Synchronous control method, device and equipment for multi-axis servo system

Abstract

The present invention relates to the technical field of multi-axis servo systems, and discloses a synchronous control method, device and equipment for a multi-axis servo system. The method includes: measuring the mechanical coupling relationship parameters, motor dynamic characteristic parameters and sampling delay time parameters of the multi-axis servo system and substituting them into the state equation modeling formula to calculate the discrete-time system state matrix; performing Z-transform processing on the discrete-time system state matrix and calculating the frequency response characteristics to obtain the transfer function matrix and the set of target coupling axis pairs; performing hierarchical optimization to obtain a preliminary control instruction; calculating the trajectory tracking error and the inter-axis synchronization error and substituting them into the optimization objective function for sampling delay compensation processing to obtain a compensation control instruction; performing real-time processing on the compensation control instruction and outputting a synchronous control signal to each servo axis to achieve multi-axis coordinated motion. The present invention improves the synchronous control accuracy in the multi-axis servo system by accurately identifying the key coupling axis pairs and sensitive frequency points.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-axis servo systems, and in particular, to a synchronous control method, device and equipment for a multi-axis servo system. Background Art

[0002] In multi-axis servo systems, problems of inter-axis synchronization error and mechanical vibration commonly exist in high-precision motion control. Compared with single-axis systems, multi-axis systems face more complex control challenges because disturbances on one axis can propagate through the mechanical structure and control system to other cooperating axes, forming systematic vibrations, thereby reducing machining accuracy and equipment life.

[0003] The differences between the sampling period and the control period in digital control systems pose a severe challenge to the modeling of multi-axis servo systems. Traditional control methods usually ignore the impact of sampling delay, resulting in a significant deviation between the model and the actual system, making it difficult to achieve high-precision requirements for inter-axis synchronous control performance. In addition, although existing cross-coupling control and master-slave synchronization control strategies can reduce the inter-axis synchronization error to a certain extent, these methods have limitations in dealing with the combined effects of complex mechanical coupling and sampling delay and cannot comprehensively solve the problem of inter-axis coordinated control. Summary of the Invention

[0004] The present invention provides a synchronous control method, device and equipment for a multi-axis servo system. By accurately identifying key coupled axis pairs and sensitive frequency points, the present invention improves the synchronous control accuracy in a multi-axis servo system.

[0005] In a first aspect, the present invention provides a synchronous control method for a multi-axis servo system, and the synchronous control method for the multi-axis servo system includes:

[0006] Measuring the mechanical coupling relationship parameters, motor dynamic characteristic parameters and sampling delay time parameters of the multi-axis servo system and substituting them into the state equation modeling formula to calculate the discrete-time system state matrix;

[0007] Performing Z-transform processing on the discrete-time system state matrix and calculating the frequency response characteristics to obtain the transfer function matrix and the set of target coupled axis pairs;

[0008] Performing hierarchical optimization on the transfer function matrix and the set of target coupled axis pairs to obtain a preliminary control instruction;

[0009] According to the preliminary control instruction, calculating the trajectory tracking error and the inter-axis synchronization error and substituting them into the optimization objective function for sampling delay compensation processing to obtain a compensation control instruction;

[0010] Performing real-time processing on the compensation control instruction and outputting a synchronous control signal to each servo axis to achieve multi-axis coordinated motion.

[0011] Second aspect, the present invention provides a synchronous control device for a multi-axis servo system, and the synchronous control device for the multi-axis servo system includes:

[0012] A measurement module, configured to measure mechanical coupling relationship parameters, motor dynamic characteristic parameters, and sampling delay time parameters of the multi-axis servo system, substitute them into a state equation modeling formula, and calculate a discrete-time system state matrix;

[0013] A calculation module, configured to perform Z-transform processing on the discrete-time system state matrix and calculate frequency response characteristics to obtain a transfer function matrix and a set of target coupling axis pairs;

[0014] A hierarchical optimization module, configured to perform hierarchical optimization on the transfer function matrix and the set of target coupling axis pairs to obtain a preliminary control instruction;

[0015] A delay compensation module, configured to calculate a trajectory tracking error and an inter-axis synchronization error according to the preliminary control instruction, substitute them into an optimization objective function for sampling delay compensation processing, and obtain a compensated control instruction;

[0016] A real-time processing module, configured to perform real-time processing on the compensated control instruction and output a synchronous control signal to each servo axis to achieve multi-axis coordinated motion.

[0017] The third aspect of the present invention provides a computer device, including: a memory and at least one processor, wherein instructions are stored in the memory; the at least one processor calls the instructions in the memory to enable the computer device to execute the above-mentioned synchronous control method for a multi-axis servo system.

[0018] In the technical solution provided by the present invention, a generalized state-space model of a multi-axis servo system considering sampling delay is established, which comprehensively describes the influence of the mechanical coupling relationship between axes and sampling delay on the dynamic characteristics of the system, provides an accurate theoretical basis for multi-axis synchronous control, and avoids the system modeling deviation caused by the traditional model ignoring sampling delay. By constructing a discrete-time transfer function matrix, the present invention directly reveals the coupling relationship between axes from the frequency domain perspective, simplifies the analysis process of complex multi-axis systems, enables system designers to intuitively evaluate the inter-axis synchronization characteristics through classical control tools, and accurately identify key coupling axis pairs and sensitive frequency points. The hierarchical control structure is adopted to separately process trajectory planning and synchronization optimization, effectively separating the goals of trajectory tracking and synchronous control, avoiding the difficulty of weight selection in traditional single-layer control, and providing flexible control strategy selection for different application scenarios. An optimization objective function considering both trajectory error and synchronization error is designed to dynamically balance the absolute trajectory accuracy and relative synchronization accuracy according to different work task requirements, introducing multi-dimensional evaluation indicators such as contour error, normal error, and tangential error, and providing a comprehensive performance evaluation standard. Combining multi-sampling technology and the principle of Smith predictor, the control parameters are dynamically adjusted to effectively compensate for the sampling delay in the digital control system, enhance the robustness of the control system, and improve the synchronous control accuracy in the multi-axis servo system. Brief Description of the Drawings

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0020] Figure 1 It is a schematic diagram of the steps of the synchronous control method for the multi-axis servo system in the embodiment of the present invention;

[0021] Figure 2 It is a schematic diagram of the structure of the synchronous control device for the multi-axis servo system in the embodiment of the present invention;

[0022] Figure 3 It is a schematic block diagram of the structure of the computer device in the embodiment of the present invention. Detailed Embodiments

[0023] Embodiments of the present invention provide a synchronous control method, device, and equipment for a multi-axis servo system. The terms "first", "second", "third", "fourth", etc. (if any) in the specification, claims, and the above-mentioned drawings of the present invention are used to distinguish similar objects and do not necessarily describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "comprising" or "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or equipment that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products, or equipment.

[0024] For ease of understanding, the specific process of the embodiments of the present invention will be described below. Please refer to Figure 1 , an embodiment of the synchronous control method for a multi-axis servo system in the embodiments of the present invention includes:

[0025] Step S1: Measure the mechanical coupling relationship parameters, motor dynamic characteristic parameters, and sampling delay time parameters of the multi-axis servo system and substitute them into the state equation modeling formula to calculate the discrete-time system state matrix;

[0026] It can be understood that the execution subject of the present invention can be a synchronous control device for a multi-axis servo system, or a terminal or a server. Specifically, it is not limited here. The embodiments of the present invention will be described by taking the server as the execution subject as an example.

[0027] Specifically, for each servo axis included in the servo system, basic data collection and key parameter measurement are performed. Through a high-precision sensor or the internal encoder of the controller, the state of each servo axis during operation is collected in real time to obtain state variables such as its position, speed, and acceleration, and a state vector of the system is constructed accordingly , where represents the complete state information of the th servo axis at the current moment; at the same time, the control input vector of each servo axis is obtained through the drive signal applied by the control system, where is the control instruction of the th servo axis at the current moment; and the actual output displacement of the servo axis is measured through a feedback device to construct the system output vector , where represents the The real-time position signals of each servo axis. Meanwhile, to accurately describe the sampling behavior in the digital control system, the sampling time of each servo axis is measured separately, that is, the time delay experienced from the signal acquisition by the controller to the response of the driver is evaluated. This delay is detected and recorded by the high-resolution time synchronization system to form the sampling delay time parameter matrix diag , where represents the sampling delay time of the th servo axis, and this parameter is used to reflect the influence of sampling delay on the system response in discrete-time modeling. The mechanical structure of the entire multi-axis servo system is analyzed and tested to identify the mechanical coupling relationship between each servo axis. By means of excitation measurement, frequency response function analysis or finite element simulation, etc., the actual parameters of the coupling stiffness and damping between axes are obtained, and the stiffness matrix and the damping matrix are constructed accordingly, where represents the rigid coupling coefficient between the th axis and the th axis, represents the damping coefficient between the two, and this part of the parameters is used to accurately model the dynamic interaction between axes. After completing the mechanical structure modeling, parameter identification is carried out for each servo motor to obtain the dynamic characteristics of the motor. Key parameters of the motor, including the torque constant , the moment of inertia and the friction coefficient , are obtained by means of step response test, frequency domain identification or system identification algorithm, and these parameters are integrated into the motor torque constant matrix , the motor inertia matrix , and the friction coefficient matrix , thus providing electromagnetic and mechanical dynamics support for state modeling. Substitute the obtained system state vector , the control input vector , the system output vector , the sampling delay time parameter , the mechanical coupling relationship parameter and the motor dynamic characteristic parameter into the generalized state space model constructed based on the principle of mechanical dynamics to form a complete continuous-time state equation: , , where is the system matrix including the coupling stiffness and damping effects, represents the influence of the control input on the state, is the external disturbance term. By discretizing this continuous-time model, combining the control period and the sampling delay term, and applying the Z-transform, the discrete-time state equation obtained is: , , where are the system matrix, control matrix, and output matrix at discrete time respectively, is the discrete form of the sampling delay.

[0028] Step S2: Perform Z-transform processing on the discrete-time system state matrix and calculate the frequency response characteristics to obtain the transfer function matrix and the set of target coupled axis pairs;

[0029] Specifically, perform a Z-transform on the state matrix of the discrete-time system to convert the time-domain state equation into a frequency-domain system expression, so that the state vector, control input vector, and system output vector of the system are all uniformly represented in the complex frequency domain. Through this Z-transform, the limitation of the time variable on the modeling expression form is eliminated, thereby realizing the frequency-domain modeling of the overall input-output relationship of the system. Derive the transfer function matrix of the system according to the functional relationship between the state variables and the control input in the frequency-domain system equation. This transfer function matrix reflects the overall mapping relationship between the control inputs of each servo axis and the output response. The elements on the diagonal are used to characterize the inherent response characteristics of a single servo axis in the frequency domain, and the elements on the off-diagonal are used to represent the cross-influence characteristics caused by mechanical coupling between different servo axes, that is, the inter-axis coupling transfer path. In this process, by analyzing the amplitude comparison relationship between the off-diagonal terms and the corresponding diagonal terms, it is distinguished how each servo axis is interfered by the dynamic behavior of other servo axes, thereby establishing an inter-axis coupling transfer model. According to the inter-axis coupling transfer relationship, select a series of frequency points within a predetermined frequency range, substitute them into the frequency-domain function model expressed by the transfer function matrix, and calculate the amplitude and phase of the transfer function at each frequency point one by one. Through this method, the response intensity and relative phase shift between each pair of servo axes at different frequencies are obtained, and the frequency response curve of the inter-axis coupling transfer function is plotted based on this. These curves graphically present the distribution pattern of the coupling path in the entire frequency domain. Calculate the coupling metric index between any two servo axes according to the frequency response curve. Calculate the ratio of the frequency response amplitude of a certain off-diagonal coupling path to the amplitude of the response of the corresponding servo axis itself, and take the maximum value within the entire frequency range as the maximum influence ratio of the inter-axis interference, fully capturing the most extreme interference scenario between a pair of servo axes, thereby accurately describing the relative coupling strength between axes. Sort the coupling metric indexes of all servo axis pairs in the system according to their magnitudes to form an inter-axis coupling strength sequence, which reflects the distribution of the dominant coupling paths and weak coupling paths existing in the system. Based on this inter-axis coupling strength sequence, perform interference-sensitive frequency point analysis to identify the servo axis pairs whose coupling metric indexes reach peaks at specific frequencies. These frequency points correspond to the key frequency bands where the system is prone to resonance or vibration interference during operation, and have high sensitivity and control risks. By extracting these frequency-sensitive coupling axis pairs, a set of target coupling axis pairs is constructed as the key object for subsequent synchronous controller design and optimization.

[0030] Step S3: Perform hierarchical optimization on the transfer function matrix and the set of target coupling axis pairs to obtain a preliminary control instruction;

[0031] Specifically, based on the transfer function matrix, an upper-layer model predictive controller is constructed. The upper-layer controller makes predictions according to the system state and the target trajectory, and optimizes the control signal within the prediction time domain. To achieve this goal, a predicted state sequence and a predicted control sequence are defined. The predicted state sequence contains the expected states of each servo axis in the future for a period of time, and the predicted control sequence describes the control signals to be applied to reach the target state. The calculation of these sequences is based on the predicted state equation, which derives the changes in future states by considering the system state and control input at the current moment. Through this predicted state equation, the control system adjusts the control input during the optimization process to minimize the trajectory tracking error and achieve the desired system response. According to the predicted state equation, a weighting function is constructed for the trajectory tracking error, control input, and control rate of change, so as to balance the weights between different objectives during the optimization process, such as trajectory tracking accuracy, the magnitude of the control input, and the smoothness of the control input change. By constructing the weighting function, the upper-layer optimization problem is clarified and an optimization objective is provided for the subsequent optimization algorithm. The solution to this upper-layer optimization problem is carried out through optimization algorithms (such as quadratic programming, gradient descent, etc.) to obtain the optimal control sequence, and the first control vector is the output result of the upper-layer controller. At the same time, the design of the lower-layer synchronous optimization controller is based on the set of target coupling axis pairs to optimize the inter-axis synchronization performance of the system. The core of synchronous control is to ensure the coordinated operation of each servo axis in the multi-axis system and minimize the synchronization error between them. To achieve this goal, a synchronization error vector is defined, which is obtained by calculating the synchronization position error between each servo axis. These errors reflect the relative position differences between different axes and are the key indicators for evaluating the synchronization performance. By integrating the error calculation results into a synchronization error matrix, the synchronization error distribution between each axis at different time steps is presented. After the synchronization error matrix is formed, the lower-layer optimization controller optimizes the control signal according to the result output by the upper-layer controller to effectively improve the synchronization performance between each servo axis of the multi-axis system. The lower-layer optimization controller constructs an objective function with weighted synchronization errors. This objective function weights the synchronization errors of each target coupling axis pair, where the weights reflect the different coupling strengths between axis pairs, and the optimization calculation is carried out for all key coupling axis pairs based on the weighted errors. During this process, the synchronization errors of the key coupling axis pairs have a greater impact on the lower-layer optimization. Therefore, key optimization is carried out through weighting measures to ensure that the calculation of the synchronization control increment is more accurate and achieve a better system synchronization effect. The result of solving the lower-layer optimization problem is the synchronization control increment, which reflects the necessity of adjusting the system state. The calculated synchronization control increment is superimposed on the output result of the upper-layer controller to obtain the final preliminary control instruction. This preliminary control instruction combines the trajectory control accuracy of the upper layer and the synchronization error adjustment of the lower layer to achieve precise control of the multi-axis servo system.Through a hierarchical optimization control strategy, the upper-layer controller ensures the accuracy of the system's trajectory tracking, while the lower-layer controller focuses on optimizing the inter-axis synchronization performance to ensure that the system can achieve precise and stable coordinated motion in a complex control environment.

[0032] Step S4: According to the preliminary control instruction, calculate the trajectory tracking error and the inter-axis synchronization error, and substitute them into the optimization objective function for sampling delay compensation processing to obtain the compensated control instruction;

[0033] Specifically, based on the difference between the preliminary control instruction and the preset reference trajectory, the trajectory tracking error of each servo axis is calculated. By comparing the control signals of each servo axis generated according to the preliminary control instruction with the preset reference trajectory, the error between the actual position and the reference position of each servo axis at each moment is obtained. Through these errors, a trajectory tracking error sequence is calculated to reflect the deviation between the system and the ideal trajectory during the entire control process. Based on the trajectory tracking error and the actual positions of each servo axis, the inter-axis synchronization error is calculated. In a multi-axis servo system, each servo axis needs to maintain relative synchronization during the control process to ensure the coordinated movement of multiple axes. The inter-axis synchronization error is calculated based on the difference between the actual positions and the reference positions of adjacent servo axes. By comparing the position information of each pair of servo axes at the same moment, the difference in the relative positions between the axes, that is, the inter-axis synchronization error sequence, is obtained to reflect the relative motion state between each servo axis. According to the type of control task, an absolute trajectory accuracy optimization strategy and a relative synchronization accuracy optimization strategy are constructed. The absolute trajectory accuracy optimization strategy focuses on the deviation of each servo axis from the reference trajectory and aims to minimize the absolute position error of each axis; while the relative synchronization accuracy optimization strategy focuses on optimizing the synchronization performance between the axes to ensure that the servo axes in the system always maintain coordination during operation. To effectively balance these two optimization requirements, weight coefficients are assigned to the trajectory error and the synchronization error respectively to form a weight coefficient matrix. Based on the weight coefficient matrix, it is applied to the trajectory tracking error sequence and the inter-axis synchronization error sequence to calculate indexes such as contour error, normal error, and tangential error. The contour error is used to evaluate whether the system can maintain the correct path trajectory during multi-axis movement, the normal error is used to measure whether the system deviates from the normal direction of the target path during movement, and the tangential error reflects the degree of deviation of the system along the direction of the target trajectory. By evaluating these comprehensive error indexes, the position tracking error term and the synchronization error term are weighted respectively to obtain an optimization objective function that balances the absolute trajectory accuracy and the relative synchronization accuracy. Through the solution calculation of the optimization objective function, a target control vector is obtained, which contains the optimal control signals required by the system to ensure that the system minimizes errors as much as possible during the control process and meets the requirements of trajectory tracking accuracy and inter-axis synchronization accuracy. Due to the sampling delay existing in the real-time execution process of the digital control system, sampling delay compensation processing is performed on the target control vector. To compensate for the error caused by the sampling delay, a sampling delay compensation algorithm is introduced. This algorithm dynamically adjusts the control signal according to the sampling period and delay characteristics of the system to obtain a compensated control instruction.

[0034] Construct a sampling delay compensator based on the state matrix of the discrete-time system. This compensator models the impact of sampling delay on the system behavior and then compensates for the control error caused by the time difference between the sampling period and the system response. The sampling delay compensator predicts the future system output by introducing the influence of sampling delay into the system model. Based on the sampling delay compensator, model predictive calculations are performed to obtain predictive output data, which represents the expected output of the system after sampling delay compensation under the given control input and system state. The difference operation is performed between the actual system output and the predictive output data to obtain model correction data, that is, the error between the actual system output and the predictive output, which reflects the deviation between the model prediction and the actual system behavior. The prediction horizon, control horizon, and weight matrix parameters are dynamically adjusted according to the model correction data and the operating state of the system. The adjustment of these parameters directly affects the response speed and control accuracy of the controller. The prediction horizon determines the time range of the predictive output data, the control horizon determines the optimal time window of the control input, and the weight matrix parameters adjust the influence degree of different error terms during the optimization process. By dynamically adjusting these parameters, the system can quickly respond to environmental changes and control task requirements, thereby optimizing the overall control performance. After completing the above parameter adjustment, multi-sampling period measurements are performed to obtain higher-frequency feedback information. m state samplings are completed within one control cycle, significantly improving the timeliness and accuracy of the feedback information. Through multi-sampling technology, more state information is obtained within each control cycle, and then the future dynamic behavior of the system can be predicted more accurately, reducing the influence caused by sampling delay and incomplete feedback. Based on the adaptive control parameters and the target feedback information, a state observer is constructed. The state observer estimates the current state of the system according to the feedback information of the system. Especially in the presence of sampling delay, the observer can effectively compensate for the error caused by the delay. During the construction of the state observer, the pole placement algorithm is used to calculate the observer gain matrix. The pole placement algorithm selects an appropriate gain matrix so that the observation error of the system can quickly converge within a certain time, ensuring the accuracy and stability of the state estimation. The state estimate value is obtained through the calculated observer gain matrix. The state estimate value is combined with the adaptive control parameters to improve the control effect. Especially in the face of sampling delay and incomplete observation information, it can effectively reduce the control error and improve the stability and accuracy of the control system. Using the state estimate value and the adaptive control parameters, the target control vector is substituted into the prediction equation to predict the system state within the next d sampling periods. The prediction process provides a basis for the generation of compensation control commands by considering the dynamic characteristics of the system and the adjustment of the prediction horizon and control horizon. In this way, the system effectively compensates for the sampling delay within the control cycle, ensuring that the control process is always in the optimal state, and finally obtaining the compensation control command.

[0035] Step S5: Perform real-time processing on the compensation control instruction and output a synchronous control signal to each servo axis to achieve multi-axis coordinated motion.

[0036] Specifically, a mathematical transformation of the compensation control instruction into the standard quadratic programming form is carried out to formalize the control optimization problem in the form of a mathematical optimization model, making it have the characteristics of clear solution structure and being executable by an efficient algorithm. During the transformation process, the control problem is rewritten as a standard quadratic objective function with the control increment as the variable, which includes a positive definite Hessian matrix and a linear term coefficient vector. The Hessian matrix is used to describe the second-order relationship between control variables, and its structure reflects the strength and direction of the influence of the control input on the objective function, while the linear term represents the linear sensitivity of the objective function to the current control state. The Cholesky decomposition algorithm is used to decompose the Hessian matrix, and matrix operation techniques such as forward substitution and backward substitution are supplemented to quickly solve the objective function. Cholesky decomposition is applicable to positive definite symmetric matrices, with high computational efficiency and strong numerical stability, suitable for optimization tasks that need to be completed within milliseconds in real-time control. Through this decomposition method, complex matrix operations are simplified into a series of recursively computable steps, improving the solution speed. Through efficient linear algebra operations, the control solution result, that is, the optimized control signal vector, is obtained. This result is the theoretical output of the multi-axis servo system that meets the optimal performance index under the current state. Considering the physical constraint conditions such as drive voltage, current, speed, and acceleration in the actual servo system, the gradient projection method is introduced to correct the control solution result on this basis. The gradient projection method adjusts the initially solved control vector to within the range that satisfies all physical constraints by performing projection operations on the feasible region of the control variables, ensuring that the control signal will not cause over-limit problems or system instability during execution. This method first calculates the gradient of the objective function at the current point, and then iteratively updates the control variables along the gradient direction until the variable satisfies all the constraints and projects it onto the boundary of the feasible region, forming a synchronous control increment that satisfies the constraints and is as close as possible to the optimal solution. After superposition processing of this control increment, the final executable control signal is formed, which is used to drive the servo axis to perform precise actions. To ensure the high-efficiency and real-time consistency of the above control signal in the multi-axis system, multi-level parallel processing is performed on the final executed control signal. In parallel processing, the system is divided into several interrelated axis groups according to the coupling relationship of the servo axes, and the axis groups are decoupled as much as possible to improve parallelism; then tasks such as state update, error estimation, and control calculation are executed in parallel within each group, and further data-level parallel acceleration is performed on intensive operations such as control matrix operations and increment updates using multi-core computing resources. After parallel processing, in order to reasonably arrange the system resource occupancy of various computing and execution tasks, the execution priority of the control tasks is divided based on the processing results. The priority setting is sorted according to the influence degree of each task on the system performance. Among them, key tasks such as state estimation and control output are given higher priorities, while delayable tasks such as parameter update and model reconstruction are set as low priorities.According to the result of this priority division, formulate a task execution strategy to ensure the stable operation of the key control chain under the conditions of resource tension or limited operation time. Based on the task execution strategy, perform real-time allocation and execution monitoring of the final execution control signal. All the calculated final execution control signals are allocated to each servo-axis control unit according to the task scheduling strategy. The real-time scheduling module flexibly arranges the timing and method of issuing control signals according to the current state and execution load of each servo axis, and simultaneously monitors the execution process of the signals in real time to prevent control deviation or synchronization failure caused by signal delay, inter-axis interference or abnormal state, and finally achieve the multi-axis synchronization control goal at the system level.

[0037] In the embodiment of the present invention, a generalized state space model of a multi-axis servo system considering sampling delay is established, which comprehensively describes the influence of the mechanical coupling relationship between axes and sampling delay on the dynamic characteristics of the system, provides an accurate theoretical basis for multi-axis synchronization control, and avoids the system modeling deviation caused by the traditional model ignoring sampling delay. By constructing a discrete-time transfer function matrix, the present invention directly reveals the inter-axis coupling relationship from the frequency domain perspective, simplifies the analysis process of complex multi-axis systems, enables system designers to intuitively evaluate the inter-axis synchronization characteristics through classical control tools, and accurately identify key coupling axis pairs and sensitive frequency points. The hierarchical control structure is adopted to separately process trajectory planning and synchronization optimization, effectively separating the goals of trajectory tracking and synchronization control, avoiding the difficulty of weight selection in traditional single-layer control, and providing flexible control strategy selection for different application scenarios. An optimization objective function considering both trajectory error and synchronization error is designed to dynamically balance the absolute trajectory accuracy and relative synchronization accuracy according to different work task requirements, introduce multi-dimensional evaluation indicators such as contour error, normal error and tangential error, and provide a comprehensive performance evaluation standard. Combining multi-sampling technology and the principle of Smith predictor, dynamically adjust control parameters, effectively compensate the sampling delay in the digital control system, enhance the robustness of the control system, and improve the synchronization control accuracy in the multi-axis servo system.

[0038] In a specific embodiment, the process of executing step S1 may specifically include the following steps:

[0039] Measure the parameters of n servo axes in the multi-axis servo system, collect the position, speed and acceleration state information of each servo axis, and obtain the system state vector, control input vector and system output vector;

[0040] Measure the sampling time of the digital control system of each servo axis to obtain the sampling delay time parameter, and the sampling delay time parameter is the time difference from signal acquisition to execution of each servo axis;

[0041] Perform stiffness and damping tests on the mechanical structure of the multi-axis servo system to obtain mechanical coupling relationship parameters, which are used to represent the physical connection characteristics between each servo axis;

[0042] Perform parameter identification on each servo motor in the multi-axis servo system to obtain motor dynamic characteristic parameters, which include motor torque constant, moment of inertia, and friction coefficient;

[0043] Substitute the system state vector, control input vector, system output vector, sampling delay time parameter, mechanical coupling relationship parameter, and motor dynamic characteristic parameter into the state equation modeling formula to perform discrete-time calculations, and obtain the discrete-time system state matrix.

[0044] Specifically, parameter measurements are performed on each servo axis in the system. For a servo system with multiple degrees of freedom, such as a multi-axis linkage CNC workbench, assuming it contains multiple independent but coupled servo axes, the state information of each servo axis during operation is collected in sequence, including position, speed, and acceleration, etc. This information is collected through high-precision encoders, speed sensors, and acceleration sensors. Among them, the encoder directly feeds back the position, the speed can be obtained by differentiating the position signal, and the acceleration is obtained through the acceleration sensor or by differentiating the speed signal again. The state data of all servo axes are uniformly organized at each sampling moment to construct the state vector of the system, describing the complete motion state of the system at a certain moment. At the same time, during the system control process, the control signals applied to each servo axis are recorded, including current, voltage, or speed set values, which are generated in real time by the upper controller according to the control algorithm and transmitted to the driver. After organizing the control inputs, a control input vector is formed, combined with the actual motion response data obtained from the system feedback, and organized into a system output vector. To model the sampling delay characteristics, the sampling time of the digital control link of each servo axis is measured. The servo control system consists of a position loop, a speed loop, and a current loop, and multiple modules are cascaded to execute the control process. Due to the differences in the calculation cycle, communication delay, and internal response time of the driver, there is a time difference between collecting the input signal and executing the control output in the system. This time difference is the sampling delay time parameter. By inserting a high-precision timestamp device between the controller and the driver, the time interval between the issuance of the control command and the actual response of the servo motor is recorded, and the delay value of each axis is accurately obtained. The stiffness and damping characteristics of the mechanical structure of the system are tested. The multi-axis servo system is not completely independent in structure. Its various axes are connected by mechanical devices, and there is a certain degree of structural coupling, which is more obvious especially in application scenarios with heavy workloads or continuous path switching. To quantify the influence of these mechanical connections, a mechanical excitation experiment is carried out on the system. For example, a periodic perturbation is applied through a shaker, and displacement or acceleration sensors are arranged on other axes to measure the response magnitude and delay. Then, combined with the frequency response function, the stiffness coefficient and damping coefficient between each servo axis are calculated to form a mechanical coupling relationship parameter matrix. For example, when a unit excitation force is applied to the X axis, an obvious vibration response is detected on the Y axis, indicating that there is a strong stiffness coupling between X and Y. At this time, the coupling term between X and Y is set to a non-zero value in the system modeling. Parameter identification is performed on each servo motor. The dynamic characteristics of the motor have a decisive influence on the control behavior of the entire servo system, which mainly includes the torque constant, moment of inertia, and friction coefficient of the motor, etc. The motor torque constant describes the linear relationship between the input current and the output torque; the moment of inertia determines the acceleration magnitude of the motor under a given torque; the friction coefficient reflects the torque required for the motor to overcome internal and external friction during operation. The parameter identification methods include the step response method and the frequency sweep method.Substitute all the obtained parameter data mentioned above, including the system state vector, control input vector, system output vector, sampling delay time parameter, mechanical coupling relationship parameter, and motor dynamic characteristic parameter, into the pre-established state equation modeling formula, and perform numerical processing in combination with the discretization strategy to obtain the discrete-time system state matrix.

[0045] In a specific embodiment, the process of executing step S2 may specifically include the following steps:

[0046] Perform a Z-transform on the discrete-time system state matrix to obtain the frequency-domain system equation;

[0047] Calculate the transfer relationship between the output and the input based on the frequency-domain system equation to obtain the transfer function matrix;

[0048] Identify the self-transfer characteristics of each servo axis and the inter-axis coupling transfer characteristics according to the diagonal elements and non-diagonal elements of the transfer function matrix to obtain the inter-axis coupling transfer relationship;

[0049] According to the inter-axis coupling transfer relationship, calculate the amplitude and phase of the transfer function matrix at different frequency points, and plot the frequency response curve of the inter-axis coupling;

[0050] Calculate the coupling metric index between any two servo axes according to the frequency response curve, evaluate the maximum interference influence ratio between the axes, and obtain the inter-axis coupling strength sequence;

[0051] Perform interference-sensitive frequency point analysis based on the inter-axis coupling strength sequence to determine the set of target coupling axis pairs.

[0052] Specifically, starting from the discrete-time state matrix after system modeling, the Z-transform is used to convert it from the time-domain form to the frequency-domain form to reveal the response characteristics of the system at different frequencies and its input-output relationship. As a mathematical tool from the time domain to the frequency domain, the Z-transform represents the time-evolution process in the discrete-time system state equation as an algebraic relationship in the complex number domain, thus significantly simplifying the complexity of system response analysis. In actual operation, after applying the Z-transform to the discrete state matrix, the original system equation involving time advancement is rewritten as an algebraic equation about the complex frequency variable, that is, the frequency-domain system equation. Based on the frequency-domain system equation, the transfer function relationship between the output vector and the input vector is derived. The transfer function is essentially a frequency-domain mapping relationship used to express how the output of the system will respond when faced with a specific frequency input. In a multi-axis servo system, each servo axis is affected not only by its own control input but also by the indirect interference transmitted from the control signals of other servo axes through the mechanical coupling path. By substituting and deriving the state vector in the frequency-domain system equation, a multi-dimensional transfer function matrix is obtained. Each element of this matrix represents the transfer path and response characteristics of a certain input component of the system to a certain output component. The diagonal elements of the matrix represent the transfer characteristics of each servo axis itself, while the off-diagonal elements characterize the coupling influence relationship between different servo axes. Analyze this transfer function matrix to identify the coupling transfer relationship between each servo axis in the system. If the value of a certain off-diagonal element is significantly non-zero and its amplitude fluctuates significantly with frequency, it indicates that there is a significant dynamic coupling effect between this servo axis and its corresponding input. Take the transfer function on the diagonal as the reference standard to measure the interference degree of other axes on the current axis. For example, it is found that the input signal of the Y-axis not only affects its own displacement response but also causes fluctuations in the vibration amplitude of the X-axis to a certain extent. This phenomenon is reflected by the non-zero value of the off-diagonal transfer function. If this off-diagonal element shows obvious response amplitudes in multiple frequency bands, it is initially judged that there is a strong coupling relationship between the X-axis and the Y-axis. Calculate the response characteristics of the transfer function matrix at multiple frequency points. Select a frequency scanning interval that covers all the working frequency bands encountered by the system, and calculate the amplitude and phase of the transfer function at each frequency point. These calculation results are used to plot the frequency response curve of the inter-axis coupling. The amplitude response curve shows the response intensity of a specific input signal to the output at a specific frequency, while the phase response curve reflects the time delay relationship between the input and output. Through these response curves, identify which frequency intervals are the regions with the most significant coupling influence, so as to provide a frequency selection basis for subsequent controller design. Calculate the coupling metric index between any two servo axes according to the frequency response curve. This index is defined as the ratio of the maximum amplitude of a certain off-diagonal transfer function to the maximum amplitude of its corresponding diagonal transfer function, used to reflect the maximum interference influence ratio of the input of other axes on the output of the current axis.The larger this index is, the stronger the interference effect of this coupling path, and it needs to be given priority attention during the control process. Sort all possible axis pairs in descending order according to the coupling metric index to form an inter-axis coupling strength sequence. Based on the coupling strength sequence, perform frequency sensitivity analysis on the key coupling paths to identify at what frequencies the system is most vulnerable to interference, posing a threat to the control performance. Combine the coupling metric and the frequency response curve to identify the frequency bands for each pair of strongly coupled axes and determine their coupling peak frequencies within the entire operating frequency range. These frequency points are the positions where vibration amplification, error transmission, or synchronization disorders are most likely to occur during system operation. Therefore, corresponding filters or predictive compensation mechanisms are introduced in the control strategy to address this issue. All axis pairs confirmed through interference sensitivity analysis constitute the set of target coupling axis pairs. This set is the key focus during the design process of the system synchronization controller and is also the optimization variable for the lower-layer synchronization optimization controller in the subsequent hierarchical control structure.

[0053] In a specific embodiment, the process of executing step S3 may specifically include the following steps:

[0054] Construct an upper-layer model predictive controller based on the transfer function matrix, define the prediction state sequence and the prediction control sequence, and obtain the prediction state equation;

[0055] According to the prediction state equation, construct a weighting function for the trajectory tracking error, control input, and control rate of change to obtain the upper-layer optimization problem;

[0056] Perform a solution calculation on the upper-layer optimization problem to obtain the first control vector of the optimal control sequence and get the output result of the upper-layer controller;

[0057] Define a synchronization error vector based on the set of target coupling axis pairs, calculate the synchronization position error between each servo axis, and obtain the synchronization error matrix;

[0058] Construct a lower-layer optimization objective function according to the synchronization error matrix and the output result of the upper-layer controller, perform a synchronization error weighting calculation on all key coupling axis pairs in the set of target coupling axis pairs, and obtain the lower-layer optimization problem;

[0059] Perform a solution operation on the lower-layer optimization problem, calculate the synchronization control increment, and superimpose the synchronization control increment on the output result of the upper-layer controller to obtain the preliminary control instruction.

[0060] Specifically, a hierarchical control structure consisting of upper and lower layers is constructed. The upper layer is responsible for trajectory tracking optimization, while the lower layer focuses on the dynamic adjustment of the inter-axis synchronization performance. Based on the system transfer function matrix, a model predictive controller covering the prediction of the global motion state is established, and an objective optimization function is constructed in combination with the system coupling characteristics to achieve fine control of the coordinated motion between each servo axis. Based on the transfer function matrix obtained by the Z-transform in the early stage, a prediction model is constructed. This transfer function matrix contains the response characteristics of each servo axis to its own input and represents the coupling path and frequency response behavior between the axes. When constructing the upper-layer model predictive controller, according to the state transition characteristics and the system input-output relationship contained in the transfer function matrix, the prediction state sequence and the prediction control sequence are defined. The prediction state sequence refers to the state trajectory that the system may reach within a certain number of future prediction steps at the current sampling moment, while the prediction control sequence represents the optimization path of the system input variable within the control time domain. These two together constitute the basic framework of the prediction state equation. The establishment of the prediction state equation aims to recursively calculate the system state in the future time domain through the state space model and predict the system response in combination with the known initial state. This prediction result serves as a prerequisite for the optimization solution. On this basis, to achieve fine regulation of the system motion performance, a weighted optimization function including multiple performance indicators such as trajectory tracking error, control input amplitude, and control input change rate is constructed. This optimization function is constrained by the prediction state equation and forms the upper-layer control objective function by introducing three key weighting functions: trajectory error weight, control signal strength weight, and control change smoothness weight. The design of each weight is balanced and configured according to the actual application scenario. By constructing this upper-layer optimization problem and solving it, a set of optimal control input sequences are obtained. The first control input is the optimal control signal to be applied during the current sampling period, and this signal constitutes the output result of the upper-layer controller. Based on the output of the upper-layer controller, a lower-layer controller is introduced to correct and optimize the inter-axis synchronization error. Based on the identified set of target coupled axis pairs, a synchronization error vector is constructed. This vector is used to quantify the relative position deviation between different servo axes. It is defined as the difference between the actual position difference and the reference trajectory difference between two axes, indicating whether the two axes maintain the required synchronization state during the actual operation of the system. The synchronization errors corresponding to all target coupled axis pairs are organized into a synchronization error matrix to model the synchronization performance of the multi-axis system on a global scale. The synchronization error matrix is combined with the output result of the upper-layer controller to construct a lower-layer optimal control objective function. Without destroying the original trajectory tracking performance, this objective function punishes the error between the target coupled axis pairs by introducing a weighted term of the synchronization error. The setting of the weighting coefficient is proportional to the coupling strength between the axes, that is, the stronger the coupling between the axis pairs, the greater the weight of their synchronization error in the objective function, to guide the optimization algorithm to preferentially eliminate the synchronization mismatch phenomenon on the strong coupling path.After the lower-level optimization problem is constructed, through corresponding solution algorithms such as the gradient method, quadratic programming method, or constrained optimization method, iterative calculations are performed on the objective function to obtain the synchronization control increment. The synchronization control increment is a further refinement of the output of the upper-level controller and represents the additional correction signal required to achieve inter-axis synchronization. This increment is superimposed on the output of the upper-level controller in software form to form the complete control instruction finally used to control the actuator. This superimposition process ensures the hierarchical nature and target separation of the control structure, that is, the upper level focuses on the global path accuracy, and the lower level deals with local synchronization coordination. The two work together without interfering with each other. The preliminary control instruction is formed through the hierarchical structure.

[0061] In a specific embodiment, the process of executing step S4 may specifically include the following steps:

[0062] Calculate the absolute trajectory error of each servo axis according to the preliminary control instruction and the preset reference trajectory to obtain the trajectory tracking error sequence;

[0063] Calculate the inter-axis relative position difference based on the actual positions and reference positions of adjacent servo axes to obtain the inter-axis synchronization error sequence;

[0064] Construct an absolute trajectory accuracy optimization strategy and a relative synchronization accuracy optimization strategy according to the control task type, and assign weight coefficients to the trajectory error and synchronization error to obtain a weight coefficient matrix;

[0065] Apply the weight coefficient matrix to the trajectory tracking error sequence and the inter-axis synchronization error sequence, and calculate the contour error index, normal error, and tangential error to obtain the comprehensive error evaluation result;

[0066] Based on the comprehensive error evaluation result, perform weighted processing on the position tracking error term and the synchronization error term respectively to obtain an optimization objective function that balances the absolute trajectory accuracy and relative synchronization accuracy;

[0067] Perform a solution calculation on the optimization objective function to obtain the target control vector;

[0068] Perform sampling delay compensation processing on the target control vector to obtain the compensated control instruction.

[0069] Specifically, based on the difference between the preliminary control instruction and the predefined reference trajectory, the absolute trajectory error of each servo axis is calculated. The absolute trajectory error is the deviation of the current operating state of the system from the ideal trajectory, reflecting the control accuracy of each axis. This error is obtained by comparing the differences between the actual position and the target position at each sampling point and is organized into a trajectory tracking error sequence in chronological order. To evaluate the coordination degree between servo axes when obtaining the trajectory error sequence, the calculation of the inter-axis synchronization error is introduced. The inter-axis synchronization error refers to the difference between the actual relative position and the reference relative position of two adjacent or functionally coupled servo axes at a given time. To calculate this error, the actual position values of adjacent axes at the current moment and their relative differences that should be maintained under the reference trajectory are obtained, and the synchronization deviation between each pair of axes is derived accordingly. Based on the type of control task, an absolute trajectory accuracy optimization strategy and a relative synchronization accuracy optimization strategy are constructed. For scenarios requiring high positioning accuracy, the absolute trajectory accuracy optimization strategy is adopted, while for application scenarios involving spatial path consistency or multi-axis coordination, the relative synchronization accuracy optimization strategy is adopted. Based on these two strategies, appropriate weight coefficients are assigned to each type of error, and the weights are uniformly constructed into a weight coefficient matrix, so as to give different error terms the mathematical meaning of matching their task importance in subsequent optimization. Based on the trajectory error sequence and the synchronization error sequence, and combined with the set weight coefficient matrix, the comprehensive error index of the system is calculated, including contour error, normal error, and tangential error. The contour error is the core index for evaluating whether the multi-axis trajectory remains coherent on the spatial path, representing the shortest distance between the actual trajectory points and the ideal trajectory path; the normal error reflects the deviation degree of the system motion trajectory in the direction perpendicular to the reference path, while the tangential error describes the forward and backward deviation of the system along the path direction. These three error dimensions constitute the error evaluation benchmark for the multi-axis servo system in spatial control, and can more comprehensively reveal the geometric properties of the system operation deviation. Based on the comprehensive error evaluation result, the position tracking error term and the synchronization error term are weighted respectively, and an optimization objective function that balances the absolute trajectory accuracy and the relative synchronization accuracy is constructed. By setting appropriate weighting factors in the objective function, it is ensured that while meeting the overall motion accuracy, the key inter-axis synchronization error is suppressed to achieve system-level coordinated control. The optimization objective function is solved to obtain the target control vector. This control vector is the optimal control input sequence obtained by solving the error minimization objective function under the current system state. To ensure the efficiency and accuracy of the solution, quadratic programming, gradient method, or predictive control algorithm is used for iterative optimization, and combined with the current state variables and historical control data, it quickly converges to the global or local optimal solution. The first element in this vector is the actual control signal at the current moment, and the rest are the preparatory inputs for multiple future cycles. The target control vector is subjected to sampling delay compensation processing. This compensation incorporates the time difference caused by the delay into the control signal calculation process in advance by constructing a prediction model or using a Smith compensator.For example, the delay compensation algorithm can predict in advance that the current control input will take effect after several milliseconds, and adjust the current control strategy accordingly, so as to ensure that the finally output compensated control instruction is at the optimal moment in the actual response of the system.

[0070] In a specific embodiment, the process of performing sampling delay compensation processing on the target control vector to obtain the compensated control instruction may specifically include the following steps:

[0071] Construct a sampling delay compensator based on the discrete-time system state matrix, and perform model predictive calculation according to the sampling delay compensator to obtain predicted output data;

[0072] Perform a difference operation on the actual system output and the predicted output data to obtain model correction data;

[0073] Dynamically adjust the prediction horizon, control horizon, and weight matrix parameters according to the model correction data and the system operating state to obtain adaptive control parameters;

[0074] Perform multi-sampling period measurement on the multi-axis servo system, complete m state samplings within one control period to obtain the target feedback information;

[0075] Construct a state observer according to the adaptive control parameters and the target feedback information, and perform observer gain matrix calculation according to the state observer using the pole placement algorithm to obtain the state estimate;

[0076] Use the state estimate and the adaptive control parameters, substitute the target control vector into the prediction equation to predict the system state in the next d sampling periods, and obtain the compensated control instruction.

[0077] Specifically, a sampling delay compensator is constructed based on the state matrix of the discrete-time system. This compensator is based on the previously established discrete-time state-space model, integrates the dynamic characteristics of the system and the mapping relationship between the control input and the state response, and introduces a sampling delay parameter in its structure to predict the system response trend in a certain future time period before the control instruction is issued. Through this compensator, the system state after several future sampling periods is estimated in advance in the current control cycle, so as to offset the response lag caused by the control delay. According to the internal state update mechanism of the delay compensator and the control input execution model, predictive calculation is performed to obtain the corresponding predictive output data. The difference operation is performed on the actual system output and the predictive output data to obtain the deviation degree of the current model under the actual operating state, and this difference is the model correction data. This data reflects the model prediction deviation caused by factors such as inaccurate modeling, system nonlinear disturbance, or environmental changes. Based on the model correction data and combined with the current operating state of the system, the core control parameters in the model predictive controller are dynamically adjusted, including the prediction horizon, control horizon, and weight matrix, etc. Among them, the prediction horizon determines how many steps of state evolution the controller considers in the future period, the control horizon limits the optimization step of the control input within the current controllable range, and the weight matrix determines the optimization priority of each performance index in the objective function. By adjusting these parameters in real time, the controller realizes the dynamic trade-off among accuracy, response speed, and control cost under different working conditions. A multi-sampling period measurement strategy is introduced at the sampling mechanism level, that is, the system state is sampled multiple times within one control cycle to obtain high-frequency feedback information. By increasing the sampling frequency, the minute changes in the system state are captured more carefully, and the state variables used in the predictive model are updated in real time to improve the accuracy of the prediction results. After obtaining the target feedback information generated by multiple samplings, combined with the aforementioned adaptive control parameters, a state observer is constructed to improve the estimation accuracy of the system for the current state. The role of the state observer is to use limited output variables, combined with the system input and the known model, to deduce the complete internal state vector of the system. In this observer, the observer gain matrix is the key parameter determining the estimation accuracy. In order to ensure that the state estimation has good dynamic response and convergence, the pole placement algorithm is used to solve the gain matrix to obtain the state estimation value. The pole placement algorithm controls the convergence speed of the observation error and the system response rate by presetting the position of the observer poles, and sets the poles in the region that meets the stability requirements and has fast response capabilities. Using the state estimation value and the adaptive control parameters, the target control vector is substituted into the prediction equation to predict the system state evolution trajectory in the future d sampling periods. By pre-deducing the dynamic behavior of the system in the delay time period, the future state feedback is incorporated into the controller decision in advance to achieve early control.Based on the prediction result, correct the current control output so that it exactly makes up for the time gap between sampling and execution when reaching the actuator, enabling the control signal to still play a timely and effective regulatory role in the system in the presence of physical delays.

[0078] In a specific embodiment, the process of executing step S5 may specifically include the following steps:

[0079] Convert the compensation control instruction into the standard quadratic programming form to obtain a control equation containing the Hessian matrix and the linear term coefficient vector;

[0080] Perform Cholesky decomposition and substitution algorithm calculation on the control equation to obtain the control solution result;

[0081] Adopt the gradient projection method to calculate the synchronous control increment that meets the physical constraints according to the control solution result to obtain the final execution control signal;

[0082] Perform multi-level parallel processing on the final execution control signal to obtain the parallel processing result, and divide the execution priority of the control task according to the parallel processing result to obtain the task execution strategy;

[0083] Based on the task execution strategy, perform real-time allocation and execution monitoring on the final execution control signal, and output the synchronous control signal to each servo axis to achieve multi-axis coordinated motion.

[0084] Specifically, the control objectives, system dynamic constraints, physical limitations, and error weight parameters included in the compensation control instruction are reorganized into an optimization model with a clear mathematical form. The standard quadratic programming form is a type of convex optimization problem used in engineering optimization. Its structure consists of a quadratic objective function and a set of linear constraints, with good solution stability and physical interpretability. In the control problem, the control increment is used as the optimization variable, and the trajectory error and synchronization error involved in the compensation control instruction are integrated into the objective function to construct an optimization model with the goal of minimizing the error cost function. In this model, the quadratic term is used to describe the second-order sensitivity of the control variable to the objective function. This term is expressed as the Hessian matrix, which has the property of being symmetric positive definite, ensuring that there is a unique optimal solution to the optimization problem. The coefficient vector of the linear term, on the other hand, is used to represent the linear sensitivity of the control variable in the objective function. Through this transformation process, the compensation control instruction is mapped into a quadratic programming control equation in standard form. After obtaining the control equation in standard form, to efficiently solve this structured optimization model, a linear algebra method suitable for solving quadratic forms is adopted. The Cholesky decomposition is combined with the forward and backward substitution algorithms to solve the control matrix. The Cholesky decomposition is an efficient and numerically stable matrix decomposition technique suitable for the fast decomposition of symmetric positive definite matrices. By decomposing the Hessian matrix into the product of a lower triangular matrix and its transpose matrix, the quadratic optimization problem is transformed into the solution process of two linear equations, simplifying the computational complexity and being applicable to real-time systems with strict requirements for the control period. After the decomposition is completed, the forward substitution and backward substitution algorithms are used to solve the intermediate variables and the final control variables in sequence to obtain the optimal control solution result for the current period. In an actual system, the control signal needs to satisfy a series of physical constraint conditions, including maximum current, voltage limit, speed upper limit, acceleration boundary, and torque load, etc. These constraint conditions are jointly determined by the motor parameters, driver capabilities, and mechanical structure. If the control signal is directly issued without being constrained, it will cause the actuator to exceed the limit, oscillate, or even be damaged. Therefore, based on the solution result, the gradient projection method is introduced to correct the control variable within the constraint domain. The gradient projection method calculates the steepest descent direction in the control increment space and projects the variables in this direction onto the boundary of the physical constraint feasible domain to ensure that the final control result is both close to the optimal and in line with the actual limitations of the system, obtaining the final execution control signal. The final execution control signal is processed in multiple levels in parallel to improve the processing speed and task allocation efficiency of the control signal, obtaining the parallel processing result. The control tasks of multiple servo axes are grouped for execution. Using the multi-thread mechanism in a multi-core computing platform or an embedded real-time processor, the signal generation, state estimation, and command scheduling operations for each group of axes are run independently, so as to complete the control tasks of multiple axes within one control cycle. According to the parallel processing result, the execution priorities of the control tasks are divided to form a task execution strategy.The setting of priorities is based on a quantitative analysis of the impact of tasks on system stability, response speed, and key indicators. For example, system state updates, error feedback, and control increment calculations are given high priorities, while non-real-time tasks such as parameter recording and log saving are postponed. In a real-time system, the execution order of tasks is dynamically adjusted through an event-triggered or time-slice scheduling mechanism to ensure that the critical control path is preferentially executed in all cycles. Based on the task execution strategy, real-time allocation and execution monitoring of the final execution control signal are performed. Real-time allocation means that according to the task scheduling result, the control signal is sent to each servo-axis drive module at precise time sequences, and the status feedback of the driver is read in real time to confirm the execution of the command. Execution monitoring includes comparison of signal sending results, fault identification, synchronization error tracking, etc., to ensure that the control instruction is accurately executed in each servo loop.

[0085] The above describes the synchronous control method of the multi-axis servo system in the embodiment of the present invention. Next, the synchronous control device of the multi-axis servo system in the embodiment of the present invention will be described. Please refer to Figure 2 , an embodiment of the synchronous control device of the multi-axis servo system in the embodiment of the present invention includes:

[0086] A measurement module, configured to measure the mechanical coupling relationship parameters, motor dynamic characteristic parameters, and sampling delay time parameters of the multi-axis servo system and substitute them into the state equation modeling formula to calculate the discrete-time system state matrix;

[0087] A calculation module, configured to perform Z-transform processing on the discrete-time system state matrix and calculate the frequency response characteristics to obtain the transfer function matrix and the set of target coupling axis pairs;

[0088] A hierarchical optimization module, configured to perform hierarchical optimization on the transfer function matrix and the set of target coupling axis pairs to obtain a preliminary control instruction;

[0089] A delay compensation module, configured to calculate the trajectory tracking error and the inter-axis synchronization error according to the preliminary control instruction and substitute them into the optimization objective function for sampling delay compensation processing to obtain a compensation control instruction;

[0090] A real-time processing module, configured to perform real-time processing on the compensation control instruction and output a synchronous control signal to each servo axis to achieve multi-axis coordinated motion.

[0091] Through the collaborative cooperation of the above-mentioned various components, the present invention establishes a generalized state-space model of a multi-axis servo system considering sampling delay, comprehensively describes the influence of inter-axis mechanical coupling relationship and sampling delay on the dynamic characteristics of the system, provides an accurate theoretical basis for multi-axis synchronous control, and avoids the system modeling deviation caused by traditional models ignoring sampling delay. By constructing a discrete-time transfer function matrix, the present invention directly reveals the inter-axis coupling relationship from the frequency domain perspective, simplifies the analysis process of complex multi-axis systems, enables system designers to intuitively evaluate the inter-axis synchronization characteristics through classical control tools, and accurately identify key coupling axis pairs and sensitive frequency points. Adopting a hierarchical control structure to separately process trajectory planning and synchronization optimization effectively separates the goals of trajectory tracking and synchronous control, avoids the difficulty of weight selection in traditional single-layer control, and provides flexible control strategy selection for different application scenarios. An optimization objective function considering both trajectory error and synchronization error is designed to dynamically balance the absolute trajectory accuracy and relative synchronization accuracy according to different work task requirements, introduces multi-dimensional evaluation indicators such as contour error, normal error, and tangential error, and provides a comprehensive performance evaluation standard. Combining multi-sampling technology and the principle of Smith predictor to dynamically adjust control parameters, effectively compensating for sampling delay in digital control systems, enhancing the robustness of the control system, and improving the synchronous control accuracy in multi-axis servo systems.

[0092] Referring to Figure 3 , an embodiment of the present invention also provides a computer device, which may be a server, and its internal structure may be as Figure 3 shown. The computer device includes a processor, a memory, a display screen, an input device, a network interface, and a database connected through a system bus. Among them, the processor of the computer design is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store the corresponding data in this embodiment. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the above method is implemented.

[0093] Those skilled in the art can understand that Figure 3 the structure shown in

[0094] merely represents a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied.

[0095] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs.

[0096] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A synchronous control method for a multi-axis servo system, characterized in that: include: The mechanical coupling relationship parameters, motor dynamic characteristic parameters and sampling delay time parameters of the multi-axis servo system are measured and substituted into the state equation modeling formula to calculate the discrete time system state matrix; Performing Z-transform processing on the discrete-time system state matrix and calculating the frequency response characteristics to obtain a transfer function matrix and a target coupling axis pair set; performing hierarchical optimization on the transfer function matrix and the target coupling axis pair set to obtain preliminary control instructions; According to the preliminary control instruction, the trajectory tracking error and the inter-axis synchronization error are calculated and substituted into the optimization objective function to perform sampling delay compensation processing to obtain a compensation control instruction; The compensation control instruction is processed in real time, and a synchronous control signal is output to each servo axis to realize multi-axis coordinated motion.

2. The synchronous control method of a multi-axis servo system according to claim 1, characterized in that: The mechanical coupling relationship parameters, motor dynamic characteristic parameters and sampling delay time parameters of the multi-axis servo system are measured and substituted into the state equation modeling formula to calculate the discrete time system state matrix, including: Measure the parameters of n servo axes in the multi-axis servo system, collect the position, velocity and acceleration state information of each servo axis, and obtain the system state vector, control input vector and system output vector; The sampling time of the digital control system of each servo axis is measured to obtain a sampling delay time parameter, wherein the sampling delay time parameter is the time difference between the acquisition and execution of each servo axis signal; Performing stiffness and damping tests on the mechanical structure of the multi-axis servo system to obtain mechanical coupling relationship parameters, wherein the mechanical coupling relationship parameters are used to represent the physical connection characteristics between the servo axes; Performing parameter identification on each servo motor in the multi-axis servo system to obtain motor dynamic characteristic parameters, wherein the motor dynamic characteristic parameters include motor torque constant, moment of inertia and friction coefficient; Substitute the system state vector, the control input vector, the system output vector, the sampling delay time parameter, the mechanical coupling relationship parameter and the motor dynamic characteristic parameter into the state equation modeling formula to perform discrete time calculation to obtain a discrete time system state matrix.

3. The synchronous control method of a multi-axis servo system according to claim 1, characterized in that: The Z-transform processing is performed on the discrete-time system state matrix and the frequency response characteristics are calculated to obtain a transfer function matrix and a target coupling axis pair set, including: Performing a Z transform on the discrete-time system state matrix to obtain a frequency domain system equation; Calculating the transfer relationship between the output and the input based on the frequency domain system equation to obtain a transfer function matrix; According to the diagonal elements and non-diagonal elements of the transfer function matrix, the transfer characteristics of each servo axis itself and the inter-axis coupling transfer characteristics are identified to obtain the inter-axis coupling transfer relationship; According to the inter-axis coupling transfer relationship, the amplitude and phase of the transfer function matrix are calculated at different frequency points, and a frequency response curve of the inter-axis coupling is plotted; Calculate the coupling metric between any two servo axes according to the frequency response curve, evaluate the maximum interference influence ratio between axes, and obtain the coupling strength sequence between axes; Interference sensitive frequency point analysis is performed based on the inter-axis coupling strength sequence to determine a target coupling axis pair set.

4. The synchronous control method of a multi-axis servo system according to claim 1, characterized in that: The step of performing hierarchical optimization on the transfer function matrix and the target coupling axis pair set to obtain a preliminary control instruction includes: Based on the transfer function matrix, an upper-layer model predictive controller is constructed, a predictive state sequence and a predictive control sequence are defined, and a predictive state equation is obtained; According to the predicted state equation, a weighted function is constructed for the trajectory tracking error, the control input and the control change rate to obtain the upper optimization problem; Execute a solution calculation on the upper-level optimization problem, obtain the first control vector of the optimal control sequence, and obtain the output result of the upper-level controller; Based on the target coupled axis pair set, a synchronization error vector is defined, and the synchronization position error between each servo axis is calculated to obtain a synchronization error matrix; Constructing a lower-level optimization objective function according to the synchronization error matrix and the output result of the upper-level controller, performing a weighted calculation of the synchronization error on all key coupling axis pairs in the target coupling axis pair set, and obtaining a lower-level optimization problem; A solution operation is performed on the lower-level optimization problem, a synchronous control increment is calculated and the synchronous control increment is superimposed on the output result of the upper-level controller to obtain a preliminary control instruction.

5. The synchronous control method of a multi-axis servo system according to claim 1, characterized in that: The step of calculating the trajectory tracking error and the inter-axis synchronization error according to the preliminary control instruction and substituting them into the optimization objective function to perform sampling delay compensation processing to obtain the compensation control instruction includes: Calculating the absolute trajectory error of each servo axis according to the preliminary control instruction and the preset reference trajectory to obtain a trajectory tracking error sequence; The relative position difference between the axes is calculated based on the actual position and reference position of the adjacent servo axes, and the inter-axis synchronization error sequence is obtained; According to the control task type, an absolute trajectory accuracy optimization strategy and a relative synchronization accuracy optimization strategy are constructed, and weight coefficients are assigned to trajectory error and synchronization error to obtain a weight coefficient matrix; Applying the weight coefficient matrix to the trajectory tracking error sequence and the inter-axis synchronization error sequence, calculating the contour error index, the normal error and the tangential error, and obtaining a comprehensive error evaluation result; Based on the comprehensive error evaluation result, the position tracking error term and the synchronization error term are weighted respectively to obtain an optimization objective function that balances the absolute trajectory accuracy and the relative synchronization accuracy; Performing a solution calculation on the optimization objective function to obtain a target control vector; A sampling delay compensation process is performed on the target control vector to obtain a compensation control instruction.

6. The synchronous control method of a multi-axis servo system according to claim 5, characterized in that: The performing sampling delay compensation processing on the target control vector to obtain a compensation control instruction includes: Constructing a sampling delay compensator based on the discrete-time system state matrix, and performing model prediction calculation according to the sampling delay compensator to obtain predicted output data; Performing a difference operation on the actual system output and the predicted output data to obtain model correction data; Dynamically adjust the prediction time domain, control time domain and weight matrix parameters according to the model correction data and the system operation status to obtain adaptive control parameters; Performing multi-sampling cycle measurement on the multi-axis servo system, completing m state samplings within one control cycle, and obtaining target feedback information; Constructing a state observer according to the adaptive control parameters and the target feedback information, and performing observer gain matrix calculation according to the state observer using a pole placement algorithm to obtain a state estimation value; The target control vector is substituted into a prediction equation using the state estimation value and the adaptive control parameter to predict the system state in the next d sampling periods, thereby obtaining a compensation control instruction.

7. The synchronous control method of a multi-axis servo system according to claim 1, characterized in that: The method of executing real-time processing on the compensation control instruction and outputting a synchronous control signal to each servo axis to realize multi-axis coordinated motion includes: Converting the compensation control instruction into a standard quadratic programming form to obtain a control equation including a Hessian matrix and a linear term coefficient vector; Perform Cholesky decomposition and substitution algorithm calculation on the control equation to obtain a control solution result; Using a gradient projection method, a synchronous control increment that meets physical constraints is calculated according to the control solution result to obtain a final execution control signal; Performing multi-level parallel processing on the final execution control signal to obtain a parallel processing result, and dividing the control task execution priorities according to the parallel processing result to obtain a task execution strategy; Based on the task execution strategy, the final execution control signal is distributed and monitored in real time, and a synchronous control signal is output to each servo axis to realize multi-axis coordinated motion.

8. A synchronous control device for a multi-axis servo system, characterized in that: Used to execute the synchronous control method of a multi-axis servo system according to any one of claims 1 to 7, the synchronous control device of the multi-axis servo system comprises: The measurement module is used to measure the mechanical coupling relationship parameters, motor dynamic characteristic parameters and sampling delay time parameters of the multi-axis servo system and substitute them into the state equation modeling formula to calculate the discrete time system state matrix; A calculation module, used for performing Z-transform processing on the discrete-time system state matrix and calculating the frequency response characteristics to obtain a transfer function matrix and a target coupling axis pair set; A hierarchical optimization module, used for performing hierarchical optimization on the transfer function matrix and the target coupling axis pair set to obtain preliminary control instructions; A delay compensation module is used to calculate the trajectory tracking error and the inter-axis synchronization error according to the preliminary control instruction and substitute them into the optimization objective function to perform sampling delay compensation processing to obtain a compensation control instruction; The real-time processing module is used to execute real-time processing on the compensation control instruction and output a synchronous control signal to each servo axis to realize multi-axis coordinated motion.

9. A computer device, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a computer program executable on the processor, and the processor implements the synchronous control method of the multi-axis servo system according to any one of claims 1 to 7 when executing the computer program.

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