed loop parameter self-tuning method based on digital-analog linkage. After obtaining the preliminary tuning parameters through the model, the method searches for the optimal parameters online based on the rule evaluation function and the motion process data drive, and optimizes the self-tuning parameters in a rolling manner, thereby improving the adaptability of the algorithm, the accuracy and availability of the self-tuning parameters.

[0077] like Figure 1-Figure 5 As shown, the servo system speed loop parameter self-tuning method based on digital-analog linkage includes the following steps:

[0078] S1. Establish the open-loop transfer function of the speed loop of the servo system ,in:

[0079] The speed loop is used to perform the following operations:

[0080] The speed command is sequentially passed through the speed PI controller and the current loop to output the electromagnetic torque of the motor, and the load is driven to operate according to the electromagnetic torque of the motor and the external interference torque. The current loop is used to sequentially pass the current command output by the speed PI controller through the current PI controller and the inverter and then send it to the motor to obtain the electromagnetic torque output by the motor and to feed back to the input end of the current PI controller through the current sensor;

[0081] The actual speed of the load is passed through the speed integration, encoder, speed conversion and filter in sequence to obtain the feedback speed, which is then transmitted to the input end of the speed PI controller;

[0082] Open loop transfer function The formula is as follows:

[0083] (1);

[0084] In the formula, s is a complex variable, is the motor rotor inertia, is the motor load inertia, and the total motor rotation inertia , is the delay time of the inverter, is the filter time constant, is the encoder delay time, is the speed loop update time, is the motor torque coefficient, is the speed proportional gain, is the speed integral gain.

[0085] In one embodiment, the speed integral is used to convert the actual speed into the actual displacement within the sampling period, the encoder is used to convert the actual displacement into a displacement in digital form, the speed conversion is used to convert the displacement in digital form into a speed in digital form, and the filter is used to low-pass filter the speed in digital form and then output the feedback speed. Figure 2 The speed feedback filter in the filter corresponds to .

[0086] In one embodiment, the motor is a permanent magnet synchronous motor, and the speed PI controller is an incremental PI controller.

[0087] In one embodiment, the speed command is a triangular wave speed command, and the update frequency of the speed command is the same as the update frequency of the speed loop.

[0088] The motor is a permanent magnet synchronous motor, and the speed PI controller is an incremental PI controller. The speed command is preferably a triangular wave speed command, and the update frequency of the speed command is the same as the update frequency of the speed loop. The speed integral is used to convert the actual speed into the actual displacement within the sampling period, the encoder is used to convert the actual displacement into the displacement in digital form, the speed conversion is used to convert the displacement in digital form into the speed in digital form, and the filter is used to output the feedback speed after low-pass filtering the speed in digital form.

[0089] In order to obtain accurate speed PI controller parameters, it is necessary to establish a transfer function (open-loop transfer function) from the permanent magnet synchronous motor current to the mechanical speed to obtain the corresponding mathematical relationship between the speed loop gain (such as the speed PI controller parameters) and the servo system parameters. Figure 2As shown in the figure, the various components of the speed loop of the servo system are analyzed. The speed loop components include speed PI controller, current loop, load, speed integral, encoder, speed conversion and filter, among which the current loop includes current PI controller, inverter, motor and current sensor. The controlled object is determined to be all parts of the speed loop except the speed PI controller, whose input is the current command and output is the feedback speed. It is known that the update frequency of the current loop is much higher than that of the speed loop, so it can be approximated as an inertia link. The speed PI controller link is added to establish the open-loop transfer function of the speed loop. This open-loop transfer function can represent the mathematical relationship between the gain parameter and the controlled object, which is also the basis for analyzing the frequency response.

[0090] S2, initialize the speed loop parameters and send the same frequency and amplitude speed command to the motor to drive the load to run, and adjust the total inertia of the motor. Perform real-time calculations as follows:

[0091] S21. Assuming that the motor friction torque is ignored and the motor load torque is zero, the mechanical motion equation is:

[0092] (2);

[0093] In the formula, Represents the electromagnetic torque of the motor, Represents the motor load torque, Indicates the motor speed Perform differentiation with respect to time t;

[0094] S22. Assuming that the motor load torque remains unchanged during the acceleration time period and the deceleration time period, then:

[0095] (3);

[0096] In the formula, Indicates the change in motor speed during the acceleration or deceleration period;

[0097] S23. Calculate the total moment of inertia of the motor :

[0098] (4);

[0099] In the formula, Represents the electromagnetic torque of the motor during the acceleration period, Indicates the electromagnetic torque of the motor during the deceleration period, Indicates the change in motor speed during the acceleration period. Indicates the change in motor speed during the deceleration period.

[0100] In order to obtain the basis for self-tuning, it is necessary to identify the servo system and let the motor follow the triangular wave speed command. In this embodiment, the acceleration of the acceleration time period and the deceleration time period are set to 3rps / s, the speed limit (maximum speed) is 5rps, the update frequency of the speed command is consistent with the update frequency of the speed loop, that is, 4000hz, and the acceleration and deceleration movement is continuously performed. Make the motor strictly follow the triangular wave speed command, and assume that the motor load torque remains unchanged during the acceleration time period and the deceleration time period, such as Figure 3 As shown, set the speed target curve with fixed acceleration (triangular wave speed command) to let the motor follow, and the total inertia of the motor rotation The real-time calculation results are as follows Figure 3 .

[0101] S3. Determine the speed loop and open loop cut-off frequency and phase margin The mapping relationship equation between them is based on the total inertia of the motor Through the open loop cut-off frequency and phase margin Calculate the parameters of the speed PI controller, which include the speed proportional gain. and speed integral gain , as follows:

[0102] Define the open loop cutoff frequency is the frequency corresponding to the point where the amplitude of the open-loop frequency response function is 1, and the phase margin is the angle between the vector from the origin of the polar coordinate system of the open-loop frequency response function to the point where the amplitude of the open-loop frequency response function is 1 and the negative real axis. Perform frequency response analysis. Substituting into formula (1), we get the following mapping equation:

[0103] (5);

[0104] In the formula, represents the open-loop frequency response function The amplitude of represents the open-loop frequency response function The phase angle, represents the imaginary unit, Represents the inverse tangent function arctan;

[0105] The parameter expression of the speed PI controller is as follows:

[0106] (6).

[0107] Among them, the mapping relationship equation between the parameters of the speed PI controller and the open-loop cutoff frequency and phase margin is established, and the parameter tuning problem of the speed PI controller is transformed into the problem of finding the optimal open-loop cutoff frequency and phase margin.

[0108] According to the open-loop transfer function, the open-loop cutoff frequency is defined is the frequency corresponding to the point where the amplitude of the open-loop frequency response function is 1, and the phase margin It is the angle between the vector corresponding to the point where the amplitude of the open-loop frequency response function is 1 and the negative real axis (the complex real axis of the complex plane) from the origin of the polar coordinate system of the open-loop frequency response function. Based on the above theory, the speed proportional gain can be established: and speed integral gain and open loop cutoff frequency and phase margin The mapping equation is used to analyze the frequency response of the open-loop transfer function. The speed proportional gain of the speed PI controller and speed integral gain The motor torque coefficient Total inertia of the motor If known, it can be calculated based on the open-loop cutoff frequency and phase margin.

[0109] S4. Use the bilinear method to discretize the parameters of the speed PI controller to obtain discrete proportional gain and discrete integral gain , as follows:

[0110] Transfer function for speed PI controller Perform Z domain transformation, the formula is as follows:

[0111] (7);

[0112] Where Z represents the Z-domain transformation, Indicates the q-axis current of the motor in the dq coordinate system at the current speed loop update time n, Indicates the difference between the speed command and the feedback speed at the current speed loop update time n;

[0113] Will Substituting into formula (7), we can get:

[0114] (8);

[0115] In the formula, Indicates the difference between the q-axis current at the current speed loop update time n and the q-axis current at the previous speed loop update time n-1. It represents the difference between the speed command and the feedback speed at the last speed loop update time n-1, and z represents a complex variable in the digital domain;

[0116] The discrete form of the speed PI controller is expressed as:

[0117] (9);

[0118] In the formula, It represents the output of the speed PI controller at the current speed loop update time n. represents the discrete proportional gain, represents the discrete integral gain;

[0119] Rearranging formula (9) yields:

[0120] (10);

[0121] because , comparing formula (8) and formula (10), we can get:

[0122] (11).

[0123] Among them, for the parameters of the speed PI controller (speed proportional gain and speed integral gain ) can be better applied to digital control systems. The speed PI controller is discretized using a bilinear method. Therefore, through formulas (6) and (11), the gain parameter tuning problem can be transformed into finding the optimal open-loop cutoff frequency. and phase margin The problem is that the open-loop cutoff frequency and phase margin It has the characteristics of being both an indicator and an independent variable for optimization.

[0124] S5. Determine the constraints of the servo system and calculate the evaluation function value according to the ITAE performance evaluation function, where:

[0125] Constraints, the formula is as follows:

[0126] (12);

[0127] In the formula, Indicates the open-loop cutoff frequency and phase margin The proportional gain function, that is, the speed proportional gain in formula (6) The corresponding formula is, Indicates the open-loop cutoff frequency and phase margin The integral gain function, that is, the speed integral gain in formula (6) The corresponding formula is, Indicates the maximum open-loop cutoff frequency;

[0128] ITAE performance evaluation function, the formula is as follows:

[0129] (13);

[0130] In the formula, represents the evaluation function value, represents the speed command at time t, Indicates the feedback speed at time t, t=0~ , Indicates the preset time.

[0131] Among them, according to the performance indicators in the time domain and frequency domain, the constraints in the frequency domain are established to determine the value range of the open-loop cutoff frequency and the phase margin, and the ITAE performance evaluation function of the servo system is established. The results of parameter optimization need to be reflected by evaluation indicators that can reflect the performance of the system. In the time domain characteristics, the time absolute error product integral performance indicator ( , Integral of Time Multiplied by the Absolute Value of Error) is used as the ITAE performance evaluation function. The characteristic of ITAE is that it can evaluate the following status of a specific signal, which directly reflects the final control performance of the servo system. Under the constraints of frequency domain characteristics, the coordinate rotation method can be used to find the optimal open-loop cutoff frequency. and phase margin .

[0132] S6. Based on the constraint conditions, the coordinate rotation method is used to obtain the optimal control parameters of the servo system. The optimal control parameters are the open-loop cutoff frequency corresponding to the minimum evaluation function value. and phase margin , as follows:

[0133] The update formulas for S61, open-loop cutoff frequency and phase margin are as follows:

[0134] (14);

[0135] In the formula, represents the open-loop cutoff frequency of the ath iteration; is the iteration step size of the open-loop cutoff frequency, represents the phase margin of the b-th iteration, represents the iteration step size of the phase margin;

[0136] S62, compare the evaluation function value of the current iteration with the evaluation function value saved in the previous iteration, and save the smaller evaluation function value and the corresponding open-loop cutoff frequency and phase margin The loop is iterated until all constraints are traversed to obtain the minimum evaluation function value and the corresponding open-loop cutoff frequency and phase margin .

[0137] Among them, the parameters of the current speed loop application are evaluated dynamically in real time. Under the constraint conditions, one variable is allowed to change each time, and the other variable remains unchanged, that is, the optimal point is searched in turn along the coordinate direction. Figure 4 As shown in the figure, the iterative process of the coordinate rotation method is as follows: First, determine the initial values ​​of the open-loop cutoff frequency and phase margin, that is, calculate the parameters of the speed PI controller by formula (6) and formula (11), and apply them directly. The motor is given a triangular wave speed command, and the value of ITAE under the parameter is calculated in real time according to the motor tracking performance and maintained. The values ​​of the open-loop cutoff frequency and phase margin are gradually increased within the constraints. The evaluation function value is calculated and compared with the evaluation function value saved in the previous iteration, and the value with a smaller evaluation function value and the corresponding open-loop cutoff frequency and phase margin are saved until the constraints are traversed and the open-loop cutoff frequency and phase margin corresponding to the minimum evaluation function value are searched.

[0138] S7, open-loop cutoff frequency corresponding to the minimum evaluation function value and phase margin , calculate the corresponding discrete proportional gain and discrete integral gain As the parameters of the speed PI controller, the parameters are set and the load operation is realized according to the speed command.

[0139] Figure 4 In the figure, the ordinate represents the evaluation function value, the abscissa represents time (in seconds), and the evaluation function value ITAE (ITAE — The value of the evaluation function gradually decreases during the tuning process. According to the definition of ITAE, it can be said that the tracking speed error during motion is also decreasing, and the dynamic performance of the entire servo system is improving. Finding the minimum value of the evaluation function is the optimal open-loop cutoff frequency and phase margin required.

[0140] like Figure 5 As shown in the figure, the gain parameters are calculated in real time during the tuning process. The vertical axis represents the gain, the horizontal axis represents the time (in seconds), and the solid line is the speed proportional gain. , the dotted line is the speed integral gain , applied to the speed loop, and the actual performance of the parameter is expressed through performance indicators. The range is specified by the constraints of the open-loop cut-off frequency and phase margin, and the best performance indicator is searched within the range to determine the open-loop cut-off frequency, phase margin and corresponding gain parameters with the best actual operating effect.

[0141] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described 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.

[0142] The above-described embodiments only express the more specific and detailed embodiments described in this application, but they cannot be understood as limiting the scope of the application. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of this application, which all belong to the protection scope of this application. Therefore, the protection scope of this application shall be based on the attached claims.

Claims

1. A servo system speed loop parameter self-tuning method based on digital-analog linkage, characterized in that: The servo system speed loop parameter self-tuning method based on digital-analog linkage comprises the following steps: S1. Establish the open-loop transfer function of the speed loop of the servo system ; S2, initialize the speed loop parameters and send the same frequency and amplitude speed command to the motor to drive the load to run, and adjust the total inertia of the motor. Perform real-time calculations; S3. Determine the speed loop and open loop cut-off frequency and phase margin The mapping relationship equation between them is based on the total inertia of the motor Through the open loop cut-off frequency and phase margin Calculate and obtain the parameters of the speed PI controller, wherein the parameters of the speed PI controller include the speed proportional gain and speed integral gain ; S4. Use the bilinear method to discretize the parameters of the speed PI controller to obtain discrete proportional gain and discrete integral gain ; S5, determining the constraint conditions of the servo system and calculating the evaluation function value according to the ITAE performance evaluation function; S6. Based on the constraint conditions, the coordinate rotation method is used to obtain the optimal control parameters of the servo system, where the optimal control parameters are the open-loop cutoff frequency corresponding to the minimum evaluation function value. and phase margin ; S7, open-loop cutoff frequency corresponding to the minimum evaluation function value and phase margin , calculate the corresponding discrete proportional gain and discrete integral gain As the parameters of the speed PI controller, the parameters are set and the load operation is realized according to the speed command.

2. The method for self-tuning speed loop parameters of a servo system based on digital-analog linkage as claimed in claim 1, characterized in that: The open-loop transfer function of the velocity loop of the servo system is established ,in: The speed loop is used to perform the following operations: The speed command is sequentially passed through the speed PI controller and the current loop to output the electromagnetic torque of the motor, and the load is driven to operate according to the electromagnetic torque of the motor and the external interference torque. The current loop is used to sequentially pass the current command output by the speed PI controller through the current PI controller and the inverter and then send it to the motor to obtain the electromagnetic torque output by the motor and to feed back to the input end of the current PI controller through the current sensor; The actual speed of the load is passed through the speed integration, encoder, speed conversion and filter in sequence to obtain the feedback speed, which is then transmitted to the input end of the speed PI controller; The open loop transfer function The formula is as follows: (1)； In the formula, s is a complex variable, is the motor rotor inertia, is the motor load inertia, and the total motor rotation inertia , is the delay time of the inverter, is the filter time constant, is the encoder delay time, is the speed loop update time, is the motor torque coefficient, is the speed proportional gain, is the speed integral gain.

3. The servo system speed loop parameter self-tuning method based on digital-analog linkage as claimed in claim 2, characterized in that: The speed integral is used to convert the actual speed into the actual displacement within the sampling period, the encoder is used to convert the actual displacement into a displacement in digital form, the speed conversion is used to convert the displacement in digital form into a speed in digital form, and the filter is used to output the feedback speed after low-pass filtering the speed in digital form.

4. The method for self-tuning speed loop parameters of a servo system based on digital-analog linkage as claimed in claim 1, characterized in that: The total inertia of the motor Perform real-time calculations as follows: S21. Assuming that the motor friction torque is ignored and the motor load torque is zero, the mechanical motion equation is: (2)； In the formula, Represents the electromagnetic torque of the motor, Represents the motor load torque, Indicates the motor speed Perform differentiation with respect to time t; S22. Assuming that the motor load torque remains unchanged during the acceleration time period and the deceleration time period, then: (3)； In the formula, Indicates the change in motor speed during the acceleration or deceleration period; S23. Calculate the total moment of inertia of the motor : (4)； In the formula, Represents the electromagnetic torque of the motor during the acceleration period, Indicates the electromagnetic torque of the motor during the deceleration period, Indicates the change in motor speed during the acceleration period. Indicates the change in motor speed during the deceleration period.

5. The servo system speed loop parameter self-tuning method based on digital-analog linkage as claimed in claim 2, characterized in that: The speed loop and the open loop cut-off frequency are determined and phase margin The mapping relationship equation between them is based on the total inertia of the motor Through the open loop cut-off frequency and phase margin The parameters of the speed PI controller are calculated as follows: Define the open loop cutoff frequency is the frequency corresponding to the point where the amplitude of the open-loop frequency response function is 1, and the phase margin is the angle between the vector from the origin of the polar coordinate system of the open-loop frequency response function to the point where the amplitude of the open-loop frequency response function is 1 and the negative real axis. Perform frequency response analysis. Substituting into formula (1), we get the following mapping equation: (5)； In the formula, represents the open-loop frequency response function The amplitude of represents the open-loop frequency response function The phase angle, represents the imaginary unit, Represents the inverse tangent function arctan; The parameter expression of the speed PI controller is as follows: (6)。 6. The method for self-tuning speed loop parameters of a servo system based on digital-analog linkage as claimed in claim 5, characterized in that: The bilinear method is used to discretize the parameters of the speed PI controller to obtain a discrete proportional gain and discrete integral gain , as follows: Transfer function for speed PI controller Perform Z domain transformation, the formula is as follows: (7)； Where Z represents the Z-domain transformation, Indicates the q-axis current of the motor in the dq coordinate system at the current speed loop update time n, Indicates the difference between the speed command and the feedback speed at the current speed loop update time n; Will Substituting into formula (7), we can get: (8)； In the formula, Indicates the difference between the q-axis current at the current speed loop update time n and the q-axis current at the previous speed loop update time n-1. It represents the difference between the speed command and the feedback speed at the last speed loop update time n-1, and z represents a complex variable in the digital domain; The discrete form of the speed PI controller is expressed as: (9)； In the formula, It represents the output of the speed PI controller at the current speed loop update time n. represents the discrete proportional gain, represents the discrete integral gain; Rearranging formula (9) yields: (10)； because , comparing formula (8) and formula (10), we can get: (11)。 7. The servo system speed loop parameter self-tuning method based on digital-analog linkage as claimed in claim 5, characterized in that: The constraint conditions of the servo system are determined and the evaluation function value is calculated according to the ITAE performance evaluation function, wherein: The constraint condition is as follows: (12)； In the formula, Indicates the open-loop cutoff frequency and phase margin The proportional gain function, that is, the speed proportional gain in formula (6) The corresponding formula is, Indicates the open-loop cutoff frequency and phase margin The integral gain function, that is, the speed integral gain in formula (6) The corresponding formula is, Indicates the maximum open-loop cutoff frequency; The ITAE performance evaluation function is as follows: (13)； In the formula, represents the evaluation function value, represents the speed command at time t, Indicates the feedback speed at time t, t=0~ , Indicates the preset time.

8. The method for self-tuning speed loop parameters of a servo system based on digital-analog linkage as claimed in claim 7, characterized in that: The optimal control parameter of the servo system is obtained by using the coordinate rotation method based on the constraint conditions, and the optimal control parameter is the open-loop cutoff frequency corresponding to the minimum evaluation function value. and phase margin , as follows: S61, the update formula of the open-loop cut-off frequency and phase margin is as follows: (14)； In the formula, represents the open-loop cutoff frequency of the a-th iteration; is the iteration step size of the open-loop cutoff frequency, represents the phase margin of the b-th iteration, represents the iteration step size of the phase margin; S62, compare the evaluation function value of the current iteration with the evaluation function value saved in the previous iteration, and save the smaller evaluation function value and the corresponding open-loop cutoff frequency and phase margin The loop is iterated until all constraints are traversed, and the minimum evaluation function value and the corresponding open-loop cutoff frequency are obtained. and phase margin .

9. The method for self-tuning speed loop parameters of a servo system based on digital-analog linkage as claimed in claim 1, characterized in that: The motor is a permanent magnet synchronous motor, and the speed PI controller is an incremental PI controller.

10. The method for self-tuning speed loop parameters of a servo system based on digital-analog linkage according to claim 1, characterized in that: The speed command is a triangular wave speed command, and the update frequency of the speed command is the same as the update frequency of the speed loop.

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