A closed-loop frequency response parameter identification method of an electric rudder

Abstract

The application provides a closed-loop frequency response parameter identification method of an electric rudder, and aims at the practical difficulties of the electric rudder modeling process, such as the existence of many links, the complexity of friction and rotational inertia analysis, and many influencing factors. The traditional scheme of directly identifying the specific electrical and mechanical parameters of the electric rudder is abandoned, and the parameter identification problem is merged into the identification problem of two comprehensive parameters and. A closed-loop identification method based on frequency response technology is adopted to establish the parameter representation of the closed-loop model and the transfer function of proportional control; a closed-loop system is constructed to obtain the closed-loop frequency response under each frequency sinusoidal input, the frequency response of each frequency point is nonlinear least square fitted to obtain the fitting value of the parameter and; and the norm of the fitting residual of each frequency point is taken as a criterion to screen out the identification result of the effective data group, so as to ensure the accuracy of parameter identification.

Description

Technical Field

[0001] This invention belongs to the field of electric servo motors, and in particular relates to a method for identifying closed-loop frequency response parameters of an electric servo motor. Background Technology

[0002] Electric servos are a widely used control actuator in aircraft, and their control performance directly affects the aircraft's motion control capability and accuracy. The control performance of electric servos depends on the accuracy and effectiveness of the controlled model, which involves many aspects such as electrical and mechanical components. Accurately identifying and modeling the parameters of each of these aspects is very difficult.

[0003] Traditional parameter identification typically employs: 1) Open-loop frequency response techniques. For sinusoidal input signals of different frequencies, the large dynamic range of the output signal often necessitates manual adjustment of the PWM duty cycle over a wide range, resulting in low signal acquisition efficiency. Furthermore, the drift at the zero point of the output signal complicates signal processing and makes it difficult to guarantee processing accuracy. 2) Closed-loop step response techniques. These use the rise time and overshoot as target values, requiring simulations within a set range of model parameters. Each simulation result is compared with the target value until model parameters that meet the error requirements are found. This approach requires extensive simulation calculations, and the rise time and overshoot are less sensitive to changes in model parameters, often resulting in significant deviations from actual values. Summary of the Invention

[0004] In view of this, the present invention aims to propose a closed-loop frequency response parameter identification method for electric servo motors, in order to solve the problems of low signal acquisition efficiency, low processing accuracy, and large deviation between the obtained model parameters and the actual values ​​in the prior art.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0006] A method for identifying the closed-loop frequency response parameters of an electric servo motor includes the following steps:

[0007] S1. Establish the dynamic equations of the electric servo motor;

[0008] S2. Based on the dynamic equations of the electric servo motor, and by introducing feedback, a closed-loop proportional control model for the electric servo motor is constructed.

[0009] S3. Based on the closed-loop proportional control model, construct the structural block diagram of the proportional control system of the electric servo motor;

[0010] S4. Based on the block diagram of the proportional control system, simplify the transfer function of the electric servo motor and construct a simplified closed-loop model block diagram of the electric servo motor.

[0011] S5. Based on the simplified closed-loop model block diagram, the parameter representations of the closed-loop transfer function and frequency response are obtained;

[0012] S6. Based on the simplified closed-loop model block diagram, construct a proportional control electric servo motor closed-loop system;

[0013] S7. Apply a sinusoidal signal with a set frequency and amplitude to the proportional control electric servo closed-loop system to obtain a measurement signal;

[0014] S8. Calculate the closed-loop frequency response based on the measured signal;

[0015] S9. Fitting comprehensive parameters based on closed-loop frequency response. and ;

[0016] S10. Based on the determined proportional gain, repeat the measurement and calculation process from steps S7 to S9 to obtain multiple sets of measurement data and comprehensive parameters. and The fitted values, based on the set fitting residual norm criterion, are used to select valid sets of measurement data and comprehensive parameters. and The effective value is used to obtain the effective synthesis parameters. and The statistical mean is used as the final parameter identification result.

[0017] Furthermore, in step S1, the dynamic equations of the electric servo motor are established, including:

[0018] Based on the voltage balance equation, the torque balance equation of the motor shaft, and the gear transmission equation, the dynamic equation of the electric servo motor is established.

[0019] Furthermore, in step S3, based on the closed-loop proportional control model, a block diagram of the proportional control system structure of the electric servo motor is constructed, including:

[0020] Based on the closed-loop proportional control model, a Laplace transform is performed under zero initial conditions to obtain the transfer function of the electric servo motor. Based on the transfer function, a block diagram of the proportional control system is constructed.

[0021] Furthermore, in step S7, based on the measured signal, the closed-loop frequency response is calculated, including:

[0022] Based on the established proportional gain selection principle, the proportional gain is determined through trial and error, and the frequency response corresponding to the proportional gain is calculated by performing a fast Fourier transform on the measured signal.

[0023] Furthermore, in step S8, based on the closed-loop frequency response, the comprehensive parameters are fitted. and ,include:

[0024] Based on the closed-loop frequency response, nonlinear least-squares fitting is performed according to the closed-loop transfer function to obtain the comprehensive parameters. and The fitted value is obtained, and the closed-loop transfer function is derived from it.

[0025] Furthermore, in step S5, the expression for the closed-loop transfer function is as follows:

[0026] ;

[0027] In the formula, and For comprehensive parameters, This is the proportional gain.

[0028] Furthermore, in step S5, the expression for the frequency response characteristic is as follows:

[0029] ;

[0030] In the formula, The input frequency is a sine wave. For amplitude characteristics, For the corresponding phase characteristics, and For comprehensive parameters, This is the proportional gain.

[0031] Compared with the prior art, the closed-loop frequency response parameter identification method for an electric servo motor described in this invention has the following advantages:

[0032] (1) Instead of directly identifying the specific electrical and mechanical parameters of the electric servo motor, these parameters are identified and grouped into two comprehensive parameters. and The identification of parameters significantly reduces the difficulty of parameter identification and provides convenience for the subsequent design of servo control schemes.

[0033] (2) Combining frequency response technology with the closed-loop scheme of proportional control solves the problems of zero-point drift of the output signal and the need for manual adjustment of PWM duty cycle in the open-loop scheme. It also avoids the problems of low parameter identification accuracy that may be caused by relying on a large number of simulation search model parameters in the step response scheme due to low sensitivity to changes in model parameters.

[0034] (3) It is easy to operate, iterates quickly, and has high identification efficiency. It can obtain the frequency response characteristics of each frequency point by acquiring a one-time measurement signal. By fitting the frequency characteristics of multiple frequency points with parameters, the accuracy of parameter identification can be effectively guaranteed.

[0035] (4) It is highly versatile and hardly relies on computer simulation. It is applicable to DC electric servo motors with various transmission forms. Attached Figure Description

[0036] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0037] Figure 1 This is a schematic diagram of the electric servo motor proportional control system structure according to an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the simplified closed-loop model structure of the electric servo motor according to an embodiment of the present invention;

[0039] Figure 3 This is a schematic diagram of typical experimental measurement signals for the electric servo motor closed-loop system described in an embodiment of the present invention;

[0040] Figure 4 This is a schematic diagram of the experimental measurement curves of the frequency response characteristics of the electric servo motor closed-loop system under different proportional gains according to an embodiment of the present invention.

[0041] Figure 5 This is a schematic diagram comparing the frequency response described in the embodiment of the present invention with the frequency response calculated from parameters. Detailed Implementation

[0042] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0043] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0044] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0046] like Figures 1 to 5 As shown, this invention provides a closed-loop parameter identification method for electric servo motors based on frequency response. Addressing the common difficulties in electric servo motor modeling, such as the numerous stages involved, particularly the complex analysis of friction and rotational inertia, and the multitude of influencing factors, this invention abandons the traditional approach of directly identifying specific electrical and mechanical parameters of the electric servo motor. Instead, it reduces these parameter identification problems to the identification of two comprehensive parameters, a and b. Employing a closed-loop identification method based on frequency response technology, a closed-loop model of proportional control and a parameter representation of the transfer function are established. A closed-loop system is constructed, and the closed-loop frequency response under sinusoidal input at each frequency is obtained. Nonlinear least-squares fitting is performed on the frequency response at each frequency point to obtain the fitted values ​​of parameters a and b. The norm of the fitting residuals at each frequency point is used as a criterion to select the identification results of valid data sets, ensuring the accuracy of parameter identification.

[0047] This invention effectively solves the problems of zero-point drift in the output signal and the need for manual adjustment of the PWM duty cycle in open-loop frequency response methods. Parameters a and b can be identified in a single measurement, significantly improving parameter identification efficiency. Furthermore, unlike the method in step response techniques that indirectly obtains model parameters through rise time and overshoot, this invention directly identifies the merged composite parameters a and b, ensuring accuracy in parameter identification. The identification results can also be directly used in the design of control schemes.

[0048] A method for identifying the closed-loop frequency response parameters of an electric servo motor includes the following steps:

[0049] (1) Establish an electric servo motor model and simplify it reasonably, and combine all electrical and mechanical parameters into two comprehensive parameters. and Therefore, the parameter identification problem of electric servo motors is reduced to the identification of parameters. and The problem of identification.

[0050] (2) Establish a closed-loop transfer function model of the proportional control electric servo motor and construct an experimental system. Based on this, use frequency response technology to identify parameters.

[0051] (3) Combine the sinusoidal input signals of each frequency and amplitude in time and apply them to the closed-loop system. Due to the presence of the feedback signal, the zero point of the output signal can be stabilized and the PWM duty cycle of the measurement process can be automatically adjusted. The frequency response of each frequency point can be obtained in one measurement.

[0052] (4) Select an appropriate proportional gain, perform a fast Fourier transform on the acquired measurement signal to obtain the amplitude and phase at the corresponding frequency points; according to the parameter representation of the closed-loop transfer function (in... and The transfer function (as an undetermined parameter) is used to perform nonlinear least-squares fitting on the frequency response at each frequency point to obtain the parameters. and The fitted value.

[0053] (5) The statistical mean of the fitting parameters of several sets of valid measurement data is used as the final parameter identification result.

[0054] Based on the specific performance of the servo motor and the signal acquisition method used for parameter identification, the principles for determining the amplitude and frequency range of the input sinusoidal signal, judging the validity of measurement data, and selecting the proportional gain are as follows:

[0055] The preferred frequency and amplitude range of the sinusoidal input signal are shown in Table 1. The signal is sampled at a period of 1ms, with 10,000 sampling points at each frequency point, and a total signal length of 150,000 points (150s).

[0056] Table 1

[0057]

[0058] The preferred criterion for determining the validity of the measurement data is that the norm of the fitting residuals at each frequency point is no greater than 1, so as to minimize the impact of random factors such as machining and assembly on the fitting accuracy.

[0059] The preferred principle for selecting the proportional gain is that the amplitude-frequency resonant peak does not exceed 2dB across the entire frequency range and the amplitude attenuation does not exceed 20dB at the highest frequency. This satisfies the amplitude-to-parameter ratio (P / P). and It has high sensitivity to changes and can ensure a sufficient signal-to-noise ratio at high frequencies.

[0060] The present invention has the following beneficial effects:

[0061] This invention does not directly identify the specific electrical and mechanical parameters of the electric servo motor, but instead combines these parameter identifications into the identification of two comprehensive parameters, a and b. This significantly reduces the difficulty of parameter identification and provides convenience for the subsequent design of servo motor control schemes.

[0062] This invention combines frequency response technology with a closed-loop proportional control scheme, which solves problems such as zero-point drift of the output signal and the need for manual adjustment of the PWM duty cycle in the open-loop scheme. It also avoids the problems of low parameter identification accuracy that may result from relying on a large number of simulation search model parameters in the step response scheme due to the low sensitivity to changes in model parameters.

[0063] This invention is simple to operate, iterates quickly, and has high identification efficiency. It obtains the frequency response characteristics of each frequency point by acquiring a single measurement signal. By fitting the frequency characteristics of multiple frequency points with parameters, the accuracy of parameter identification can be effectively guaranteed.

[0064] This invention is highly versatile, requires almost no computer simulation, and is applicable to DC electric servos with various transmission methods.

[0065] Example 1

[0066] The present invention will be further illustrated using an air servo motor-driven DC servo motor as an example. A method for identifying the closed-loop frequency response parameters of an electric servo motor includes the following steps:

[0067] Step 1: Establish the dynamic equations of the electric servo system

[0068] Based on the voltage balance equation of a DC motor, the torque balance equation of the motor shaft, and the gear transmission equation, the dynamic equation of the electric servo motor is established, and the expression is as follows:

[0069] (1);

[0070] In the formula, For armature inductance, For armature resistance, For armature current, The voltage applied across the armature, The back electromotive force constant is... This is the motor torque constant, which has numerical values ​​when using the International System of Units (SI). , The total moment of inertia referred to the motor shaft, The total viscous friction coefficient referred to the motor shaft, For load torque, This refers to the reduction ratio of the transmission mechanism. The angular velocity of the motor shaft rotation. This refers to the rotation angle of the motor shaft. To output the corner, It is a time variable.

[0071] Step 2: Establish a closed-loop proportional control model for the electric servo motor.

[0072] Based on the dynamic equations of the electric servo motor, feedback is introduced to establish a closed-loop model of proportional control, that is, the following expression is added to equation (1):

[0073] (2);

[0074] In the formula, The voltage applied across the armature, To output the corner, For time variables, For proportional gain, This is the reference input for the corner.

[0075] Step 3: Obtain the block diagram representation of the electric servo motor.

[0076] Based on the entire closed-loop model consisting of equations (1) and (2), the Laplace transform is performed under zero initial conditions, and the transfer functions of each part are obtained as follows:

[0077] (3);

[0078] In the formula, For complex variables, In equation (1) Laplace transform, The input signal in equation (2) Laplace transform, The output rotation angle in equation (2) The Laplace transform of the variables is similar, and the correspondence of the other variables is similar.

[0079] like Figure 1 As shown, the block diagram of the proportional control system corresponding to equation (3) is shown in the figure. This indicates an error signal.

[0080] Step 4: Simplify the block diagram of the proportional control system and separate the parameters to be identified.

[0081] Based on the characteristics of DC motors, armature inductance is ignored. and load Move to At the same summation point, such as Figure 2 As shown in the simplified model block diagram, the simplified transfer function of the electric servo motor is as follows:

[0082] (4);

[0083] In the formula, Let be the transfer function of the electric servo motor. For complex variables, and These are comprehensive parameters.

[0084] Among them, parameters , Process parameters The relationship between the mechanical and electrical parameters is expressed as follows:

[0085] ; ; ;

[0086] In the formula, and For comprehensive parameters, The torque constant of the motor. This refers to the reduction ratio of the transmission mechanism. For armature resistance, For process parameters, The total moment of inertia referred to the motor shaft, The total viscous friction coefficient referred to the motor shaft, is the back electromotive force constant.

[0087] Step 5: Obtain the parameter representations of the closed-loop transfer function and frequency response.

[0088] based on Figure 2 The simplified model block diagram is shown below. The closed-loop transfer function from the reference input to the corner output is calculated, and the expression is as follows:

[0089] (5);

[0090] In the formula, For closed-loop transfer function. For complex variables, and For comprehensive parameters, This is the proportional gain.

[0091] Under sinusoidal input conditions, the frequency response is expressed as follows:

[0092] (6);

[0093] In the formula: The input frequency is a sine wave. For amplitude characteristics, For the corresponding phase characteristics, and For parameters, This is the proportional gain.

[0094] Step 6: Construct an electric servo motor closed-loop system and acquire the output signal.

[0095] according to Figure 2A simplified block diagram is used to construct a proportionally controlled electric servo motor closed-loop system. Sine signals of various frequencies and amplitudes as shown in Table 1 are applied continuously at once, and the output rotation angle signal is recorded. Typical measurement signals include... Figure 3 As shown, the zero point of the output sine signal is stable.

[0096] Step 7: Calculate the closed-loop frequency response

[0097] Based on the selection principle of proportional gain, a suitable proportional gain is determined through trial and error. A fast Fourier transform is then performed on the measured signal to obtain the system's frequency response characteristics. For example... Figure 4 As shown, the frequency responses are for proportional gains of 8, 10, and 12. Figure 4 In the diagram, the vertical axis represents Magnitude and the horizontal axis represents Frequency.

[0098] Step 8: Fitting Parameters and

[0099] Using the amplitude-frequency data of the frequency response, nonlinear least-squares fitting is performed on each frequency point according to equation (6) to obtain the parameters. and The fitted value is obtained, and thus the closed-loop transfer function described by equation (5) is obtained.

[0100] like Figure 5 As shown, when the proportional gain is 8, a comparison is made between the frequency response obtained from measurement and the frequency response calculated from the fitted transfer function. Figure 5 In the diagram, the vertical axis represents Magnitude and the horizontal axis represents Frequency.

[0101] Step 9: Repeated measurements and calculations to obtain parameters. and Identification results

[0102] Based on the selected proportional gain, repeat steps six through eight of the above measurement and calculation process to obtain multiple sets of measurement data and parameter fitting values. Based on the fitting residual norm criterion, select the valid data and calculate the parameters for each valid data set. and The statistical mean is used as the final parameter identification result.

[0103] For each channel of the two servos (each servo has 4 independent channels, numbered I) IV markings) respectively in no bias and With a 12° bias, the sinusoidal input signal as shown in Table 1 was applied, and signal acquisition and processing were performed. The fitted parameters are shown in Table 2. In order to interpret the fitting effect, the norm of the fitting residuals (represented by Nres in the table) is also given in the table.

[0104] Table 2. Parameter identification results for each channel of the two servos ( )

[0105]

[0106] After discarding invalid data (residuals greater than 1), the parameters in Table 2 are... and Statistical analysis yielded the following parameter identification values ​​(mean) and standard deviations:

[0107] ; ;

[0108] ; ;

[0109] In the formula, and Parameters and The statistical mean and The standard deviation of the corresponding parameter, This represents the number of valid data sets.

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying closed-loop frequency response parameters of an electric servo motor, characterized in that: Includes the following steps: S1. Establish the dynamic equations of the electric servo motor; S2. Based on the dynamic equations of the electric servo motor, and by introducing feedback, a closed-loop proportional control model for the electric servo motor is constructed. S3. Based on the closed-loop proportional control model, construct the structural block diagram of the proportional control system of the electric servo motor; S4. Based on the block diagram of the proportional control system, simplify the transfer function of the electric servo motor and construct a simplified closed-loop model block diagram of the electric servo motor. S5. Based on the simplified closed-loop model block diagram, the parameter representations of the closed-loop transfer function and frequency response are obtained; In step S5, the expression for the closed-loop transfer function is as follows: ； In the formula, and For comprehensive parameters, For proportional gain, It is a complex variable; The expression for the frequency response characteristic is as follows: ； In the formula, The input frequency is a sine wave. For amplitude characteristics, For the corresponding phase characteristics, and For comprehensive parameters, For proportional gain; S6. Based on the simplified closed-loop model block diagram, construct a proportional control electric servo motor closed-loop system; S7. Apply a sinusoidal signal with a set frequency and amplitude to the proportional control electric servo closed-loop system to obtain a measurement signal; S8. Calculate the closed-loop frequency response based on the measured signal; S9. Fitting comprehensive parameters based on closed-loop frequency response. and ; S10. Based on the determined proportional gain, repeat the measurement and calculation process from steps S7 to S9 to obtain multiple sets of measurement data and comprehensive parameters. and The fitted values, based on the set fitting residual norm criterion, are used to select valid sets of measurement data and comprehensive parameters. and The effective value is used to obtain the effective synthesis parameters. and The statistical mean is used as the final parameter identification result.

2. The method for identifying closed-loop frequency response parameters of an electric servo motor according to claim 1, characterized in that: In step S1, the dynamic equations of the electric servo motor are established, including: Based on the voltage balance equation, the torque balance equation of the motor shaft, and the gear transmission equation, the dynamic equation of the electric servo motor is established.

3. The method for identifying closed-loop frequency response parameters of an electric servo motor according to claim 1, characterized in that: In step S3, based on the closed-loop proportional control model, a block diagram of the proportional control system structure of the electric servo motor is constructed, including: Based on the closed-loop proportional control model, a Laplace transform is performed under zero initial conditions to obtain the transfer function of the electric servo motor. Based on the transfer function, a block diagram of the proportional control system is constructed.

4. The method for identifying closed-loop frequency response parameters of an electric servo motor according to claim 1, characterized in that: In step S7, the closed-loop frequency response is calculated based on the measured signal, including: Based on the established proportional gain selection principle, the proportional gain is determined through trial and error, and the frequency response corresponding to the proportional gain is calculated by performing a fast Fourier transform on the measured signal.

5. The method for identifying closed-loop frequency response parameters of an electric servo motor according to claim 1, characterized in that: In step S8, the comprehensive parameters are fitted based on the closed-loop frequency response. and ,include: Based on the closed-loop frequency response, nonlinear least-squares fitting is performed according to the closed-loop transfer function to obtain the comprehensive parameters. and The fitted value is obtained, and the closed-loop transfer function is derived from it.

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