Servo system bandwidth extension method, apparatus and device

Abstract

This application relates to the field of servo control technology, and in particular to a method, apparatus, and device for extending the bandwidth of a servo system. The method includes: acquiring speed data, current data, and panel gain data of the servo system; identifying speed loop parameters of the servo system based on the speed data, current data, and panel gain data; identifying low-frequency rigid body model parameters based on the speed data; identifying high-frequency flexible model parameters based on the speed data; constructing a speed loop controlled object model based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters; and extending the bandwidth of the servo system based on the speed loop controlled object model and the speed loop parameters. This solves the problems of limited bandwidth extension and low control accuracy in related technologies for servo closed-loop systems.

Description

Technical Field

[0001] This application relates to the field of servo control technology, and in particular to a method, apparatus and device for extending the bandwidth of a servo system. Background Technology

[0002] In high-end manufacturing and precision automation, servo drive systems need to balance high bandwidth and closed-loop stability. Actual electromechanical systems exhibit flexible modes and mechanical resonance caused by elastic deformation of transmission components. Related technologies struggle to accurately identify the parameters of these flexible modes. When increasing controller gain to expand bandwidth, resonance can easily lead to insufficient phase margin, oscillation, or even instability, limiting the improvement of servo system bandwidth and control performance. Summary of the Invention

[0003] This application provides a method, apparatus, and device for expanding the bandwidth of a servo system, in order to solve the problems of limited bandwidth enhancement and low control accuracy in related technologies.

[0004] The first aspect of this application provides a method for extending the bandwidth of a servo system, comprising the following steps: acquiring speed data, current data, and panel gain data of the servo system; identifying speed loop parameters of the servo system based on the speed data, current data, and panel gain data; identifying low-frequency rigid body model parameters based on the speed data; identifying high-frequency flexible model parameters based on the speed data; constructing a speed loop controlled object model based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters; and extending the bandwidth of the servo system based on the speed loop controlled object model and the speed loop parameters.

[0005] Based on the aforementioned technical means, this application embodiment constructs a rigid-flexible coupled velocity loop controlled object model by separately identifying the parameters of low-frequency rigid body and high-frequency flexible model. Based on this model, the system bandwidth is expanded, solving the bandwidth bottleneck caused by the single rigid body model ignoring flexible modes and conservative tuning in related technologies. It also predicts the system stability boundary and achieves high bandwidth and high stability. At the same time, this method relies on the measured data of the servo system to complete the identification, eliminating the need for complex offline calibration and directly connecting to the industrial controller parameter system. This significantly reduces the difficulty of engineering implementation and greatly improves the practicality and promotion value of the technology.

[0006] Optionally, identifying high-frequency flexible model parameters based on speed data includes: extracting speed command and actual speed response data from the speed data; determining a high-order empirical model of the closed-loop speed transfer function based on the speed command and actual speed response data; reconstructing the open-loop frequency response function based on the high-order empirical model; acquiring vibration signals during the motion of the servo system; and identifying high-frequency flexible model parameters based on the spectral analysis results of the vibration signals and the open-loop frequency response function.

[0007] Based on the aforementioned technical means, this application embodiment extracts speed commands and actual speed response data, constructs a high-order empirical model, reconstructs the open-loop frequency response, and then combines vibration signal spectrum analysis to accurately locate the flexible mode, achieving precise identification of high-frequency flexible model parameters. This solves the problem in related technologies where high-frequency flexible dynamics are suppressed and difficult to accurately capture in closed-loop conditions, providing reliable parameter support for constructing a high-fidelity rigid-flexible coupling model. This ensures the scientific validity and stability of subsequent bandwidth expansion. Furthermore, identification based on measured data adapts to industrial closed-loop operating conditions without requiring additional excitation devices, improving engineering adaptability.

[0008] Optionally, the parameters of the high-frequency flexible model are identified based on the spectral analysis results and open-loop frequency response function of the vibration signal, including: identifying the resonant frequency range in the spectral analysis results of the vibration signal; determining the target frequency band based on the resonant frequency range; fitting the high-frequency flexible model to the open-loop frequency response function in the target frequency band; and determining the parameters of the high-frequency flexible model based on the fitting results.

[0009] Based on the aforementioned technical means, this embodiment of the application first identifies the resonant frequency range in the vibration signal spectrum to define the target frequency band, then specifically fits the high-frequency flexible model to the open-loop frequency response function of that frequency band, and finally accurately extracts the high-frequency flexible model parameters. This approach avoids the drawbacks of blindly fitting across the entire frequency band, focusing on the key frequency band dominated by the flexible mode. It effectively solves the problems of suppressed high-frequency flexible dynamic signals and low identification accuracy in closed-loop systems, ensuring that the identified model parameters not only satisfy the dynamic laws but also adapt to practical application scenarios, laying a data foundation for the subsequent construction of rigid-flexible coupled controlled object models.

[0010] Optionally, the bandwidth of the servo system is extended based on the controlled object model and speed loop parameters, including: establishing the open-loop transfer function of the speed loop based on the controlled object model and speed loop parameters; analyzing the open-loop transfer function of the speed loop and constructing a stable parameter region based on the analysis results; establishing a multi-objective optimization problem based on the stable parameter region and the performance objectives of the servo system, with the performance objectives being to maximize the closed-loop bandwidth and integral gain; and determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem.

[0011] Based on the aforementioned technical means, this embodiment establishes the open-loop transfer function of the velocity loop, analyzes and obtains the stable parameter region, and then constructs a multi-objective optimization problem by combining the performance objectives of maximizing closed-loop bandwidth and integral gain, ultimately determining the target control parameters of the servo system. It abandons the empirical trial-and-error tuning mode in related technologies, using a clear stability boundary as a constraint and guided by optimal performance indicators to conduct parameter optimization. This not only overcomes the bandwidth improvement bottleneck caused by conservative tuning strategies but also ensures the stability and reliability of system operation, significantly improving the scientific rigor and accuracy of the bandwidth expansion method.

[0012] Optionally, the open-loop transfer function of the velocity loop is:

[0013] in, For the velocity loop proportional gain, For velocity loop integral gain, The total inertia of the system. For external damping of the system, , , These are the parameters for the high-frequency flexible model. These are the complex parameters of the Laplace transform; The stable parameter region is bounded by two stability boundary curves, which include a linear boundary and a quadratic boundary. The linear boundary is:

[0014] in This refers to intermediate constant terms that are completely determined by the parameters of the controlled object. The boundary of the quadratic curve is:

[0015] in, and It is about A linear function:

[0016] in, For the overall damping term of the controlled object, Let be the rigid-flexible coupling constant of the controlled object. These are intermediate constants determined by the parameters of the controlled object. The modal coupling coefficient of the controlled object is denoted as .

[0017] Optionally, the multi-objective optimization problem includes an objective function and constraints, wherein the objective function is:

[0018] Among them, weight , For closed-loop bandwidth, The velocity loop integral gain; The constraints include global robustness constraints and flexible mode suppression constraints, among which, The global robustness constraint is:

[0019] The flexible modal suppression constraint is: .

[0020] Optionally, before determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem, the method further includes: converting the multi-objective optimization problem into an unconstrained penalty function; and determining the solution results of the multi-objective optimization problem based on the unconstrained penalty function, wherein the unconstrained penalty function is:

[0021] in It has a high weight.

[0022] Optionally, the target control parameters of the servo system are determined based on the solution results of the multi-objective optimization problem, including: traversing the PI controller parameter combinations that satisfy the hardware constraints within the stable parameter region; calculating the closed-loop frequency response of each PI controller parameter combination; evaluating the objective function value and the degree of constraint violation based on the closed-loop frequency response; generating a two-dimensional mapping map covering the performance and robustness of the entire stable domain; screening candidate control parameters based on the two-dimensional mapping map; and determining the target control parameters from the candidate control parameters.

[0023] Based on the aforementioned technical means, this embodiment of the application traverses the PI controller parameter combinations that satisfy hardware constraints within the stable parameter region, calculates the closed-loop frequency response corresponding to each parameter combination, and evaluates the objective function value and the degree of constraint violation. Finally, it generates a two-dimensional performance and robustness mapping diagram covering the entire stable domain, and then uses this diagram to select and determine the target control parameters. This transforms the abstract parameter optimization problem into an intuitive visual graph, abandoning the blind trial-and-error mode of parameter tuning in related technologies. This not only significantly shortens the on-site debugging cycle but also ensures that the selected control parameters meet both performance requirements and system robustness constraints, significantly improving engineering practicality and implementation efficiency.

[0024] A second aspect of this application provides a servo system bandwidth expansion device, comprising: an acquisition module for acquiring speed data, current data, and panel gain data of the servo system; a construction module for identifying speed loop parameters of the servo system based on the speed data, current data, and panel gain data, identifying low-frequency rigid body model parameters based on the speed data, identifying high-frequency flexible model parameters based on the speed data, and constructing a speed loop controlled object model based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters; and an expansion module for expanding the servo system bandwidth based on the speed loop controlled object model and the speed loop parameters.

[0025] Optionally, the construction module is further used to: identify high-frequency flexible model parameters based on speed data, including: extracting speed command and actual speed response data from the speed data; determining a high-order empirical model of the closed-loop speed transfer function based on the speed command and actual speed response data, and reconstructing the open-loop frequency response function based on the high-order empirical model; acquiring vibration signals during the motion of the servo system, and identifying high-frequency flexible model parameters based on the spectral analysis results of the vibration signals and the open-loop frequency response function.

[0026] Optionally, the construction module is further used to: identify high-frequency flexible model parameters based on the spectral analysis results and open-loop frequency response function of the vibration signal, including: identifying the resonant frequency range in the spectral analysis results of the vibration signal; determining the target frequency band based on the resonant frequency range; fitting the high-frequency flexible model to the open-loop frequency response function in the target frequency band; and determining the high-frequency flexible model parameters based on the fitting results.

[0027] Optionally, the extension module is further used to: establish the open-loop transfer function of the speed loop based on the controlled object model and speed loop parameters; analyze the open-loop transfer function of the speed loop and construct a stable parameter region based on the analysis results; establish a multi-objective optimization problem based on the stable parameter region and the performance objectives of the servo system, with the performance objectives being to maximize the closed-loop bandwidth and integral gain; and determine the target control parameters of the servo system based on the solution results of the multi-objective optimization problem.

[0028] Optionally, the open-loop transfer function of the velocity loop is:

[0029] in, For the velocity loop proportional gain, For velocity loop integral gain, The total inertia of the system. For external damping of the system, , , These are the parameters for the high-frequency flexible model. Let be the complex parameters of the Laplace transform; the stable parameter region is bounded by two stability boundary curves, which include a linear boundary and a quadratic boundary. The linear boundary is:

[0030] in The intermediate constant term is completely determined by the parameters of the controlled object; the boundary of the quadratic curve is: ;in, and It is about A linear function:

[0031] in, For the overall damping term of the controlled object, Let be the rigid-flexible coupling constant of the controlled object. These are intermediate constants determined by the parameters of the controlled object. The modal coupling coefficient of the controlled object is denoted as .

[0032] Optionally, the multi-objective optimization problem includes an objective function and constraints, wherein the objective function is:

[0033] Among them, weight , For closed-loop bandwidth, The integral gain of the velocity loop is given; the constraints include global robustness constraints and flexible mode suppression constraints, wherein the global robustness constraints are:

[0034] The flexible modal suppression constraint is: .

[0035] Optionally, it also includes a determination module, used to convert the multi-objective optimization problem into an unconstrained penalty function before determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem; and to determine the solution results of the multi-objective optimization problem based on the unconstrained penalty function, wherein the unconstrained penalty function is:

[0036] in It has a high weight.

[0037] Optionally, the extension module is further configured to: determine the target control parameters of the servo system based on the solution results of the multi-objective optimization problem, including: traversing the PI controller parameter combinations that satisfy the hardware constraints within the stable parameter region; calculating the closed-loop frequency response of each PI controller parameter combination; evaluating the objective function value and the degree of constraint violation based on the closed-loop frequency response; generating a two-dimensional mapping map covering the performance and robustness of the entire stable domain; screening candidate control parameters based on the two-dimensional mapping map; and determining the target control parameters from the candidate control parameters.

[0038] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the program to implement the servo system bandwidth expansion method as described in the above embodiments.

[0039] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0040] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a servo system bandwidth expansion method provided according to an embodiment of this application; Figure 2 This is a schematic diagram of the speed loop controlled object according to an embodiment of this application; Figure 3 This is a flowchart of a servo system parameter identification method provided according to an embodiment of this application; Figure 4 This is a schematic diagram of the stability domain of the speed loop PI control parameters according to an embodiment of this application; Figure 5 To obtain a robust stability constraint contour plot for numerical solution of the multi-objective velocity loop closed-loop frequency response shaping algorithm provided in the embodiments of this application; Figure 6 To numerically solve the first-order natural frequency gain constraint contour plot according to the multi-target velocity loop closed-loop frequency response shaping algorithm provided in the embodiments of this application; Figure 7 To numerically solve the closed-loop bandwidth performance contour plot according to the multi-target velocity loop closed-loop frequency response shaping algorithm provided in the embodiments of this application; Figure 8 Numerical solution of the optimal control parameter closed-loop Bode plot using the multi-objective velocity loop closed-loop frequency response shaping algorithm provided in the embodiments of this application; Figure 9 Performance graphs provided according to embodiments of this application; Figure 10 This is a block diagram of a servo system bandwidth expansion device according to an embodiment of this application; Figure 11 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0041] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0042] Currently, in high-end manufacturing, precision automation, and robotics systems, the dynamic performance of servo drive systems directly determines the processing accuracy, production efficiency, and operational stability of equipment. Improving system bandwidth and positional stiffness while ensuring closed-loop stability has become a key challenge in the field of servo control. However, practical electromechanical systems commonly suffer from flexible modes and mechanical resonance caused by elastic deformation of transmission components. Related technologies have the following shortcomings in addressing this problem: First, the conservative PID tuning method simplifies the system into a rigid body model, treats resonance as a hard constraint, and sets the closed-loop bandwidth in a range far below the first-order resonance frequency, which seriously sacrifices the dynamic performance of the system. Secondly, resonance suppression filtering technology introduces local phase lag, compresses phase margin, and static notch filters are sensitive to changes in operating conditions, and are prone to secondary oscillations due to frequency mismatch. Thirdly Advanced control methods, such as control, rely heavily on the selection of weight functions. Simplified weight functions are difficult to accurately characterize complex performance requirements, resulting in conservative optimization results and a lack of universality. Fourth, the relevant technical methods generally lack theoretical understanding of the relationship between flexible modal parameters and closed-loop amplitude-frequency characteristics, and the control parameter tuning lacks clear basis, which limits the space for machine-control collaborative optimization.

[0043] In summary, the relevant technologies struggle to balance high bandwidth and high stability in scenarios where the resonant frequency is close to the target bandwidth, thus failing to fully tap the performance potential of flexible servo systems and hindering the development of servo control technology in high-precision and high-speed applications.

[0044] The following description, with reference to the accompanying drawings, outlines a servo system bandwidth expansion method, apparatus, and device according to embodiments of this application. Addressing the limitations in bandwidth enhancement and low control accuracy of servo closed-loop systems mentioned in the background section, this application provides a servo control optimization method suitable for high-precision motion control systems exhibiting structural flexibility and mechanical resonance. This method focuses on system identification, closed-loop frequency response shaping, multi-objective performance optimization under stability constraints, and correlation analysis between flexible modal parameters and the topological structure of the closed-loop response amplitude-frequency characteristics. Through direct closed-loop frequency response shaping and multi-objective optimization within the analytical stability domain, it effectively utilizes structural resonance characteristics. This method can be applied to high-precision equipment such as CNC machine tools, industrial robots, and precision positioning platforms, providing a theoretically rigorous, engineering-feasible, and performance-approaching-physical-limits servo control scheme to improve the tracking accuracy, contour control performance, and dynamic response capability of highly flexible electromechanical systems.

[0045] Specifically, Figure 1 This is a flowchart illustrating a servo system bandwidth expansion method provided in an embodiment of this application.

[0046] like Figure 1As shown, the servo system bandwidth expansion method includes the following steps: In step S101, the speed data, current data, and panel gain data of the servo system are acquired.

[0047] It is understood that the embodiments of this application directly collect measured data on speed, current, and panel gain during the actual operation of the servo system, without the need for additional complex sensing equipment or the construction of a dedicated data acquisition platform. This adapts to actual industrial conditions and reduces the difficulty of engineering implementation. Simultaneously, these data accurately reflect the system's motion state, power output state, and control parameter state, avoiding deviations from offline simulations or theoretical assumptions. This provides accurate and reliable raw data for subsequent operations such as speed loop parameter identification, low-frequency rigid body and high-frequency flexible model construction, and bandwidth expansion optimization.

[0048] It should be noted that the speed data can be the measured data related to the motor speed command and actual speed response during the operation of the servo system, the current data can be the measured data of the input current driving the motor, and the panel gain data can be the basic gain parameters that can be directly viewed and set on the servo system operation panel.

[0049] Specifically, this application collects measured signals such as position error, speed command, speed error, motor current, and panel gain of the servo system to provide raw data for subsequent parameter mapping and dynamic identification. Among them, speed data is used for high-frequency flexible model parameter identification and closed-loop frequency response estimation, current data assists in speed loop parameter calibration, and panel gain data is used to establish the mapping relationship between control system panel parameters and theoretical control parameters, providing basic data for subsequent control system parameter identification and controlled object dynamic parameter identification.

[0050] In step S102, the speed loop parameters of the servo system are identified based on the speed data, current data, and panel gain data. The low-frequency rigid body model parameters are identified based on the speed data. The high-frequency flexible model parameters are identified based on the speed data. The speed loop controlled object model is constructed based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters.

[0051] It is understood that the embodiments of this application identify the velocity loop parameters, low-frequency rigid body model parameters, and high-frequency flexible model parameters of the servo system based on different measured data, and then combine the two types of model parameters to construct a velocity loop controlled object model, thus overcoming the limitations of a single rigid body model. This restores the rigid-flexible coupling characteristics of the servo system, avoids model deviations caused by ignoring flexible modes, and provides a model foundation that fits the actual system for subsequent bandwidth expansion and parameter optimization.

[0052] It should be noted that low frequency refers to the frequency range within the closed-loop bandwidth of the servo system's speed loop, where rigid body inertia and damping characteristics dominate. This corresponds to the system's low-frequency rigid body model, which describes low-frequency dynamics such as inertia, damping, and friction, and can be obtained through conventional time-domain identification methods. High frequency refers to the frequency range near the flexible modal resonance frequency, where elastic vibration characteristics dominate. This corresponds to the system's high-frequency flexible sub-model, which describes high-frequency dynamics such as flexible resonance frequency and damping ratio. Due to the low-pass filtering effect of the closed-loop controller, conventional time-domain identification is difficult to obtain accurately, and the frequency-domain focusing gray-box identification algorithm proposed in this invention is required for accurate identification.

[0053] Specifically, the invention is based on a servo system controlled by three loops (position loop, velocity loop, and current loop). First, the controlled object in the velocity loop is modeled using a two-mass block model, such as... Figure 2 As shown, the controlled object is a rigid-flexible coupled structure consisting of a motor and a load, and the original model is... Then, based on the number of zeros and poles and the different frequency ranges of rigid and flexible modes, it is decomposed into the product of rigid body modes and flexible body modes; relying on speed, current, and panel gain data, a mapping relationship between panel parameters and theoretical control parameters is established to accurately identify the speed loop PI controller parameters; using speed data, the low-frequency rigid body model parameters are identified to obtain the rigid body sub-model. ,in For the overall inertia of the system, The model incorporates external damping for the motor and load, and includes low-frequency characteristics such as friction and inertia. Based on velocity data, the high-frequency flexible model parameters are identified using a frequency-domain focusing gray-box identification algorithm, resulting in a flexible sub-model. ,in The first-order natural frequency of the controlled object, For flexible body modal damping; finally, the two sub-models are multiplied to obtain the complete velocity loop controlled object model. This model is a rigid-flexible coupling form, which can accurately match the actual dynamic characteristics of the system.

[0054] In this embodiment, identifying high-frequency flexible model parameters based on speed data includes: extracting speed command and actual speed response data from the speed data; determining a high-order empirical model of the closed-loop speed transfer function based on the speed command and actual speed response data; reconstructing the open-loop frequency response function based on the high-order empirical model; acquiring vibration signals during the motion of the servo system; and identifying high-frequency flexible model parameters based on the spectral analysis results of the vibration signals and the open-loop frequency response function.

[0055] It is understood that the embodiments of this application achieve accurate identification of high-frequency flexible model parameters by extracting speed commands and actual speed response data, constructing a high-order empirical model and reconstructing the open-loop frequency response, and then combining vibration signal spectrum analysis to accurately locate the flexible mode. This solves the problem in related technologies where high-frequency flexible dynamics are suppressed and difficult to accurately capture in closed-loop states, providing reliable parameter support for constructing a high-fidelity rigid-flexible coupling model, thereby ensuring the scientific nature and stability of subsequent bandwidth expansion. Furthermore, identification based on measured data adapts to industrial closed-loop operating conditions without the need for additional excitation devices, improving engineering adaptability.

[0056] Specifically, to address the challenges of closed-loop operation of servo systems, low-pass filtering in controllers leading to attenuation of high-frequency flexible modal information, high time-domain goodness of the rigid body model (e.g., >0.99), and difficulty in obtaining flexible body parameters through time-domain black-box identification, a frequency-domain focused gray-box identification algorithm is employed. A broadband excitation signal is applied to the actual servo system, and speed command and actual speed response data are extracted from the speed data. Then, non-parametric identification methods such as Fourier transform or spectral analysis are used to obtain a high-order empirical model of the closed-loop velocity transfer function. Based on the algebraic relationship between closed-loop and open-loop transfer functions It reconstructs the open-loop frequency response function to recover the high-frequency dynamic information suppressed by the closed loop; it acquires the vibration signal during the system's motion, locates the resonant frequency range through spectral analysis methods such as FFT (Fast Fourier Transform) or power spectral density estimation, and combines the reconstructed open-loop frequency response function to complete the accurate identification of high-frequency flexible model parameters, adapting to industrial closed-loop operating conditions without the need to build an additional excitation platform.

[0057] In this embodiment of the application, the high-frequency flexible model parameters are identified based on the spectral analysis results of the vibration signal and the open-loop frequency response function, including: identifying the resonant frequency range in the spectral analysis results of the vibration signal; determining the target frequency band based on the resonant frequency range; fitting the high-frequency flexible model to the open-loop frequency response function in the target frequency band; and determining the high-frequency flexible model parameters based on the fitting results.

[0058] Understandably, this application first identifies the resonant frequency range in the vibration signal spectrum to define the target frequency band, then specifically fits the high-frequency flexible model to the open-loop frequency response function of that frequency band, and finally accurately extracts the high-frequency flexible model parameters. This approach avoids the drawbacks of blindly fitting across the entire frequency band, focusing on the key frequency band dominated by the flexible mode. It effectively solves the problems of suppressed high-frequency flexible dynamic signals and low identification accuracy in closed-loop systems, ensuring that the identified model parameters not only satisfy the dynamic laws but also adapt to practical application scenarios, laying a data foundation for the subsequent construction of rigid-flexible coupled controlled object models.

[0059] It should be noted that the target frequency band is determined based on the resonant frequency range in the vibration signal spectrum analysis results, and is the frequency band for fitting the high-frequency flexible model and open-loop frequency response function. This application does not specifically limit the specific range of the target frequency band.

[0060] Specifically, the vibration signal spectrum analysis results are identified to determine the resonant frequency range of the dominant flexible mode. For example, the resonant frequency range for the feed axis of a large machine tool is typically 60–100 Hz. This is used to define the target frequency band for parameter fitting, avoiding overfitting and uninterpretability caused by full-band fitting. Within this target frequency band, a high-frequency flexible model with physical structural constraints is then applied. Fit to the reconstructed open-loop frequency response data, the parameters to be identified are: These correspond to the zero-point time constants of the flexible body modality, respectively. Flexible modal frequencies Flexible body modal damping ratio Based on the fitting results, the above parameters are determined to ensure that the model conforms to the dynamic laws of mechanical structures and can accurately match the measured high-frequency dynamics.

[0061] The identified flexible sub-model is multiplied with the low-frequency rigid body model identified by conventional methods to form a complete velocity loop controlled object model, providing a high-fidelity, physically decoupled system model foundation for subsequent closed-loop optimization based on the analytical stability domain.

[0062] The following will elaborate on the servo system parameter representation method from data acquisition in step S101 to model construction in step S102 through a specific embodiment, such as Figure 3 As shown, the specific steps are as follows: In step one, measured signals such as position error, speed command, speed error, motor current, and panel gain of the servo system are collected to provide raw data for subsequent parameter mapping and dynamic identification.

[0063] The data includes location errors. Speed ​​command Speed ​​error Motor current Panel gain: (Position ring panel gain) (Speed ​​loop proportional panel gain) (Gain of the velocity loop integral panel) In step two, based on the acquired signals, the panel parameter mapping relationship of the position loop and velocity loop is identified, the gain parameters on the operation panel are converted into theoretical control parameters, and the correspondence between panel parameters and theoretical parameters is established.

[0064] The identification of position loop mapping relationships includes: disabling velocity feedforward and acceleration feedforward, isolating the position loop feedback controller; and solving the least squares problem. The mapping relationship is obtained as follows: , The position loop is the theoretical proportional gain. Identification of the velocity loop mapping includes: solving the least squares problem based on the PI controller principle. The mapping relationship is obtained as follows: , For the velocity loop theoretical proportional gain, This is the theoretical integral gain of the velocity loop.

[0065] In step three, based on the mapped theoretical parameters, the low-frequency rigid body model, the friction-containing flexible body model, and the high-frequency flexible body model are identified respectively. Finally, the two types of models are coupled to obtain a complete servo system controlled object model, thereby achieving accurate characterization of the system's dynamic characteristics.

[0066] The low-frequency rigid body model and friction identification include: identifying Coulomb friction. Remove Coulomb friction and calculate the effective torque. The rigid body model parameters are estimated using the least squares method to obtain the rigid body model: , For total inertia, External damping is used. High-frequency flexible body model identification includes: fitting the system response using a higher-order model. ; Computational system open-loop response The flexible modal frequency band was located by analyzing vibration signals, and the fitting frequency band was determined; the open-loop model derived from first principles was used for fitting. The soft body model is obtained: , , , For the parameters of the flexible model. Synthesize the complete controlled object model of the servo system: .

[0067] Based on the rigid-flexible coupled controlled object model constructed in the above embodiments, we will now proceed to step S103 to carry out the servo system bandwidth expansion work.

[0068] In step S103, the servo system bandwidth is expanded according to the speed loop controlled object model and speed loop parameters.

[0069] It is understandable that the embodiments of this application rely on the constructed speed loop controlled object model and combine the identified speed loop parameters to carry out bandwidth expansion, changing the mode of relying on experience to try and improve gain in related technologies. Based on a precise system model, this application can promote bandwidth expansion while ensuring closed-loop stability, breaking through the performance bottleneck caused by conservative tuning, and achieving a synergistic balance between high bandwidth and high stability of the system.

[0070] Specifically, a direct closed-loop frequency response shaping multi-objective tuning algorithm is adopted. Based on the constructed high-fidelity rigid-flexible coupled velocity loop controlled object model, and combined with the identified velocity loop PI (Proportional Integral) parameters, bandwidth expansion is achieved through the process of establishing an open-loop transfer function, constructing a stable parameter region, establishing a multi-objective optimization problem, and solving to determine the target parameters. Abandoning the empirical trial-and-error approach, the algorithm relies on the model's analytical results and strictly limits parameter optimization within the stable region. This overcomes the limitation of conservative tuning that restricts bandwidth to far below the resonance frequency, and avoids resonance-induced oscillations and instability through constraints, achieving a synergy of high bandwidth and high stability. Simultaneously, it can predict the closed-loop amplitude-frequency topology, providing theoretical support for parameter tuning. The theoretical basis for the closed-loop amplitude-frequency topology is as follows: The rigid body closed-loop model of the velocity loop is ,in, Let be the natural frequency of the closed-loop velocity ring rigid body. For rigid body closed-loop damping, the peak frequency of the rigid body can be obtained by differentiating its amplitude frequency. This indicates that a rigid body peak must exist within the effective bandwidth; the derivative of the flexible body closed-loop transfer function with respect to the amplitude-frequency ratio yields... ,in, , For normalized frequency, These are constants related to the mechanical structure. Related to current flexible body damping, when the flexible modal damping ratio The optimal solution will inevitably converge to a bimodal topology, with a critical damping ratio. .

[0071] In this embodiment, expanding the servo system bandwidth based on the speed loop controlled object model and speed loop parameters includes: establishing an open-loop transfer function of the speed loop based on the speed loop controlled object model and speed loop parameters; analyzing the open-loop transfer function of the speed loop and constructing a stable parameter region based on the analysis results; establishing a multi-objective optimization problem based on the stable parameter region and the performance objectives of the servo system, with the performance objectives being to maximize the closed-loop bandwidth and integral gain; and determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem.

[0072] It is understood that this application embodiment establishes the open-loop transfer function of the speed loop, analyzes and obtains the stable parameter region, and then constructs a multi-objective optimization problem by combining the performance objectives of maximizing closed-loop bandwidth and integral gain, ultimately determining the target control parameters of the servo system. It abandons the empirical trial-and-error tuning mode in related technologies, using a clear stability boundary as a constraint and performance optimization as a guide to conduct parameter optimization. This not only breaks through the bandwidth improvement bottleneck caused by conservative tuning strategies but also ensures the stability and reliability of system operation, significantly improving the scientific nature and accuracy of the bandwidth expansion method.

[0073] It should be noted that the stable parameter region refers to the range of speed loop PI controller parameters that can guarantee the absolute stability of the closed-loop operation of the servo system after analyzing the open-loop transfer function of the speed loop. It is bounded by the linear boundary and the quadratic curve boundary, which is actually a hyperbola. The target control parameters refer to the speed loop PI controller parameters that are adapted to the actual operating conditions of the servo system after solving the multi-objective optimization problem in combination with the performance target of the servo system within the stable parameter region.

[0074] Specifically, based on the controlled object model of the velocity loop and the PI parameters of the velocity loop, an open-loop transfer function of the velocity loop is established; this transfer function is then analyzed using the Routh-Hurwitz stability criterion, such as... Figure 4 As shown, the stable parameter region is obtained by combining the linear boundary and the quadratic boundary, where the quadratic boundary is a hyperbolic boundary, constituting the main constraint of the stability region and limiting the feasible solution space of the PI parameters; in order to maximize the closed-loop bandwidth. and integral gain To achieve performance targets, a multi-objective optimization problem is established by combining global robustness constraints and flexible modal suppression constraints. This algorithm does not rely on open-loop shaping or artificially designed frequency domain weighting functions, but directly uses the closed-loop frequency response as the optimization object. The problem is solved by grid search and penalty function method to determine the target control parameters that meet the system requirements. The entire process does not require artificial design of frequency domain weighting functions, thus improving the scientific nature and accuracy of the optimization.

[0075] In this embodiment of the application, before determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem, the method further includes: converting the multi-objective optimization problem into an unconstrained penalty function; and determining the solution results of the multi-objective optimization problem based on the unconstrained penalty function, wherein the unconstrained penalty function is:

[0076] in It has a high weight.

[0077] Specifically, regarding the closed-loop peak constraint with respect to ( For non-convex problems where industrial CNC (Computer Numerical Control) controllers typically only support integer gain settings, this problem transforms a constrained multi-objective optimization problem into an unconstrained penalty function form, facilitating efficient solution and performance evaluation, while also supporting secondary parameter tuning by engineers. In the formula... The weights for performance targets can be adjusted according to application requirements, with a focus on high-speed machining. Heavy-duty cutting focuses on ; Set to a high weight, such as 10, to severely punish combinations of parameters that violate constraints, where the first term punishes violations of global robustness constraints. The second penalty is a violation of the flexible modal suppression constraint. This penalty function can transform the parameter optimization results into quantifiable performance indicators, providing a basis for subsequent generation of performance maps and parameter selection, while reducing the difficulty of solving non-convex problems.

[0078] In this embodiment, the target control parameters of the servo system are determined based on the solution results of the multi-objective optimization problem, including: traversing the PI controller parameter combinations that satisfy hardware constraints within the stable parameter region; calculating the closed-loop frequency response of each PI controller parameter combination; evaluating the objective function value and the degree of constraint violation based on the closed-loop frequency response; generating a two-dimensional mapping map covering the performance and robustness of the entire stable domain; screening candidate control parameters based on the two-dimensional mapping map; and determining the target control parameters from the candidate control parameters.

[0079] Understandably, this application's embodiments traverse the PI controller parameter combinations that satisfy hardware constraints within the stable parameter region, calculate the closed-loop frequency response corresponding to each parameter combination, and evaluate the objective function value and constraint violation degree. Ultimately, a two-dimensional performance and robustness mapping diagram covering the entire stable domain is generated, and the target control parameters are then selected based on this map. This transforms the abstract parameter optimization problem into an intuitive visual graph, abandoning the blind trial-and-error mode of parameter tuning in related technologies. This not only significantly shortens the on-site debugging cycle but also ensures that the selected control parameters meet both performance requirements and system robustness constraints, significantly improving engineering practicality and implementation efficiency.

[0080] It should be noted that hardware constraints refer to the parameter value limitations determined by the hardware performance of the servo system itself; PI controller parameter combinations refer to the combination of proportional gain and integral gain in the speed loop; closed-loop frequency response refers to the frequency characteristic relationship between the output and input signals during the closed-loop operation of the servo system; objective function value refers to a quantitative indicator that measures the degree to which the parameter combination achieves the system performance target; constraint violation degree refers to the degree to which the parameter combination deviates from the various constraint requirements of the system; the two-dimensional performance and robustness mapping diagram refers to a chart that visually presents the performance and robustness levels of each parameter combination within a stable parameter region; candidate control parameters refer to parameter combinations that meet the performance and constraint requirements selected from the two-dimensional mapping diagram; and target control parameters refer to the parameter combinations that are finally determined from the candidate control parameters and are suitable for the actual operating conditions of the system.

[0081] Specifically, within the stable parameter region obtained from the analysis, all integer PI gain combinations that satisfy the hardware constraints of the servo system are traversed. Parameters exceeding the hardware's capacity are excluded; for each gain combination, the corresponding closed-loop frequency response is calculated, and its performance and constraint violation degree are evaluated by combining the established objective function and penalty function; based on the evaluation results of all combinations, a two-dimensional performance-robustness mapping diagram covering the entire stability domain is generated. Figure 5 Contour plot for robust stability (infinite norm) constraints. Figure 6 The contour plot shows the first-order natural frequency gain constraint. Figure 7 A contour plot of closed-loop bandwidth performance visually presents the system performance and constraint satisfaction corresponding to different PI parameter combinations; during on-site commissioning, priority should be given to selecting... Candidate parameters are selected based on areas that basically meet the constraints and have good performance. The final target control parameters are then determined through rapid verification on a real machine. Figure 8 As shown, the closed-loop Bode plot at the optimal control parameters (asterisk positions) contains two peaks: the first is a rigid body peak, and the second is a flexible body peak, verifying the amplitude-frequency topology characteristics of the rigid-flexible coupling of the system; as shown... Figure 9 As shown, the pentagram represents the optimal control parameters given by the algorithm. Engineers can perform secondary parameter tuning based on the nine local minima on the graph to further adapt to actual working conditions, significantly reduce the search space, shorten the debugging cycle, and improve the efficiency of project implementation.

[0082] In this embodiment of the application, the open-loop transfer function of the velocity loop is:

[0083] in, For the velocity loop proportional gain, For velocity loop integral gain, The total inertia of the system. For external damping of the system, , , These are the parameters for the high-frequency flexible model. These are the complex parameters of the Laplace transform; The stable parameter region is bounded by two stability boundary curves, which include a linear boundary and a quadratic boundary. The linear boundary is:

[0084] in This refers to intermediate constant terms that are completely determined by the parameters of the controlled object. The boundary of the quadratic curve is:

[0085] in, and It is about A linear function:

[0086] in, For the overall damping term of the controlled object, Let be the rigid-flexible coupling constant of the controlled object. These are intermediate constants determined by the parameters of the controlled object. The modal coupling coefficient of the controlled object is denoted as .

[0087] Specifically, the open-loop transfer function of the velocity loop is obtained by multiplying the transfer function of the velocity loop PI controller with the transfer function of the rigid-flexible coupled controlled object model. It accurately reflects the velocity loop control logic and system dynamics characteristics, where the complex frequency... Used for frequency domain analysis, this application bridges the gap between the time and frequency domains. Based on the Routh criterion, this embodiment derives two boundaries of the stable parameter region, ensuring that the parameter combination satisfies closed-loop absolute stability: the constant term of the linear boundary... , It is only related to the inertia, damping, and flexibility model parameters of the controlled object, without any additional manually set parameters; the quadratic boundary is actually a hyperbolic boundary, which is the main constraint of the stability region, and its expression contains... and The structure parameters of the controlled object ( ) and coupling coefficient ( ), comprehensive damping term This structure ensures that the stability domain boundary accurately matches the actual characteristics of the system, defining a reliable range for parameter optimization.

[0088] In this embodiment of the application, the multi-objective optimization problem includes an objective function and constraints, wherein the objective function is:

[0089] Among them, weight , For closed-loop bandwidth, The velocity loop integral gain; The constraints include global robustness constraints and flexible mode suppression constraints, among which, The global robustness constraint is:

[0090] The flexible modal suppression constraint is: .

[0091] Specifically, the objective function adopts a weighted sum form to achieve the synergistic maximization of closed-loop bandwidth and low-frequency stiffness: closed-loop bandwidth Defined as the frequency at which the amplitude of the closed-loop velocity transfer function drops to -3dB, characterizing the system's tracking speed; integral gain. The weight directly determines the system's low-frequency stiffness, reflecting its ability to suppress disturbances such as cutting forces. It can be flexibly adjusted according to actual application scenarios to meet the needs of different working conditions. Based on the above objective function, a constrained multi-objective optimization problem is constructed by combining two types of constraints. The constraints ensure system stability from both global and local dimensions: global robustness constraints limit the total transfer function of the closed loop. The infinite norm of the equation suppresses the "main resonance peak" dominated by rigid body modes, and a preset upper limit is used. Typically, 5dB is chosen to ensure the system has a minimum phase margin and avoid oscillations caused by model uncertainties; flexible mode suppression constraints are applied to the identified flexible mode frequencies. Delineate frequency bands in its vicinity Preset threshold Typically, 0dB is chosen to ensure that the system does not amplify flexible vibrations, achieve local attenuation of resonant energy, and balance high bandwidth and robustness.

[0092] The servo system bandwidth expansion method proposed in this application solves the bandwidth bottleneck caused by ignoring flexible modes and conservative tuning in related technologies by separately identifying the parameters of low-frequency rigid body and high-frequency flexible models, constructing a rigid-flexible coupled velocity loop controlled object model, and expanding the system bandwidth based on the model. It also predicts the system stability boundary and achieves high bandwidth and high stability. At the same time, the method relies on the measured data of the servo system to complete the identification, without the need for complex offline calibration, and directly connects to the parameter system of industrial controllers, which greatly reduces the difficulty of engineering implementation and significantly improves the practicality and promotion value of the technology.

[0093] In summary, the embodiments of this application have at least the following beneficial effects: (1) This application abandons the overly conservative avoidance of resonant frequency in PID tuning of related technologies. Within the analytical stable parameter space based on the rigorous derivation of the Routh-Hurwitz criterion, it directly optimizes the closed-loop frequency response, synergistically maximizing the bandwidth and the integral gain characterizing static stiffness, thereby approximating the physical performance limit. When applied to the linear feed axis of a five-axis machining center, this method can increase the effective bandwidth of the velocity loop to close to the first-order flexible mode frequency, while maintaining system stability without significant oscillation. Unlike techniques that rely on open-loop notch filtering or filters, this method achieves "safe crossing" of the resonant frequency band through overall shape control of the closed-loop response. It does not require the introduction of additional phase lag elements and is not affected by resonant frequency drift, thus avoiding the phase lag and detuning risks caused by notch filtering. It is suitable for first-order structural resonant frequencies. For challenging industrial scenarios where bandwidth control is desired, such as large machine tools with a speed loop bandwidth of 80Hz and a resonant frequency of 70–80Hz, the applicability bottleneck of related technical methods has been overcome.

[0094] (2) This application uses performance indicators such as bandwidth, low-frequency gain, and closed-loop peak limit as explicit constraints and optimization objectives, directly embedding them into a multi-objective optimization problem, without the need for design. The frequency domain weighting function, which is difficult to precisely match in control, not only simplifies the controller design process but also expands the feasible solution space, allowing the optimization results to more closely approximate the physical performance boundaries. Simultaneously, a closed-loop optimization architecture driven by a gray-box model, based on a two-mass-spring-damped model identified by combining rigid body dynamics priors and experimental data, accurately characterizes the first-order flexible mode, including the damping ratio, while effectively avoiding overfitting and uninterpretability of higher-order black-box models, ensuring good physical realizability and robustness of the optimization results. The entire controller tuning process can be fully parameterized, enabling automatic tuning of servo system control parameters with high consistency. This facilitates the construction of a standardized process knowledge base, reducing reliance on operator experience.

[0095] (3) This application clarifies the topological convergence characteristics of the closed-loop system under the optimization framework. Regardless of the initial parameters, the system will inevitably converge to one of two typical topologies at the performance limit: a lightly damped system forms a bimodal structure with a main bandwidth peak and a resonant auxiliary peak, while a high-damped system forms a single-peak / fusion peak structure. This rule provides a basis for closed-loop performance design. At the same time, the sufficient condition for the optimal closed-loop response to exhibit a bimodal structure is derived, when the flexible modal damping ratio is... Strictly less than the critical value When, the optimal solution will necessarily converge to a bimodal topology; when Significantly greater than When it is in a unimodal state, it tends to form a single-peak structure; while when near At this time, the closed-loop amplitude-frequency response maintains approximately unity gain within the effective bandwidth, exhibiting a flat characteristic of 0dB and no significant resonance peaks or attenuation valleys. This critical damping ratio... It has a clear analytical expression and depends only on the basic parameters of the system's flexible modes, thus bridging the gap between theoretical analysis and engineering applications.

[0096] (4) This application uses the critical flexible damping ratio As a common target parameter for both mechanical structure design and servo controller design, a cross-domain collaborative optimization method was constructed. During the mechanical design phase, this method can be actively controlled by adjusting structural stiffness, mass distribution, or introducing passive damping elements. Make it approach During the controller design phase, if actual measurements... For values ​​deviating significantly from the critical value, active damping compensation strategies can be embedded within the velocity loop, such as flexible modal damping injection based on state observation, to adjust the equivalent... This guides the system towards the desired topology, resulting in a flat, high-bandwidth response; during the system selection and configuration phase, it can be based on... The criteria predict the control potential of different mechanical platforms to avoid configuring excessively high bandwidth requirements for low-damping, high-resonance systems.

[0097] (5) The method in this application embodiment can significantly reduce debugging costs and downtime losses. Taking a five-axis machining center as an example, the debugging time of the servo system can be shortened from multiple working days in related technical methods to within a single working day, effectively improving equipment availability and reducing losses caused by production interruptions. From the perspective of process inheritance, the parameterized tuning process realizes process reproducibility and knowledge solidification, reduces dependence on senior operators, and facilitates standardized promotion.

[0098] This application not only theoretically establishes a complete mapping relationship between structural flexibility, stability domain, closed-loop topology, and performance limits, but also achieves the unification of higher bandwidth, stronger stiffness, better robustness, and better machining accuracy in engineering practice. It provides a systematic, predictable control scheme for highly flexible servo systems that can fully tap the potential of dynamic performance, and has good practical value and promotion prospects.

[0099] Next, the servo system bandwidth expansion device proposed according to the embodiments of this application is described with reference to the accompanying drawings.

[0100] Figure 10 This is a block diagram of a servo system bandwidth expansion device according to an embodiment of this application.

[0101] like Figure 10 As shown, the servo system bandwidth expansion device 100 includes: an acquisition module 1001, a construction module 1002, and an expansion module 1003.

[0102] The acquisition module 1001 is used to acquire the speed data, current data, and panel gain data of the servo system; the construction module 1002 is used to identify the speed loop parameters of the servo system based on the speed data, current data, and panel gain data, identify the low-frequency rigid body model parameters based on the speed data, identify the high-frequency flexible model parameters based on the speed data, and construct the speed loop controlled object model based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters; the expansion module 1003 is used to expand the bandwidth of the servo system based on the speed loop controlled object model and the speed loop parameters.

[0103] In this embodiment, the construction module 1002 is further configured to: extract speed command and actual speed response data from the speed data; determine a high-order empirical model of the closed-loop speed transfer function based on the speed command and actual speed response data; reconstruct the open-loop frequency response function based on the high-order empirical model; acquire vibration signals during the motion of the servo system; and identify high-frequency flexible model parameters based on the spectral analysis results of the vibration signals and the open-loop frequency response function.

[0104] In this embodiment of the application, the construction module 1002 is further configured to: identify the resonant frequency range in the spectral analysis results of the vibration signal; determine the target frequency band based on the resonant frequency range; fit the high-frequency flexible model to the open-loop frequency response function in the target frequency band; and determine the parameters of the high-frequency flexible model based on the fitting results.

[0105] In this embodiment, the extension module 1003 is used to: establish the open-loop transfer function of the speed loop based on the controlled object model and speed loop parameters; analyze the open-loop transfer function of the speed loop and construct a stable parameter region based on the analysis results; establish a multi-objective optimization problem based on the stable parameter region and the performance objective of the servo system, wherein the performance objective is to maximize the closed-loop bandwidth and integral gain; and determine the target control parameters of the servo system based on the solution results of the multi-objective optimization problem.

[0106] In this embodiment of the application, the open-loop transfer function of the velocity loop is:

[0107] in, For the velocity loop proportional gain, For velocity loop integral gain, The total inertia of the system. For external damping of the system, , , These are the parameters for the high-frequency flexible model. Let be the complex parameters of the Laplace transform; the stable parameter region is bounded by two stability boundary curves, which include a linear boundary and a quadratic boundary. The linear boundary is:

[0108] in The intermediate constant term is completely determined by the parameters of the controlled object; the boundary of the quadratic curve is: ;in, and It is about A linear function:

[0109] in, For the overall damping term of the controlled object, Let be the rigid-flexible coupling constant of the controlled object. These are intermediate constants determined by the parameters of the controlled object. The modal coupling coefficient of the controlled object is denoted as .

[0110] Optionally, the multi-objective optimization problem includes an objective function and constraints, wherein the objective function is:

[0111] Among them, weight , For closed-loop bandwidth, The integral gain of the velocity loop is given; the constraints include global robustness constraints and flexible mode suppression constraints, wherein the global robustness constraints are:

[0112] The flexible modal suppression constraint is: .

[0113] In this embodiment of the application, the apparatus 100 further includes a determination module.

[0114] The determination module is used to convert the multi-objective optimization problem into an unconstrained penalty function before determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem; and to determine the solution results of the multi-objective optimization problem based on the unconstrained penalty function, wherein the unconstrained penalty function is:

[0115] in It has a high weight.

[0116] In this embodiment, the extension module 1003 is further configured to: determine the target control parameters of the servo system based on the solution results of the multi-objective optimization problem, including: traversing the PI controller parameter combinations that satisfy the hardware constraints within the stable parameter region; calculating the closed-loop frequency response of each PI controller parameter combination; evaluating the objective function value and the degree of constraint violation based on the closed-loop frequency response; generating a two-dimensional mapping map covering the performance and robustness of the entire stable domain; screening candidate control parameters based on the two-dimensional mapping map; and determining the target control parameters from the candidate control parameters.

[0117] It should be noted that the foregoing explanation of the servo system bandwidth expansion method embodiment also applies to the servo system bandwidth expansion device of this embodiment, and will not be repeated here.

[0118] The servo system bandwidth expansion device proposed in this application solves the bandwidth bottleneck caused by ignoring flexible modes and conservative tuning in related technologies by separately identifying the parameters of low-frequency rigid body and high-frequency flexible models, constructing a rigid-flexible coupled velocity loop controlled object model, and expanding the system bandwidth based on the model. It also predicts the system stability boundary and achieves high bandwidth and high stability. At the same time, the method relies on the measured data of the servo system to complete the identification, without the need for complex offline calibration, and directly connects to the parameter system of industrial controllers, which greatly reduces the difficulty of engineering implementation and significantly improves the practicality and promotion value of the technology.

[0119] Figure 11 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 1101, the processor 1102, and the computer program stored on the memory 1101 and capable of running on the processor 1102.

[0120] When the processor 1102 executes the program, it implements the servo system bandwidth expansion method provided in the above embodiments.

[0121] Furthermore, electronic devices also include: Communication interface 1103 is used for communication between memory 1101 and processor 1102.

[0122] The memory 1101 is used to store computer programs that can run on the processor 1102.

[0123] The memory 1101 may include high-speed RAM (Random Access Memory) memory, and may also include non-volatile memory, such as at least one disk storage.

[0124] If the memory 1101, processor 1102, and communication interface 1103 are implemented independently, then the communication interface 1103, memory 1101, and processor 1102 can be interconnected via a bus to complete communication between them. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 11 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0125] Optionally, in a specific implementation, if the memory 1101, processor 1102, and communication interface 1103 are integrated on a single chip, then the memory 1101, processor 1102, and communication interface 1103 can communicate with each other through an internal interface.

[0126] The processor 1102 may be a CPU (Central Processing Unit), an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of this application.

[0127] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0128] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0129] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0130] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any of the following techniques known in the art, or a combination thereof: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (FPGAs), field-programmable gate arrays (FPGAs), etc.

[0131] Those skilled in the art will understand that all or part of the steps of the methods implementing the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0132] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for extending the bandwidth of a servo system, characterized in that, Includes the following steps: Acquire speed data, current data, and panel gain data of the servo system; The speed loop parameters of the servo system are identified based on the speed data, the current data, and the panel gain data. The low-frequency rigid body model parameters are identified based on the speed data. The high-frequency flexible model parameters are identified based on the speed data. The speed loop controlled object model is constructed based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters. The servo system bandwidth is extended based on the speed loop controlled object model and the speed loop parameters.

2. The servo system bandwidth expansion method according to claim 1, characterized in that, The step of identifying high-frequency flexible model parameters based on the velocity data includes: Extract the speed command and actual speed response data from the speed data; Based on the speed command and the actual speed response data, a higher-order empirical model of the closed-loop speed transfer function is determined, and the open-loop frequency response function is reconstructed based on the higher-order empirical model. The vibration signal during the motion of the servo system is acquired, and the parameters of the high-frequency flexible model are identified based on the spectral analysis results of the vibration signal and the open-loop frequency response function.

3. The servo system bandwidth expansion method according to claim 2, characterized in that, The step of identifying high-frequency flexible model parameters based on the spectral analysis results of the vibration signal and the open-loop frequency response function includes: Identify the resonant frequency range in the spectral analysis results of the vibration signal; The target frequency band is determined based on the resonant frequency range, and the high-frequency flexible model is fitted to the open-loop frequency response function within the target frequency band. The parameters of the high-frequency flexible model are determined based on the fitting results.

4. The servo system bandwidth expansion method according to claim 1, characterized in that, The step of expanding the servo system bandwidth based on the speed loop controlled object model and the speed loop parameters includes: Establish the open-loop transfer function of the velocity loop based on the controlled object model and velocity loop parameters; Analyze the open-loop transfer function of the velocity loop, and construct a stable parameter region based on the analysis results; A multi-objective optimization problem is established based on the stable parameter region and the performance objective of the servo system, wherein the performance objective is to maximize the closed-loop bandwidth and integral gain. The target control parameters of the servo system are determined based on the solution results of the multi-objective optimization problem.

5. The servo system bandwidth expansion method according to claim 4, characterized in that, The open-loop transfer function of the velocity loop is: in, For the velocity loop proportional gain, For velocity loop integral gain, The total inertia of the system. For external damping of the system, , , These are the parameters for the high-frequency flexible model. These are the complex parameters of the Laplace transform; The stable parameter region is bounded by two stability boundary curves, which include a linear boundary and a quadratic boundary. The linear boundary is: in This refers to intermediate constant terms that are completely determined by the parameters of the controlled object. The boundary of the quadratic curve is: in, and It is about A linear function: in, For the overall damping term of the controlled object, Let be the rigid-flexible coupling constant of the controlled object. These are intermediate constants determined by the parameters of the controlled object. The modal coupling coefficient of the controlled object is denoted as .

6. The servo system bandwidth expansion method according to claim 4, characterized in that, The multi-objective optimization problem includes an objective function and constraints, wherein the objective function is: Among them, weight , For closed-loop bandwidth, The velocity loop integral gain; The constraints include global robustness constraints and flexible mode suppression constraints, wherein, The global robustness constraint is: The flexible mode suppression constraint is: 。 7. The servo system bandwidth expansion method according to claim 4, characterized in that, Before determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem, the process also includes: The multi-objective optimization problem is transformed into an unconstrained penalty function; The solution to the multi-objective optimization problem is determined based on the unconstrained penalty function, wherein the unconstrained penalty function is: in It has a high weight.

8. The servo system bandwidth expansion method according to claim 4, characterized in that, Determining the target control parameters of the servo system based on the solution results of the multi-objective optimization problem includes: The PI controller parameter combinations that satisfy the hardware constraints are traversed within the stable parameter region. Calculate the closed-loop frequency response for each PI controller parameter combination, evaluate the objective function value and constraint violation degree based on the closed-loop frequency response, and generate a two-dimensional mapping diagram covering the entire stability domain of performance and robustness; Candidate control parameters are selected based on the two-dimensional mapping, and the target control parameters are determined from the candidate control parameters.

9. A servo system bandwidth expansion device, characterized in that, include: The acquisition module is used to acquire speed data, current data, and panel gain data of the servo system. The construction module is used to identify the speed loop parameters of the servo system based on the speed data, the current data and the panel gain data, identify the low-frequency rigid body model parameters based on the speed data, identify the high-frequency flexible model parameters based on the speed data, and construct the speed loop controlled object model based on the low-frequency rigid body model parameters and the high-frequency flexible model parameters. An extension module is used to extend the servo system bandwidth based on the speed loop controlled object model and the speed loop parameters.

10. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the servo system bandwidth expansion method according to any one of claims 1-8.

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