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

Abstract

The 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, and the method comprises the steps: measuring a mechanical coupling relation parameter, a motor dynamic characteristic parameter and a sampling delay time parameter of the multi-axis servo system, and substituting the parameters into a state equation modeling formula, calculating to obtain a discrete time system state matrix; performing Z transformation processing on the discrete time system state matrix and calculating frequency response characteristics to obtain a transfer function matrix and a target coupling axis pair set; executing hierarchical optimization to obtain a preliminary control instruction; a trajectory tracking error and an inter-axis synchronization error are calculated and substituted into the optimization objective function for sampling delay compensation processing, and a compensation control instruction is obtained; the compensation control instruction is processed in real time, synchronous control signals are output to the servo shafts to achieve multi-shaft coordinated movement, and the synchronous control precision in the multi-shaft servo system is improved by accurately recognizing the key coupling shaft pairs and the 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] Multi-axis servo systems generally have problems with inter-axis synchronization errors and mechanical vibration in high-precision motion control. Compared with single-axis systems, multi-axis systems face more complex control challenges because interference on one axis will propagate to other coordinated axes through the mechanical structure and control system, forming systematic vibrations, thereby reducing processing accuracy and equipment life.

[0003] The difference between the sampling period and the control period in digital control systems poses a severe challenge to the modeling of multi-axis servo systems. Traditional control methods usually ignore the influence of sampling delay, resulting in significant deviations between the model and the actual system, making it difficult for the inter-axis synchronization control performance to meet high-precision requirements. In addition, although the 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 fully 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. The present invention improves the synchronous control accuracy in the multi-axis servo system by accurately identifying key coupling axis pairs and sensitive frequency points.

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

[0006] In a second aspect, the present invention provides a synchronous control device for a multi-axis servo system, the synchronous control device for the multi-axis servo system comprising: 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.

[0007] The third aspect of the present invention provides a computer device, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor calls the instructions in the memory so that the computer device executes the above-mentioned synchronous control method of the multi-axis servo system.

[0008] In the technical solution provided by the present invention, the present invention establishes a generalized state space model of a multi-axis servo system taking into account sampling delay, comprehensively describes the influence of the mechanical coupling relationship between axes and the 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 the 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, and enables system designers to intuitively evaluate the synchronization characteristics between axes through classical control tools, and accurately identify key coupling axis pairs and sensitive frequency points. The hierarchical control structure is used to separate trajectory planning and synchronization optimization, effectively separate the goals of trajectory tracking and synchronization control, avoid the difficulty of weight selection in traditional single-layer control, and provide flexible control strategy selection for different application scenarios. An optimization objective function that comprehensively considers trajectory error and synchronization error is designed, dynamically balances 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 Smith predictor principle, 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 synchronization control accuracy in the multi-axis servo system. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying any creative work.

[0010] Figure 1 A schematic diagram of the steps of a synchronous control method for a multi-axis servo system according to an embodiment of the present invention; Figure 2 Schematic diagram of the structure of a synchronous control device for a multi-axis servo system according to an embodiment of the present invention; Figure 3 It is a schematic block diagram of the structure of a computer device in an embodiment of the present invention. DETAILED DESCRIPTION

[0011] Embodiments of the present invention provide a method, device and equipment for synchronous control of a multi-axis servo system. The terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0012] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 , an embodiment of the synchronous control method of the multi-axis servo system in the embodiment of the present invention includes: Step S1, 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; It is understandable that the execution subject of the present invention may be a synchronous control device of a multi-axis servo system, or a terminal or a server, which is not limited here. The embodiment of the present invention is described by taking a server as the execution subject as an example.

[0013] Specifically, for the servo system The basic data collection and key parameter measurement of each servo axis are carried out separately. Through high-precision sensors or internal encoders of the controller, the state of each servo axis during operation is collected in real time to obtain its state variables such as position, speed and acceleration, and the state vector of the system is constructed accordingly. ,in Indicates The complete status information of each 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 ,in For the The control instructions of the servo axis at the current moment; and the actual output displacement of the servo axis is measured by the feedback device to construct the system output vector ,in Indicates The real-time position signal of each servo axis. At the same time, in order 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 controller collecting the signal to the drive response is evaluated. This delay is detected and recorded by a high-resolution time synchronization system to form a sampling delay time parameter matrix diag ,in Indicates The sampling delay time of each servo axis is used to reflect the effect of sampling delay on 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 the servo axes. The actual parameters of the coupling stiffness and damping between axes are obtained by vibration measurement, frequency response function analysis or finite element simulation, and the stiffness matrix is ​​constructed accordingly. and the damping matrix ,in Indicates Axis and The rigid coupling coefficient between the axes, Represents the damping coefficient between the two. This part of the parameters is used to accurately model the dynamic interaction between the axes. After completing the mechanical structure modeling, perform parameter identification on each servo motor to obtain the dynamic characteristics of the motor. Use step response testing, frequency domain identification or system identification algorithms to obtain the key parameters of the motor, including the torque constant , moment of inertia and friction coefficient , and integrate these parameters into the motor torque constant matrix , motor inertia matrix , friction coefficient matrix , thus providing electromagnetic and mechanical dynamics support for state modeling. , control input vector , system output vector , sampling delay time parameters , Mechanical coupling relationship parameters And motor dynamic characteristic parameters Substitute all of them into the generalized state space model based on the principle of mechanical dynamics to form a complete continuous-time state equation: , ,in is the system matrix including coupled stiffness and damping effects, represents the effect of control input on the state, is the external disturbance term. By discretizing the continuous-time model, combining the control period and sampling delay term, and applying Z transform, the discrete-time state equation is obtained as follows: , ,in are the system matrix, control matrix and output matrix in discrete time respectively, is the discrete form of the sampling delay.

[0014] Step S2, 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; Specifically, the discrete time system state matrix is ​​Z-transformed, and the time domain state equation is converted into a frequency domain system expression, so that the system state vector, control input vector and system output vector are uniformly represented in the complex frequency domain. Through this Z-transformation, 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. The transfer function matrix of the system is derived according to the functional relationship between the state variable and the control input in the frequency domain system equation. The transfer function matrix reflects the overall mapping relationship between the control input of each servo axis and the output response, in which the elements on the diagonal are used to characterize the body 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 disturbed by the dynamic behavior of other servo axes, thereby establishing an inter-axis coupling transfer model. According to the inter-axis coupling transfer relationship, a series of frequency points are selected within the predetermined frequency range, substituted into the frequency domain function model expressed by the transfer function matrix, and the amplitude and phase of the transfer function at each frequency point are calculated point by point. In this way, the response strength 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. These curves graphically present the distribution of the coupling path in the entire frequency domain. According to the frequency response curve, the coupling metric between any two servo axes is calculated, and the frequency response amplitude of a non-diagonal coupling path is calculated by the ratio of the amplitude of the corresponding servo axis's own response. The maximum value in the entire frequency range is taken as the maximum impact ratio of the inter-axis interference, which fully captures the most extreme interference scenario between a pair of servo axes, thereby accurately describing the relative coupling strength between axes. The coupling metric of all servo axis pairs in the system are sorted by size to form an inter-axis coupling strength sequence, which reflects the distribution of the dominant coupling path and the weak coupling path in the system. Based on the inter-axis coupling strength sequence, interference sensitive frequency point analysis is performed to identify the servo axis pairs whose coupling metric reaches the peak at a specific frequency. 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 target coupling axis pair set is constructed as the focus of subsequent synchronous controller design and optimization.

[0015] Step S3, performing hierarchical optimization on the transfer function matrix and the target coupling axis pair set to obtain preliminary control instructions; Specifically, based on the transfer function matrix, an upper-level model predictive controller is constructed. The upper-level controller predicts the state and target trajectory of the system and optimizes the control signal in 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 state of each servo axis in the future, and the predicted control sequence describes the control signal required to achieve the target state. The calculation basis of these sequences is the predicted state equation, which deduces the change of future state by considering the system state and control input at the current moment. Through the predicted state equation, the control system adjusts the control input to minimize the trajectory tracking error and achieve the desired system response during the optimization process. According to the predicted state equation, a weighted function is constructed for the trajectory tracking error, control input and control change rate, so as to balance the weights between different objectives during the optimization process, such as trajectory tracking accuracy, control input amplitude and smoothness of control input change. Through the construction of the weighted function, the upper-level optimization problem is clarified and the optimization target is provided for the subsequent optimization algorithm. The solution of the upper-level optimization problem is carried out by an optimization algorithm (such as quadratic programming, gradient descent, etc.), and the optimal control sequence is obtained, in which the first control vector is the output result of the upper-level controller. At the same time, the design of the lower-level synchronization optimization controller is based on the target coupling axis pair set to optimize the inter-axis synchronization performance of the system. The core of synchronization control is to ensure the coordinated work of each servo axis in the multi-axis system and to ensure that the synchronization error between them is minimized. In order 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 difference in relative position between different axes and are key indicators for evaluating synchronization performance. By integrating the error calculation results into a synchronization error matrix, the distribution of synchronization errors between axes at different time steps is presented. After the synchronization error matrix is ​​formed, the lower-level optimization controller optimizes the control signal according to the results output by the upper-level controller to ensure that the synchronization performance between the servo axes of the multi-axis system is effectively improved. The lower-level optimization controller constructs a weighted objective function of synchronization error. This objective function weights the synchronization error of each target coupling axis pair, where the weight reflects the different coupling strengths between the axis pairs, and optimizes all key coupling axis pairs based on the weighted error. In this process, the synchronization error of the key coupling axis pair has a greater impact on the lower-level optimization, so weighted measures are used for key optimization to ensure that the calculation of the synchronization control increment is more accurate and achieve better system synchronization effect. The result of solving the lower optimization problem is the synchronous control increment, which reflects the necessity of adjusting the system state. The calculated synchronous control increment is superimposed on the output result of the upper controller to obtain the final preliminary control instruction. This preliminary control instruction will combine 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 hierarchical optimization control strategy, the upper-level controller ensures the accuracy of the system's tracking trajectory, while the lower-level 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.

[0016] 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 to perform sampling delay compensation processing to obtain the compensation control instruction; 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. The control signal of each servo axis generated according to the preliminary control instruction is compared with the preset reference trajectory to obtain the error between the actual position and the reference position of each servo axis at each moment. Through these errors, the 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 position 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 position and the reference position of adjacent servo axes. By comparing the position information of each pair of servo axes at the same time, the difference in relative position between the axes, that is, the inter-axis synchronization error sequence, is obtained, reflecting the relative motion state between each servo axis. According to the control task type, the absolute trajectory accuracy optimization strategy and the 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, aiming 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. In order to effectively balance these two optimization requirements, weight coefficients are assigned to trajectory error and 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 indicators such as contour error, normal error and tangential error. Contour error is used to evaluate whether the system can maintain the correct path trajectory in multi-axis motion, normal error is used to measure whether the system deviates from the normal direction of the target path during motion, and tangential error reflects the degree of deviation of the system along the target trajectory. Through the evaluation of these comprehensive error indicators, the position tracking error term and the synchronization error term are weighted respectively to obtain an optimization objective function that balances absolute trajectory accuracy and relative synchronization accuracy. By solving and calculating the optimization objective function, the target control vector is obtained, which contains the optimal control signal required by the system, ensuring that the system minimizes the error as much as possible during the control process and meets the requirements of trajectory tracking accuracy and inter-axis synchronization accuracy. Since there is sampling delay in the real-time execution of the digital control system, the target control vector is subjected to sampling delay compensation. In order to compensate for the error caused by sampling delay, a sampling delay compensation algorithm is introduced. The algorithm dynamically adjusts the control signal according to the sampling period and delay characteristics of the system to obtain the compensation control instruction.

[0017] A sampling delay compensator is constructed based on the discrete time system state matrix. The compensator models the effect of sampling delay on 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 effect of sampling delay in the system model. Based on the sampling delay compensator, the model prediction calculation is performed according to the compensator to obtain the predicted output data, which represents the expected output of the system after sampling delay compensation under given control input and system state. The difference operation is performed on the actual system output and the predicted output data to obtain the model correction data, that is, the error between the actual system output and the predicted output, reflecting the deviation between the model prediction and the actual system behavior. The prediction time domain, control time domain 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 time domain determines the time range of the predicted output data, the control time domain determines the optimal time window of the control input, and the weight matrix parameters adjust the degree of influence of different error terms during the optimization process. By dynamically adjusting these parameters, the system can respond quickly to environmental changes and control task requirements, thereby optimizing the overall control performance. After completing the above parameter adjustment, perform multi-sampling cycle measurement to obtain feedback information with a higher frequency. Complete m state samplings in one control cycle, significantly improving the timeliness and accuracy of feedback information. Through multi-sampling technology, more state information is obtained in each control cycle, thereby more accurately predicting the future dynamic behavior of the system and reducing the impact caused by sampling delay and incomplete feedback. Based on adaptive control parameters and target feedback information, a state observer is constructed. The state observer estimates the current state of the system based on 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. In the process of constructing 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 converge quickly within a certain time, ensuring the accuracy and stability of the state estimation. The state estimation value is obtained by calculating the observer gain matrix. The state estimation value is combined with the adaptive control parameters to improve the control effect, especially in the face of sampling delay and incomplete observation information, which can effectively reduce the control error and improve the stability and accuracy of the control system. Using the state estimation value and adaptive control parameters, the target control vector is substituted into the prediction equation to predict the system state in the next d sampling cycles. The prediction process provides a basis for the generation of compensation control instructions by considering the dynamic characteristics of the system and the adjustment of the prediction time domain and the control time domain. In this way, the system can effectively compensate for the sampling delay within the control cycle, ensuring that the control process is always in the optimal state, thereby obtaining the final compensation control instruction.

[0018] Step S5: Process the compensation control instruction in real time and output a synchronous control signal to each servo axis to achieve multi-axis coordinated motion.

[0019] Specifically, the compensation control instructions are mathematically transformed into the standard quadratic programming form, and the control optimization problem is formalized in the form of a mathematical optimization model, so that it has the characteristics of clear solution structure and can be executed by efficient algorithms. During the conversion process, the control problem is rewritten as a standard quadratic objective function with control increment as a variable, which contains a positive Hessian matrix and a linear term coefficient vector. The Hessian matrix is ​​used to describe the second-order relationship between control variables. 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 the objective function is quickly solved with the help of matrix operation techniques such as forward substitution and backward substitution. Cholesky decomposition is applicable to positive definite symmetric matrices. It has high computational efficiency and strong numerical stability, and is suitable for optimization tasks that need to be completed in milliseconds in real-time control. Through this decomposition method, complex matrix operations are simplified into a series of steps that can be recursively calculated, which improves 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 in the current state. Considering that there are physical constraints such as driving voltage, current, speed and acceleration in the actual servo system, the gradient projection method is introduced on this basis to correct the control solution result. The gradient projection method adjusts the control vector obtained initially to the range that satisfies all physical constraints by performing projection operations on the feasible domain of the control variable, 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 variable along the gradient direction until the variable meets all constraints, and projects it to the boundary of the feasible domain to form a synchronous control increment that satisfies the constraints and is as close to the optimal solution as possible. After the control increment is superimposed, the final executable control signal is formed to drive the servo axis to perform precise actions. In order to ensure that the above control signals have efficient and real-time consistency in the multi-axis system, the final execution control signal is processed in parallel at multiple levels. 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 in each group, and multi-core computing resources are further used to perform data-level parallel acceleration for intensive operations such as control matrix operations and incremental updates. After the parallel processing is completed, in order to reasonably arrange the system resource usage of various calculation and execution tasks, the control task execution priority is divided based on the processing results. The priority setting is based on the degree of influence of each task on the system performance. Among them, key tasks such as state estimation and control output are given higher priority, while delayed tasks such as parameter update and model reconstruction are set to low priority.According to the result of this priority division, a task execution strategy is formulated to ensure the stable operation of the key control chain under the conditions of tight resources or limited computing time. The final execution control signal is distributed and monitored in real time based on the task execution strategy. All calculated final execution control signals are distributed 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 the control signal according to the current state and execution load of each servo axis, and monitors the execution process of the signal in real time to prevent control deviation or synchronization failure caused by signal delay, inter-axis interference or abnormal state, and finally achieves the system-level multi-axis synchronous control goal.

[0020] In the embodiment of the present invention, the present invention establishes a generalized state space model of a multi-axis servo system considering sampling delay, comprehensively describes the influence of the mechanical coupling relationship between axes and the 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 the 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, and enables system designers to intuitively evaluate the synchronization characteristics between axes through classical control tools, and accurately identify key coupling axis pairs and sensitive frequency points. The hierarchical control structure is used to separate trajectory planning and synchronization optimization, effectively separate the goals of trajectory tracking and synchronization control, avoid the difficulty of weight selection in traditional single-layer control, and provide flexible control strategy selection for different application scenarios. An optimization objective function that comprehensively considers trajectory error and synchronization error is designed, dynamically balances 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 Smith predictor principle, 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 synchronization control accuracy in the multi-axis servo system.

[0021] In a specific embodiment, the process of executing step S1 may specifically include the following steps: 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, which is the time difference between the acquisition and execution of each servo axis signal; 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 the servo axes; Perform parameter identification on each servo motor in the multi-axis servo system to obtain the motor dynamic characteristic parameters, which include motor torque constant, moment of inertia and friction coefficient; Substitute the system state vector, control input vector, system output vector, sampling delay time parameters, mechanical coupling relationship parameters and motor dynamic characteristic parameters into the state equation modeling formula to perform discrete time calculation and obtain the discrete time system state matrix.

[0022] Specifically, the parameters of each servo axis in the system are measured. For a servo system with multiple degrees of freedom, such as a multi-axis linkage CNC workbench, it is assumed that it contains multiple independent but mutually coupled servo axes, and the state information of each servo axis during operation is collected in turn, including position, speed, acceleration, etc. This information is collected by high-precision encoders, speed sensors, and acceleration sensors, where the encoder directly feedbacks the position, the speed can be obtained by differential position signals, and the acceleration is obtained by the acceleration sensor or by differential velocity signals. 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, including current, voltage or speed setting values, are recorded, and are generated in real time by the upper controller according to the control algorithm and transmitted to the driver. The control input is organized to form a control input vector, which is combined with the actual motion response data obtained by system feedback and organized into a system output vector. In order 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 the control process is executed by cascading multiple modules. Due to differences in calculation cycles, communication delays, and the internal response time of the driver, the system has a time difference from collecting input signals to executing control outputs. 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 control command being issued 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 especially obvious in application scenarios with heavy workloads or continuous path switching. In order to quantify the impact of these mechanical connections, a mechanical excitation experiment is conducted on the system, such as applying periodic disturbances through an exciter, and disposing displacement or acceleration sensors on other axes to measure their response size and delay. 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 X and Y coupling terms are set to non-zero values ​​in the system modeling. Parameter identification is performed for each servo motor. The dynamic characteristics of the motor have a decisive influence on the control behavior of the entire servo system, which mainly include the torque constant, moment of inertia and friction coefficient of the motor. The motor torque constant describes the linear relationship between the input current and the output torque; the moment of inertia determines the acceleration of the motor at a given torque; and the friction coefficient reflects the torque required for the motor to overcome internal and external friction during operation. Parameter identification methods include step response method and frequency scanning method.All the parameter data obtained above, including the system state vector, control input vector, system output vector, sampling delay time parameters, mechanical coupling relationship parameters and motor dynamic characteristic parameters, are substituted into the pre-established state equation modeling formula, and numerically processed in combination with the discretization strategy to obtain the discrete-time system state matrix.

[0023] In a specific embodiment, the process of executing step S2 may specifically include the following steps: Perform Z-transform on the discrete-time system state matrix to obtain the frequency-domain system equation; The transfer relationship between output and input is calculated based on the frequency domain system equation to obtain the 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, and the inter-axis coupling transfer relationship is obtained; According to the inter-axis coupling transfer relationship, the amplitude and phase of the transfer function matrix are calculated at different frequency points, and the frequency response curve of the inter-axis coupling is drawn; Calculate the coupling metric between any two servo axes based on the frequency response curve, evaluate the maximum interference impact 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 the target coupling axis pair set.

[0024] Specifically, starting from the discrete time state matrix after system modeling, the Z transform is used to transform 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 expresses the time evolution process in the discrete time system state equation as an algebraic relationship in the complex domain, thereby significantly simplifying the complexity of the system response analysis. In actual operation, after the discrete state matrix is ​​processed by the Z transform, the original system equation involving time advancement is rewritten as an algebraic equation about complex frequency variables, namely 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, which is used to express how the system's output will respond when facing a specific frequency input. In a multi-axis servo system, each servo axis is affected by both its own control input and the indirect interference transmitted by 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 the 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 non-diagonal elements characterize the coupling influence relationship between different servo axes. The transfer function matrix is ​​analyzed to identify the coupling transfer relationship between the servo axes in the system. If the value of a non-diagonal element is obviously not zero, and its amplitude fluctuates significantly with frequency, it means that there is a significant dynamic coupling effect between the servo axis and its corresponding input. The transfer function on the diagonal is used as a benchmark to measure the degree of interference 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 transfer function on the non-diagonal line. If the non-diagonal element shows obvious response amplitude in multiple frequency bands, it is preliminarily judged that there is a strong coupling relationship between the X-axis and the Y-axis. The response characteristics of the transfer function matrix are calculated at multiple frequency points. A frequency scanning interval is selected to cover all working frequency bands encountered by the system, and the amplitude and phase of the transfer function are calculated at each frequency point. These calculation results are used to draw the frequency response curve of the inter-axis coupling. The amplitude response curve shows the response strength 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 the output. Through these response curves, it is possible to identify which frequency ranges are the areas where the coupling effect is most significant, thereby providing a basis for frequency selection for subsequent controller design. The coupling metric between any two servo axes is calculated based on the frequency response curve. This metric is defined as the ratio between the maximum amplitude of a non-diagonal transfer function and the maximum amplitude of its corresponding diagonal transfer function, which is used to reflect the maximum interference effect ratio of other axis inputs on the current axis output.The larger the index is, the stronger the interference effect of the coupling path is, and it needs to be given priority in the control process. All possible axis pairs are sorted from high to low according to the coupling metric index to form an inter-axis coupling strength sequence. Based on the coupling strength sequence, the frequency sensitivity analysis of the key coupling path is performed to identify at which frequency the system is most susceptible to interference, posing a threat to the control performance. Combining the coupling metric with the frequency response curve, the frequency band of each pair of strongly coupled axes is identified to determine its coupling peak frequency within the entire operating frequency range. These frequency points are the locations where vibration amplification, error transmission or synchronization misalignment are most likely to occur during system operation, so corresponding filters or predictive compensation mechanisms are introduced into the control strategy to deal with them. All axis pairs confirmed by the interference sensitivity analysis constitute the target coupling axis pair set. This set is the focus of attention in the design process of the system synchronous controller, and is also the optimization variable of the lower-level synchronous optimization controller in the subsequent hierarchical control structure.

[0025] In a specific embodiment, the process of executing step S3 may specifically include the following steps: Based on the transfer function matrix, an upper-level 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, control input and control change rate to obtain the upper optimization problem; Perform 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; The lower-level optimization objective function is constructed according to the synchronization error matrix and the output result of the upper-level controller, and the synchronization error weighted calculation is performed on all the key coupling axis pairs in the target coupling axis pair set to obtain the lower-level optimization problem; The solution operation is performed on the lower optimization problem, the synchronous control increment is calculated and superimposed on the synchronous control increment on the output result of the upper controller to obtain the preliminary control instruction.

[0026] Specifically, a hierarchical control structure consisting of upper and lower layers is constructed, in which the upper layer is responsible for trajectory tracking optimization, and the lower layer focuses on the dynamic adjustment of inter-axis synchronization performance. Based on the system transfer function matrix, this control method establishes a model predictive controller covering the global motion state prediction, and constructs the target optimization function in combination with the system coupling characteristics, so as to achieve fine control of the coordinated motion between each servo axis. Based on the transfer function matrix obtained by Z transform in the early stage, a prediction model is constructed. The 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 axes. When constructing the upper model predictive controller, the predicted state sequence and predicted control sequence are defined according to the state transition characteristics contained in the transfer function matrix and the input-output relationship of the system. The predicted state sequence refers to the state trajectory that the system may reach in several future prediction steps at the current sampling time, while the predicted control sequence represents the optimization path of the system input variables in the control time domain. The two together constitute the basic framework of the predicted state equation. The establishment of the predicted state equation aims to recursively infer 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. The prediction result is used as a prerequisite for the optimization solution. On this basis, in order to achieve fine control of the system's 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 takes the predicted state equation as a constraint, and forms the upper-level control objective function by introducing three key weighted functions: trajectory error weight, control signal strength weight, and control change smoothness weight. The design of each weight is weighed and configured in combination with the actual application scenario. By constructing and solving the upper-level optimization problem, a set of optimal control input sequences is obtained, where the first control input is the optimal control signal to be applied in the current sampling period, which constitutes the output result of the upper-level controller. Based on the output of the upper-level controller, the lower-level 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 between the two axes and the reference trajectory difference, indicating whether the two axes maintain the proper synchronization state in actual operation. The synchronization errors corresponding to all target coupled axis pairs are organized into a synchronization error matrix, and the synchronization performance of the multi-axis system is modeled on a global scale. The synchronization error matrix is ​​combined with the output results of the upper-level controller to construct the lower-level optimization control objective function. This objective function penalizes the error between the target coupled axis pairs by introducing a weighted term of the synchronization error without destroying the original trajectory tracking performance. The setting of the weighted coefficient is proportional to the coupling strength between the axes, that is, the stronger the coupling of the axis pair, the greater the weight of its synchronization error in the objective function, so as to guide the optimization algorithm to preferentially eliminate the synchronization mismatch phenomenon on the strong coupling path.After the lower optimization problem is constructed, the objective function is iteratively calculated through the corresponding solution algorithm, such as the gradient method, quadratic programming method or constrained optimization method, to obtain the synchronous control increment. The synchronous control increment is a further refinement of the output of the upper controller, representing the additional correction signal required to achieve inter-axis synchronization. This increment is superimposed on the output of the upper controller in the form of software to form a complete control instruction for controlling the actuator. This superposition process ensures the hierarchy and target separation of the control structure, that is, the upper layer focuses on global path accuracy, and the lower layer handles local synchronization and coordination, and the two work together without interfering with each other. The preliminary control instructions are formed through the hierarchical structure.

[0027] In a specific embodiment, the process of executing step S4 may specifically include the following steps: The absolute trajectory error of each servo axis is calculated according to the preliminary control instruction and the preset reference trajectory to obtain the 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; Apply the weight coefficient matrix to the trajectory tracking error sequence and the inter-axis synchronization error sequence, calculate the contour error index, normal error and tangential error, and obtain the comprehensive error evaluation result; Based on the comprehensive error evaluation results, the position tracking error term and the synchronization error term are weighted respectively to obtain the optimization objective function that balances the absolute trajectory accuracy and relative synchronization accuracy. Perform solution calculation on the optimization objective function to obtain the target control vector; A sampling delay compensation process is performed on the target control vector to obtain a compensation control instruction.

[0028] Specifically, the absolute trajectory error of each servo axis is calculated based on the difference between the preliminary control instruction and the pre-defined reference trajectory. 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. The error is obtained by comparing the difference between the actual position and the target position at each sampling point, and is organized into a trajectory tracking error sequence in chronological order. After obtaining the trajectory error sequence to evaluate the coordination degree between the servo axes, 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 the error, the actual position value of the adjacent axis at the current moment and the relative difference that should be maintained under the reference trajectory are obtained, and the synchronization deviation between each axis pair is derived based on this. The absolute trajectory accuracy optimization strategy and the relative synchronization accuracy optimization strategy are constructed according to the control task type. 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 collaboration, the relative synchronization accuracy optimization strategy is adopted. On the basis of these two strategies, appropriate weight coefficients are assigned to each error, and the weights are uniformly constructed into a weight coefficient matrix, so that different error terms are given mathematical meanings to match their task importance in subsequent optimization. Based on the trajectory error sequence and synchronization error sequence, and combined with the set weight coefficient matrix, the comprehensive error indicators of the system are calculated, including contour error, normal error and tangential error. Contour error is the core indicator for evaluating whether the multi-axis trajectory remains coherent on the spatial path, which represents the shortest distance between the actual trajectory point and the ideal trajectory path; normal error reflects the degree of deviation of the system motion trajectory in the direction perpendicular to the reference path, while tangential error describes the advance and retreat deviation of the system along the path direction. These three error dimensions constitute the error evaluation benchmark of the multi-axis servo system in spatial control, which can more comprehensively reveal the geometric properties of the system operation deviation. Based on the comprehensive error evaluation results, the position tracking error term and the synchronization error term are weighted respectively to construct an optimization objective function that balances the absolute trajectory accuracy and relative synchronization accuracy. By setting appropriate weighting factors in the objective function, it is ensured that the synchronization error between key axes is suppressed while meeting the overall motion accuracy, and system-level collaborative control is achieved. The optimization objective function is solved and calculated 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. In order to ensure the efficiency and accuracy of the solution, quadratic programming, gradient method or predictive control algorithm is used for iterative optimization, and the current state variables and historical control data are combined to quickly converge to the global or local optimal solution. The first element in the vector is the actual control signal at the current moment, and the rest are preparatory inputs for multiple cycles in the future. 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 building 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 in several milliseconds, and adjust the current control strategy accordingly, thereby ensuring that the final output compensation control instruction is at the best moment in the actual system response.

[0029] In a specific embodiment, the execution step performs sampling delay compensation processing on the target control vector to obtain a compensation control instruction, which may specifically include the following steps: A sampling delay compensator is constructed based on a discrete time system state matrix, and a model prediction calculation is performed according to the sampling delay compensator to obtain predicted output data; Perform difference calculation on actual system output and 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 system operation status to obtain adaptive control parameters; Perform multi-sampling cycle measurement on the multi-axis servo system, complete m state samplings in one control cycle, and obtain target feedback information; A state observer is constructed according to the adaptive control parameters and the target feedback information, and a pole placement algorithm is used to perform observer gain matrix calculation according to the state observer to obtain a state estimation value; Using the state estimation value and adaptive control parameters, the target control vector is substituted into the prediction equation to predict the system state in the next d sampling periods and obtain the compensation control instruction.

[0030] Specifically, a sampling delay compensator is constructed based on the discrete time system state matrix. The compensator is based on the discrete time state space model established in the early stage, integrates the mapping relationship between the system dynamic characteristics, the control input and the state response, and introduces the sampling delay parameter in the structure, so that it can predict the system response trend in a certain time period in the future before the control instruction is issued. Through the compensator, the system state after several sampling cycles in the future is estimated in advance in the current control cycle, thereby offsetting the response lag caused by the control delay. The model prediction calculation is performed according to the internal state update mechanism of the delay compensator and the control input to obtain the corresponding predicted output data. The actual system output and the predicted output data are differenced to obtain the deviation degree of the current model under the actual operating state, and the difference is the model correction data. This data reflects the model prediction deviation caused by factors such as inaccurate modeling, nonlinear disturbance of the system or environmental changes. Based on the model correction data and combined with the current system operating state, the core control parameters in the model predictive controller are dynamically adjusted, including the prediction time domain, the control time domain and the weight matrix. The prediction time domain determines how many steps the controller considers in the future period, the control time domain limits the optimization step of the control input within the current controllable range, and the weight matrix determines the optimization priority of each performance indicator in the objective function. By adjusting these parameters in real time, the controller can achieve a dynamic trade-off between accuracy, response speed and control cost under different working conditions. A multi-sampling cycle measurement strategy is introduced at the sampling mechanism level, that is, multiple sampling of the system state is performed within a control cycle to obtain high-frequency feedback information. By increasing the sampling frequency, the subtle changes in the system state can be captured more carefully, and the state variables used in the prediction model can be updated in real time to improve the accuracy of the prediction results. After obtaining the target feedback information generated by multiple samplings, the aforementioned adaptive control parameters are combined to construct a state observer to improve the system's estimation accuracy of 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 infer the complete internal state vector of the system. In this observer, the observer gain matrix is ​​the key parameter that determines 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 pole, and sets the pole in a region that meets the stability requirements and has fast response capabilities. Using the state estimation value and adaptive control parameters, the target control vector is substituted into the prediction equation to predict the system state evolution trajectory for the next d sampling periods. By predicting the dynamic behavior of the system in the delay time period in advance, the future state feedback is incorporated into the controller decision in advance to achieve advance control.Based on the prediction results, the current control output is corrected so that when it reaches the execution end, it just fills the time gap between sampling and execution, so that the control signal can still play a timely and effective role in regulating the system in the presence of physical delays.

[0031] In a specific embodiment, the process of executing step S5 may specifically include the following steps: The compensation control instructions are converted into a standard quadratic programming form to obtain a control equation containing a Hessian matrix and a linear term coefficient vector; Perform Cholesky decomposition and substitution algorithm calculation on the control equation to obtain the control solution; The gradient projection method is used to calculate the synchronous control increment that meets the physical constraints according to the control solution results to obtain the final execution control signal; Perform multi-level parallel processing on the final execution control signal to obtain parallel processing results, and divide the control task execution priorities according to the parallel processing results to obtain the 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 achieve multi-axis coordinated motion.

[0032] Specifically, the control objectives, system dynamic constraints, physical limitations and error weight parameters contained in the compensation control instructions are rearranged 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, and has good solution stability and physical interpretation. 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 characterize the second-order sensitivity of the control variable to the objective function. The term is expressed as a Hessian matrix with the property of symmetric positive definiteness, ensuring that the optimization problem has a unique optimal solution; while the coefficient vector of the first-order term is used to represent the linear sensitivity of the control variable in the objective function. Through this conversion process, the compensation control instruction is mapped into a standard form of quadratic programming control equation. After obtaining the standard form of the control equation, in order to efficiently solve this structured optimization model, a linear algebra method suitable for quadratic form solution is used. The Cholesky decomposition is used in conjunction with the forward and backward substitution algorithm to solve the control matrix. Cholesky decomposition is an efficient and numerically stable matrix decomposition technology suitable for fast decomposition of symmetric positive definite matrices. By decomposing the Hessian matrix into the product of the lower triangular matrix and its transposed matrix, the quadratic optimization problem is transformed into the solution process of two linear equations, simplifying the computational complexity and being suitable for real-time systems with strict control cycle requirements. After the decomposition is completed, the intermediate variables and the final control variables are solved in turn by the forward substitution and backward substitution algorithms to obtain the optimal control solution results in the current cycle. In actual systems, the control signal needs to meet a series of physical constraints, including maximum current, voltage limit, speed limit, acceleration boundary and torque load. These constraints are jointly determined by motor parameters, drive capabilities and mechanical structure. If the control signal is not directly issued without constraint processing, it will cause the actuator to exceed the limit, oscillate or even be damaged. Therefore, based on the solution results, the gradient projection method is introduced to correct the control variables within the constraint domain. The gradient projection method calculates the direction of the fastest descent in the control increment space and projects the variables in this direction onto the boundary of the feasible domain of physical constraints to ensure that the final control result is both close to the optimal and meets the actual limitations of the system, and obtains the final execution control signal. The final execution control signal is processed in multi-level parallel to improve the processing speed of the control signal and the efficiency of task allocation, and obtain parallel processing results. The control tasks of multiple servo axes are executed in groups, and the signal generation, state estimation and command scheduling operations of each group of axes are independently operated by using the multi-core computing platform or the multi-threading mechanism in the embedded real-time processor, so as to complete the control tasks of multiple axes in one control cycle. The control task execution priority is divided according to the parallel processing results to form a task execution strategy.Priority setting is based on quantitative analysis of the impact of tasks on system stability, response speed and key indicators. For example, system status update, error feedback and control increment calculation are given high priority, while non-real-time tasks such as parameter recording and log saving are deferred. In real-time systems, the order of task execution is dynamically adjusted through mechanisms based on event triggering or time slice scheduling to ensure that critical control paths are executed first in all cycles. The final execution control signal is allocated and monitored in real time based on the task execution strategy. Real-time allocation means that according to the task scheduling results, the control signal is sent to each servo axis drive module at a precise timing, and the drive status feedback is read in real time to confirm the execution of the command. Execution monitoring includes signal sending result comparison, fault identification, synchronization error tracking, etc., to ensure that the control instructions are accurately executed in each servo loop.

[0033] The above describes the synchronous control method of the multi-axis servo system in the embodiment of the present invention. The following describes the synchronous control device of the multi-axis servo system in the embodiment of the present invention. Figure 2 , an embodiment of a synchronous control device for a multi-axis servo system in an embodiment of the present invention 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 is used 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 target coupling axis pair set; A hierarchical optimization module is used to perform hierarchical optimization on a transfer function matrix and a set of target coupling axis pairs 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 of the compensation control instructions and output synchronous control signals to each servo axis to realize multi-axis coordinated motion.

[0034] Through the synergy of the above-mentioned components, the present invention establishes a generalized state space model of a multi-axis servo system taking into account sampling delay, comprehensively describes the influence of the mechanical coupling relationship between axes and the 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 the 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, and enables system designers to intuitively evaluate the synchronization characteristics between axes through classical control tools, and accurately identify key coupling axis pairs and sensitive frequency points. The hierarchical control structure is used to separate trajectory planning and synchronization optimization, effectively separate the goals of trajectory tracking and synchronization control, avoid the difficulty of weight selection in traditional single-layer control, and provide flexible control strategy selection for different application scenarios. An optimization objective function that comprehensively considers trajectory error and synchronization error is designed, dynamically balances 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 Smith predictor principle, 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 synchronization control accuracy in the multi-axis servo system.

[0035] Reference Figure 3 In an embodiment of the present invention, a computer device is also provided. The computer device may be a server, and its internal structure may be as follows: Figure 3 As 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 designed by the computer 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 the 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.

[0036] Those skilled in the art will understand that Figure 3 The structure shown in the figure is merely a block diagram of a portion 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.

[0037] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems, systems and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0038] If 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 this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the whole 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, including several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program code.

[0039] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the 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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