A mechanical system model identification method

Abstract

The application discloses a mechanical system model identification method, which comprises a driver, a motor, a guide rail, a load in sliding motion and a displacement detection device. The method comprises the following steps: sweeping the frequency of the mechanical system, collecting the swept frequency voltage signal on the driver and the displacement of the displacement detection device as input and output data; obtaining the speed data by differentiating the displacement, transforming the speed data into the frequency domain and smoothing the speed data to obtain a frequency response curve; identifying the frequency of each pair of zero and pole points in a preset frequency identification range, and retaining multiple pairs of zero and pole points with the amplitude and phase change greater than the corresponding change threshold; regarding the frequency before the first zero point as a low frequency band and equivalent to a first-order inertia link, and identifying a first-order transfer function; regarding the frequency after the first zero point as a high frequency band, and identifying the damping ratio of each zero and pole point by using a particle swarm algorithm; and finally obtaining the transfer function of the mechanical system. The application can improve the system identification speed and precision.

Description

Technical Field

[0001] This invention relates to the field of mechanical control technology, and more specifically to a method for identifying mechanical system models. Background Technology

[0002] A typical mechanical system usually includes components such as a driver, guide rail, motor, load, and displacement detection device. The motor is connected to the driver and drives the load, allowing it to slide along the guide rail. The displacement detection device detects and reports changes in the load's position. Generally, model identification of a mechanical system involves first exciting the system to obtain its frequency response function; then fitting the frequency response function curve to obtain the system's transfer function. Given the frequency response curve, current methods for identifying the system's transfer function typically use the model identification toolbox in MATLAB or algorithms such as least squares to identify the overall transfer function. However, the results obtained are generally of a high order, and it is difficult to precisely control the fitting accuracy of each mode.

[0003] By dividing the system into modes, the problem is transformed into identifying the system's zeros and poles, which improves the identification accuracy and allows focus on modal information that has a greater impact on control. The frequencies of zeros and poles are relatively easy to obtain; simply identifying the peaks and troughs is sufficient. However, identifying the damping ratio of zeros and poles is more complicated. After identifying the damping of one zero or pole, the result of identifying the next zero or pole will affect the previous one, requiring readjustment of the previous one. This process is repeated, which is very time-consuming. Currently, this method is generally used manually or semi-automatically, requiring human intervention and resulting in low fitting accuracy. Summary of the Invention

[0004] One objective of this invention is to provide a mechanical system model identification method that significantly improves the system identification speed and accuracy while reducing the system order.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for identifying a mechanical system model, wherein the mechanical system includes a driver, a motor connected to the driver, a guide rail, a load that slides along the guide rail driven by the motor, and a displacement detection device for detecting the load displacement, characterized in that: the method includes the following steps:

[0006] Step S100: Generate a sweep frequency voltage signal and excite the mechanical system. Collect the input data and output data of the mechanical system, where the input data is the sweep frequency voltage signal input to the driver and the output data is the displacement of the load.

[0007] Step S200: Process the displacement to obtain velocity data; process the velocity data and the swept frequency voltage signal into frequency domain data, smooth the frequency domain data, and obtain a frequency response curve composed of multiple discrete points, including the amplitude-frequency response curve and the phase-frequency response curve.

[0008] Step S300: Based on the characteristics of the mechanical system, preset the frequency identification range, amplitude change threshold, and phase change threshold; identify each pair of zero-pole frequencies of the frequency response curve within the frequency identification range; then make a judgment on the above frequencies and retain multiple pairs of zero-pole frequencies whose amplitude change is greater than the amplitude change threshold and whose phase change is greater than the phase change threshold.

[0009] Step S400: Extract the frequency band before the first zero as the low frequency band and identify the transfer function;

[0010] Step S500: Extract the frequency band after the first zero as the high frequency band, and use the particle swarm algorithm to identify the damping ratio of each zero and pole.

[0011] Step S600: Based on the identified zero-pole frequencies, transfer functions, and damping ratios, the transfer function of the mechanical system is obtained.

[0012] Furthermore, in step S500, the step of identification using the particle swarm optimization algorithm includes the following steps:

[0013] Step S501: Construct the evaluation function of the particle swarm optimization algorithm, the expression of which is:

[0014]

[0015] Where J represents the evaluation value, N represents the total number of frequency points in the high-frequency band of the frequency response curve, M'i represents the amplitude of the i-th point of the frequency response curve in the high-frequency band, m is the number of zero-pole pairs obtained in step S3, ωi represents the frequency of the i-th frequency point of the frequency response curve in the high-frequency band, ωzj and ωpj correspond to the frequencies of the j-th pair of zeros and poles, and ζzj and ζpj correspond to the damping ratios of the j-th pair of zeros and poles.

[0016] Step S502: Initialize and set particle swarm algorithm parameters;

[0017] Step S503: Initialize population position and velocity;

[0018] Step S504: Call the evaluation function to calculate the evaluation value of all particles, and update the calculated new velocity and new position;

[0019] Step S505, repeat steps S503-S504, and use the obtained optimal group position as the optimal zero-pole damping ratio output.

[0020] Furthermore, in step S502, the initialized particle swarm optimization (PSO) parameters include population size, maximum number of iterations, inertia factor, learning factor, search boundary, and particle dimension.

[0021] Furthermore, in step S503, the initial position value is randomly generated within the search boundary range, and the initial velocity value is set to 0.

[0022] Furthermore, in step S504, with the optimization objective of minimizing the evaluation value, the corresponding individual optimal position and group optimal position are obtained to update the new velocity and new position.

[0023] Further, in step S505, steps S503-S504 are repeated until the maximum number of iterations is reached.

[0024] Furthermore, in step S400, the low-frequency band is equivalent to a first-order inertial element, and the expression for the transfer function is: Where K is the identified gain coefficient and T is the identified time constant.

[0025] Furthermore, the expression for the transfer function of the mechanical system is:

[0026]

[0027] Where m is the number of zero-pole pairs obtained in step S3, ωzj and ωpj correspond to the frequencies of the j-th zero-pole pair, respectively; ζzj and ζpj correspond to the damping ratios of the j-th zero-pole pair, respectively.

[0028] Furthermore, the maximum value of the frequency identification range is 2-3 times the maximum bandwidth of the mechanical system.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] (1) This invention introduces the particle swarm algorithm to identify the damping ratio of zero poles. It can search for the damping ratio of multiple zero poles at the same time, quickly find the optimal solution, ensure the fitting degree of the frequency response curve, effectively improve the system identification accuracy, and reduce the order of the system. The lower the order of the system transfer function obtained by identification, the lower the order of the controller designed, which is more convenient to implement in code and occupies less resources.

[0031] (2) The method of the present invention has high robustness, can effectively filter out noise, extract effective information, and has a good system recognition rate. It can also be extended to other more complex control systems. More modes will not reduce the recognition accuracy. It is also highly feasible. The particle swarm algorithm evaluation function is simple and practical, with low computational load. It only needs to provide the frequency and amplitude data of the frequency response curve, and shows good optimization effect. Attached Figure Description

[0032] Figure 1 Here is a flowchart of the mechanical system model identification method according to this application;

[0033] Figure 2 This is a schematic diagram of a mechanical system structure according to some embodiments of this application.

[0034] In the diagram: 1. Driver; 2. Motor; 3. Guide rail; 4. Load; 5. Displacement detection device. Detailed Implementation

[0035] The present invention will now be further described in conjunction with specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0036] The terms “comprising” and “having”, and any variations thereof, in the specification and claims of this application are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0037] like Figure 2 As shown, this embodiment proposes a mechanical system model identification method. The mechanical system includes a driver 1, a motor 2 connected to the driver 1, a guide rail 3, a load 4 driven by the motor 2 and sliding along the guide rail 3, and a displacement detection device 5 for detecting the displacement of the load 4. The displacement detection device 5 is installed on at least one side of the guide rail 2.

[0038] like Figure 1 As shown, this method includes the following steps:

[0039] Step S100: Generate a sweep frequency voltage signal and excite the mechanical system. Collect the input data and output data of the system. The input data is the sweep frequency voltage signal input to the driver 1, and the output data is the displacement of the load 4.

[0040] Step S200: Process the displacement to obtain velocity data; process the velocity data and the swept frequency voltage signal into frequency domain data, smooth the frequency domain data, and obtain a frequency response curve composed of multiple discrete points, including the amplitude-frequency response curve and the phase-frequency response curve.

[0041] Step S300: Based on the characteristics of the mechanical system, preset the frequency identification range, amplitude change threshold, and phase change threshold. The maximum value of the frequency identification range is 2-3 times the maximum bandwidth of the mechanical system. Within this frequency identification range, identify each pair of zero-pole frequencies of the frequency response curve, where the poles correspond to the peaks of the amplitude-frequency response curve, and the zeros correspond to the troughs of the amplitude-frequency response curve. Then, make a judgment on the above frequencies and retain multiple pairs of zero-pole frequencies whose amplitude changes are greater than the amplitude change threshold and whose phase changes are greater than the phase change threshold.

[0042] Step S400: Extract the frequency band before the first zero as the low frequency band and identify the transfer function;

[0043] Step S500: Extract the frequency band after the first zero as the high frequency band, and use the particle swarm algorithm to identify the damping ratio of each zero and pole.

[0044] Step S600: Based on the identified zero-pole frequencies, damping ratios, and first-order transfer functions, the transfer function of the mechanical system is obtained.

[0045] Understandably, the particle swarm optimization algorithm can process the damping ratio of multiple zeros and poles simultaneously, thereby obtaining the optimal solution quickly, effectively improving the system identification accuracy, and exhibiting high robustness. It can effectively filter out noise, resulting in a good system recognition rate, and can be applied to more complex control systems.

[0046] Specifically, in step S100, a sweep frequency voltage signal is generated by the sweep frequency signal generation module and used to excite the mechanical system. The sweep frequency voltage signal on the driver of the system is collected by the acquisition module, and the displacement of the load 4 is read by the displacement detection device 5.

[0047] In step S200, the velocity data and swept-frequency voltage signal can be processed into frequency domain data using either the Fast Fourier Transform (FFT) method or the Discrete Fourier Transform (DFT) method. This application does not impose any specific limitations. It is worth noting that compared to the DFT method, the FFT method has lower computational complexity and is faster; therefore, the FFT method is preferred.

[0048] In step S400, the low-frequency band is equated to a first-order inertial element, and the transfer function is identified based on the frequency response curve data in the low-frequency band. This identification can be achieved using software such as MATLAB, LabVIEW, SCILAB, or Octave; this application does not impose specific limitations. The expression for the transfer function is as follows: Where K is the identified gain coefficient and T is the identified time constant.

[0049] Accordingly, in step S600, the expression for the mechanical system transfer function is:

[0050] Where m is the number of pole-zero pairs obtained in step S3, ωzj and ωpj correspond to the frequencies of the j-th pole-zero pair, respectively; ζzj and ζpj correspond to the damping ratios of the j-th pole-zero pair, respectively. It is understandable that the mathematical model of a first-order inertial element is relatively simple, easy to model and analyze, and less prone to instability. Furthermore, the lower the order of the system transfer function identified using the particle swarm optimization algorithm, the lower the order of the controller designed, making it easier to implement in code and requiring fewer resources.

[0051] In step S500, the identification process using the particle swarm optimization algorithm includes the following steps:

[0052] Step S501: Construct the evaluation function of the particle swarm optimization algorithm, the expression of which is:

[0053]

[0054] Where J represents the evaluation value, N represents the total number of frequency points of the frequency response curve in the high-frequency band, M'i represents the amplitude of the i-th point of the frequency response curve in the high-frequency band, m is the number of zero-pole pairs obtained in step S3, ωi represents the frequency of the i-th frequency point of the frequency response curve in the high-frequency band, ωzj and ωpj correspond to the frequencies of the j-th pair of zeros and poles, and ζzj and ζpj correspond to the damping ratios of the j-th pair of zeros and poles, respectively.

[0055] Step S502: Initialize and set particle swarm optimization (PSO) algorithm parameters; specifically including: setting population size, maximum number of iterations, inertia factor, learning factor, search boundary, and particle dimension;

[0056] Step S503: Initialize the population position and velocity; wherein, the initial position value is randomly generated within the search boundary range, and the initial velocity value is set to 0;

[0057] Step S504: Call the evaluation function to calculate the evaluation value of all particles. With minimizing the evaluation value as the optimization objective, find the corresponding individual optimal position and the group optimal position, and update the calculated new velocity and new position.

[0058] Step S505, repeat steps S503-S504 until the maximum number of iterations is reached, and use the obtained optimal position of the population as the optimal zero-pole damping ratio output; it is worth mentioning that it can also be set to end the loop when the deviation between two adjacent generations is within a specified range, and this application does not impose specific restrictions.

[0059] Understandably, this invention utilizes the particle swarm optimization algorithm to identify the zero-pole damping ratio in the high-frequency range, automatically and quickly finding the optimal solution. The particle swarm optimization algorithm evaluation function is simple, practical, and computationally inexpensive. It only requires the frequency and assignment data of the evaluation response curve to achieve good optimization results without human intervention, greatly improving the fitting degree of the frequency response curve, increasing the system identification accuracy, and reducing the system order.

[0060] The basic principles, main features, and advantages of this invention have been described above. Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made without departing from the spirit and scope of the invention, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection claimed by this invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying a mechanical system model, the mechanical system comprising a driver, a motor connected to the driver, a guide rail, a load sliding along the guide rail driven by the motor, and a displacement detection device for detecting the load displacement, characterized in that: This method includes the following steps: Step S100: Generate a sweep frequency voltage signal and excite the mechanical system, and collect the input data and output data of the mechanical system, wherein the input data is the sweep frequency voltage signal input to the driver, and the output data is the displacement of the load; Step S200: Process the displacement to obtain velocity data; process the velocity data and the swept frequency voltage signal into frequency domain data, smooth the frequency domain data to obtain a frequency response curve composed of multiple discrete points, including amplitude-frequency response curve and phase-frequency response curve; Step S300: Based on the characteristics of the mechanical system, preset the frequency identification range, amplitude change threshold, and phase change threshold; identify each pair of zero-pole frequencies of the frequency response curve within the frequency identification range; then make a judgment on the frequencies and retain multiple pairs of zero-pole frequencies whose amplitude change is greater than the amplitude change threshold and whose phase change is greater than the phase change threshold. Step S400: Extract the frequency band before the first zero as the low frequency band and identify the transfer function; Step S500: Extract the frequency band after the first zero as the high frequency band, and use the particle swarm algorithm to identify the damping ratio of each zero and pole. Step S600: Based on the identified zero-pole frequencies, the transfer function, and the zero-pole damping ratio, the mechanical system transfer function is obtained; In step S400, the low-frequency band is equivalent to a first-order inertial element, and the expression for the transfer function is: Where K is the identified gain coefficient and T is the identified time constant; In step S500, the identification process using the particle swarm optimization algorithm includes the following steps: Step S501: Construct the evaluation function of the particle swarm optimization algorithm, the expression of which is: ， ； Where J represents the evaluation value, N represents the total number of frequency points of the frequency response curve in the high-frequency band, M'i represents the amplitude of the i-th point of the frequency response curve in the high-frequency band, m is the number of zero-pole pairs obtained in step S3, ωi represents the frequency of the i-th frequency point of the frequency response curve in the high-frequency band, ωzj and ωpj correspond to the frequencies of the j-th pair of zeros and poles, and ζzj and ζpj correspond to the damping ratios of the j-th pair of zeros and poles. Step S502: Initialize and set particle swarm algorithm parameters; Step S503: Initialize population position and velocity; Step S504: Call the evaluation function to calculate the evaluation value of all particles, and update the calculated new velocity and new position; Step S505, repeat steps S503-S504, and use the obtained optimal group position as the optimal zero-pole damping ratio output.

2. The mechanical system model identification method according to claim 1, characterized in that: In step S502, the initialized particle swarm optimization (PSO) parameters include population size, maximum number of iterations, inertia factor, learning factor, search boundary, and particle dimension.

3. The mechanical system model identification method according to claim 1, characterized in that: In step S503, the initial position value is randomly generated within the search boundary range, and the initial velocity value is set to 0.

4. The mechanical system model identification method according to claim 1, characterized in that: In step S504, with the optimization objective of minimizing the evaluation value, the corresponding individual optimal position and group optimal position are obtained to update the new velocity and new position.

5. The mechanical system model identification method according to claim 2, characterized in that: In step S505, steps S503-S504 are repeated until the maximum number of iterations is reached.

6. The mechanical system model identification method according to any one of claims 1-5, characterized in that: The expression for the transfer function of the mechanical system is: Where m is the final zero-pole logarithm obtained in step S3, and ωz j ,ωp j The frequencies corresponding to the j-th pair of zeros and poles are respectively; ζz j、 ζp j These correspond to the damping ratios of the j-th pair of zero poles.

7. The mechanical system model identification method according to claim 1, characterized in that: The maximum value of the frequency identification range is 2-3 times the maximum bandwidth of the mechanical system.

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