Cooperative control and disturbance suppression method for multi-axis servo system

Abstract

The invention discloses a cooperative control and disturbance suppression method for a multi-axis servo system, and relates to the technical field of cooperative and disturbance control of servo systems, position and speed signals of each servo axis are acquired in real time, a cooperative error vector is calculated based on a graph theory model, the vector reflects the deviation between the state of each axis and an expected cooperative trajectory, and the cooperative control and disturbance suppression of the multi-axis servo system are realized. And synchronous movement is ensured. The collaborative error is used for generating a preliminary control signal, and a proportional, differential and integral term combination strategy is adopted to quickly correct the error and eliminate the steady-state error. Meanwhile, disturbance vectors are estimated through an observer, and external interference or internal changes are compensated. And after the preliminary control signal and the disturbance compensation are added, amplitude limiting processing is carried out to prevent saturation of the driver. The control parameters are adjusted through an off-line optimization algorithm to minimize errors and disturbance influences, so that the tracking precision, the anti-interference capability and the adaptability of the multi-axis servo system are improved, and the method is suitable for the fields of high-precision manufacturing, robot control and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of servo system coordination and disturbance control, and particularly relates to a method for coordinated control and disturbance suppression of a multi-axis servo system. BACKGROUND

[0002] Multi-axis servo systems have important applications in industrial automation, robot control, numerical control machine tools, and precision manufacturing, etc. The core requirement is to achieve high-precision synchronous motion among multiple servo axes to ensure coordinated operation of the overall system and improve task execution precision. However, traditional control strategies have significant limitations and are difficult to effectively cope with challenges in complex dynamic environments. First, due to differences in dynamic characteristics of each servo axis, such as inertia, friction, and inconsistent response times, coupled with internal coupling effects of the system, it is easy to cause coordination errors, which are manifested as asynchronous position or speed among axes, thereby affecting processing quality or motion trajectory accuracy. Second, external disturbance factors such as load changes, mechanical vibrations, environmental disturbances, etc. will continuously act on the system, and traditional methods lack an efficient real-time estimation mechanism, leading to disturbance accumulation and propagation, which cannot be compensated in time, causing tracking error to increase, response delay, or steady-state deviation. In addition, traditional control gains usually use fixed parameter design, which cannot adapt to changes in system parameters such as load changes or component aging, which may cause control signal saturation, driver overload, or system instability, limiting its robustness and reliability in dynamic working conditions. These technical problems jointly restrict the performance improvement of multi-axis servo systems in high-precision applications, and need to be improved to enhance the synchronous control and anti-disturbance ability. SUMMARY

[0003] The present application provides a method for coordinated control and disturbance suppression of a multi-axis servo system, the multi-axis servo system comprising a plurality of servo axes, each servo axis having a driver, a motor, and a feedback sensor, comprising the following steps: Step S1: Real-time acquisition of current state information of each servo axis, including position signal and speed signal; Step S2: Based on the current state information, calculating a coordination error vector among multiple axes, wherein the coordination error vector is determined by the deviation between the state of each axis and the expected coordinated trajectory; Step S3: According to the coordination error vector, generating a preliminary control signal from a coordinated control calculation formula, the coordinated control calculation formula is defined as: wherein, is a preliminary control signal vector, is a coordination error vector, is a derivative of the coordination error vector, and are preset proportional gain matrix and derivative gain matrix; ​Step S4: determining a disturbance estimation vector based on a disturbance calculation formula, the disturbance calculation formula being: ; wherein, is the disturbance estimation vector, is a system measurement output vector, is an observer output vector, is an observer gain matrix; Step S5: adding the preliminary control signal and a disturbance compensation signal to generate a control signal, and outputting the control signal to a driver of each servo axis.

[0004] Further, in step S2, the calculation of the cooperative error vector is based on a graph theory model, wherein each servo axis is a node, and the inter-axis connection relationship is defined by an adjacency matrix, and the cooperative error vector is calculated by the following formula: ; wherein, is a graph Laplacian matrix, is a multi-axis state vector.

[0005] Further, in step S3, the cooperative control calculation formula further includes an integral term to eliminate steady-state error, and the cooperative control calculation formula including the integral term is: ; wherein, is an integral gain matrix.

[0006] Further, in step S5, the generation of the control signal further includes a limiting processing to constrain the amplitude of the control signal and prevent the saturation of the driver, and the limiting processing is defined by the following formula: ; is a saturation function, and the upper and lower limits are preset based on the allowable input range of the servo driver.

[0007] Further, the desired cooperative trajectory is generated in real time by a task planning module, and is subjected to coordinate transformation based on a kinematics model to ensure the synchronous movement of each axis.

[0008] Further, the parameters of the proportional gain matrix , the derivative gain matrix , and the observer gain matrix are determined by an offline optimization algorithm, and the offline optimization algorithm is based on system identification data to minimize the cooperative error and the influence of disturbance.

[0009] Further, the method further includes a real-time adaptive adjustment step, wherein the proportional gain matrix , the derivative gain matrix , and the observer gain matrix The adaptive adjustment is based on the following formula: ; wherein, is the initial gain, is the adjustment amount that changes with the system parameters , which is calculated online by gradient descent method.

[0010] The embodiments of the present application have the following beneficial effects: The technical scheme of the present application aims to realize high-precision cooperative control and effective disturbance suppression of a multi-axis servo system, thereby improving the motion synchronization and robustness of the system under complex working conditions. By real-time acquisition of position and speed signals of each servo axis, the system can dynamically calculate a cooperative error vector among the multi-axes. The vector is constructed based on a graph theory model, each axis is regarded as a node, and an adjacency matrix is used to define the connection relationship, to ensure that the cooperative error accurately reflects the deviation of each axis state from the expected cooperative trajectory. The expected cooperative trajectory is generated in real time by a task planning module and is subjected to coordinate transformation by a kinematics model to ensure the motion synchronization of each axis. The calculation of the cooperative error provides a basis for subsequent control, enabling the system to quickly respond to state changes.

[0011] Based on the cooperative error vector, the system generates a preliminary control signal and adopts a combination control strategy of proportional, differential and integral terms. The proportional term is used to quickly correct the error, the differential term suppresses overshoot, and the integral term eliminates steady-state error, thereby realizing accurate compensation of the cooperative error. Disturbance estimation is achieved by an observer, and the integral difference between the measured output and the observer output is used to calculate a disturbance estimation vector to effectively identify and compensate for the influence of external disturbances or internal parameter changes. After adding the preliminary control signal and the disturbance compensation signal, amplitude limiting processing is performed to constrain the amplitude of the control signal, prevent the driver from being saturated, and ensure the safe and stable operation of the system.

[0012] Parameter optimization is completed by an offline algorithm. The proportional gain, differential gain and observer gain are adjusted based on system identification data to minimize the cooperative error and disturbance influence, thereby improving the control efficiency. In addition, the system has real-time adaptive adjustment capability. The control gain is dynamically updated according to the online estimated system parameters, the adjustment amount is calculated by gradient descent method, the load changes or environmental fluctuations are adapted, the consistency of the control performance is maintained, and through the organic combination of cooperative control and disturbance suppression, the tracking accuracy, anti-interference ability and adaptability of the multi-axis servo system are significantly improved. The system is suitable for fields such as high-precision manufacturing and robot control that require multi-axis coordination. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments description. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0014] Figure 1 An exemplary flowchart of a method for cooperative control and disturbance rejection of a multi-axis servo system is shown. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application.

[0016] In order to further illustrate the technical solutions provided by the embodiments of the present application, the following will combine the drawings and the specific embodiments to make a detailed description. Although the embodiments of the present application provide the method operation steps as shown in the following embodiments or drawings, more or less operation steps can be included in the method based on conventional or non-creative labor. The execution order of these steps is not limited to the execution order provided by the embodiments of the present application in the logical sense.

[0017] The present application provides a method for cooperative control and disturbance rejection of a multi-axis servo system, the multi-axis servo system includes a plurality of servo axes, each servo axis has a driver, a motor and a feedback sensor, comprising the following steps.

[0018] Step S1: Real-time acquisition of current state information of each servo axis, including position signal and speed signal.

[0019] Real-time acquisition of current state information of each servo axis, including position signal and speed signal, is the initial step in the method of cooperative control and disturbance rejection of multi-axis servo system. This step monitors the motion state of each servo axis in real time through the feedback sensor, provides accurate and timely input data for subsequent control calculation, ensures that the control algorithm can be dynamically adjusted based on the actual running condition of the system, thereby improving the response speed and cooperative accuracy of the whole system.

[0020] Real-time acquisition of state information enables the system to quickly capture the instantaneous position and speed changes of each axis, which is crucial for the synchronous motion between multiple axes. By continuously monitoring the position and speed signals, the system can timely identify the deviation between each axis and the expected trajectory, lay a foundation for subsequent calculation of cooperative error vector, effectively reduce the control error caused by delay or noise, and enhance the robustness of the system in dynamic environment.

[0021] Step S2: Calculate the coordination error vector among multiple axes based on the current state information, where the coordination error vector is determined by the deviation between the state of each axis and the expected coordination trajectory. The expected coordination trajectory is generated in real-time by the task planning module and is coordinate-transformed based on the kinematic model to ensure the synchronization of each axis during movement.

[0022] The calculation of the coordination error vector is based on a graph theory model, where each servo axis is a node, the inter-axis connection relationship is defined by an adjacency matrix, and the coordination error vector is calculated by the following formula: .

[0023] where, is the graph Laplacian matrix, is the multi-axis state vector.

[0024] Step S2 involves calculating the coordination error vector among multiple axes based on the current state information obtained in real-time, which is determined by the deviation between the state of each servo axis and the expected coordination trajectory. The expected coordination trajectory is generated in real-time by the task planning module and is coordinate-transformed based on the kinematic model to ensure the synchronization of each axis during movement.

[0025] The purpose of this step is to quantify the coordination deviation in the multi-axis system, providing accurate error input for subsequent control calculations, thereby effectively solving the problem of reduced movement precision caused by asynchronous axes. By calculating the coordination error in real-time, the system can dynamically adjust the movement state of each axis, improving overall coordination performance.

[0026] The formula for calculating the coordination error vector A graph theory model is used, where the multi-axis servo system is abstracted as a graph structure, each servo axis is a node, the inter-axis connection relationship is defined by an adjacency matrix, and the Laplacian matrix L is used to capture the topological characteristics of the system.

[0027] This formula mathematically maps the multi-axis state vector x(t) to the coordination error vector, so that the error calculation can systematically reflect the interaction between axes, simplifying the error modeling of complex multi-axis systems, enhancing the scalability and adaptability of the algorithm, and especially suitable for scenarios where the number of axes or connection relationships change dynamically.

[0028] By introducing the graph Laplacian matrix, the standardization of inter-axis deviation is achieved, reducing the dependence on manual parameter tuning. This not only improves the response speed of the system, but also reduces the accumulation of errors caused by external disturbances or internal parameter changes.

[0029] Real-time calculation of the coordination error vector ensures that the control algorithm can quickly compensate for deviations, thereby improving movement synchronization and stability, providing core support for disturbance suppression and adaptive adjustment of the entire method.

[0030] Step S3: Generating a preliminary control signal from the cooperative error vector based on a cooperative control calculation formula defined as: .

[0031] wherein, is the preliminary control signal vector, is the cooperative error vector, is the derivative of the cooperative error vector, and are preset proportional gain matrix and derivative gain matrix.

[0032] The cooperative control calculation formula also includes an integral term to eliminate steady-state error. The cooperative control calculation formula including the integral term is: ; wherein, is the integral gain matrix.

[0033] Step S3 generates a preliminary control signal from the cooperative error vector, aiming to convert error information into actual control output to drive each servo axis to achieve cooperative motion. By applying the cooperative control calculation formula, the system can dynamically adjust the control signal based on real-time errors, thereby correcting inter-axis deviations and improving the synchronization accuracy and response speed of the multi-axis system.

[0034] This step compensates for the instantaneous changes in the cooperative error, ensuring the timeliness and accuracy of the control action, and providing core support for disturbance suppression and stability of the entire method.

[0035] The proportional term directly responds to the size of the current cooperative error, used to quickly reduce the deviation; the derivative term is based on the error rate to predict future trends to suppress system oscillation and overshoot.

[0036] To further eliminate steady-state error, the formula is expanded to include an integral term that compensates for long-term deviations by accumulating historical errors, ensuring the accuracy of the system in the steady state. 、 and Through offline optimization, the parameters are preset to balance response speed and stability, and their selection directly affects the robustness of control performance.

[0037] This calculation formula realizes high-precision cooperative control of multi-axis servo systems by combining proportional, derivative, and integral actions. The proportional term provides fast response, the derivative term enhances damping characteristics, and the integral term eliminates residual errors, thereby improving the dynamic performance and steady-state accuracy of the system as a whole. This feature addresses the problem of cooperative error accumulation and disturbance sensitivity in multi-axis environments, simplifies control logic through mathematical modeling, reduces implementation costs, and lays a reliable foundation for subsequent disturbance compensation and adaptive adjustment steps.

[0038] Step S4: Determine the disturbance estimation vector based on the disturbance calculation formula: .

[0039] where, is the disturbance estimation vector, is the system measurement output vector, is the observer output vector, is the observer gain matrix.

[0040] Step S4 determines the disturbance estimation vector based on the disturbance calculation formula, aiming to estimate various disturbances existing in the multi-axis servo system in real time, such as external disturbances, load changes or unmodeled dynamics, thereby providing accurate compensation basis for the control signal. This step compares the difference between the system measurement output vector and the observer output vector, and uses the integral operation to accumulate historical deviations to capture the persistent impact of disturbances. The disturbance calculation formula enhances the estimation ability of low-frequency and steady-state disturbances through the integral term, while the gain matrix L is used to adjust the convergence speed and robustness of the estimation, ensuring that the disturbance estimation can quickly track actual changes.

[0041] Step S4 addresses the problem of increased cooperative error and decreased stability caused by disturbances in the multi-axis servo system by actively estimating the disturbance vector to provide input for the subsequent compensation step. The observer mechanism allows the system to distinguish between real motion errors and disturbance effects, thereby achieving targeted suppression.

[0042] The parameters of the gain matrix L can be optimized offline or adjusted adaptively to minimize estimation errors and improve the adaptability of the system in uncertain environments. This feature reduces the impact of disturbances on cooperative control performance, improving the accuracy and reliability of the overall system.

[0043] The introduction of the disturbance estimation vector significantly reduces the steady-state error and overshoot of the multi-axis system, improving dynamic response. By compensating for disturbances in real time, the system can maintain synchronized motion between axes, even in the presence of external disturbances or parameter changes.

[0044] This step provides key support for the robustness of the entire control method, ensuring the effective integration of cooperative control and disturbance suppression, thereby improving the practicality and performance of multi-axis servo systems in industrial applications.

[0045] Step S5: Add the preliminary control signal and the disturbance compensation signal to generate the control signal, and output the control signal to the driver of each servo axis.

[0046] The generation of the control signal also includes amplitude limiting processing to constrain the amplitude of the control signal and prevent driver saturation, which is defined by the following formula: .

[0047] is a saturation function, whose upper and lower limits are preset based on the allowable input range of the servo driver.

[0048] Step S5 adds the preliminary control signal and the disturbance compensation signal to generate a final control signal, and outputs the signal to the driver of each servo axis. The purpose of this step is to integrate the outputs of cooperative control and disturbance suppression to form a complete control instruction, so as to ensure that the multi-axis servo system can maintain stable and accurate cooperative motion in the presence of external disturbances or internal changes.

[0049] By combining disturbance compensation, step S5 can actively offset the estimated disturbance effect, thereby reducing the cooperative error and improving the dynamic response and steady-state accuracy of the system. The generation process of the control signal also includes amplitude limiting processing to constrain the signal amplitude, prevent the driver from being saturated or damaged due to the control signal being too large, and enhance the safety and reliability of the system.

[0050] wherein the saturation function is preset with upper and lower limits based on the allowable input range of the servo driver, for limiting the amplitude of the control signal within a safe interval. This formula mathematically realizes signal constraint, ensuring that the control amount output to the driver is always within an acceptable range, avoiding overload conditions.

[0051] Amplitude limiting processing constrains the amplitude of the control signal through a saturation function, the core purpose of which is to prevent the input signal of the driver from exceeding the allowable range. When the control signal is too large, the saturation function will limit it within the preset safe interval, avoiding the driver from entering a saturated state. This processing not only protects the hardware devices from overload damage, but also maintains the linear working interval of the control system.

[0052] The amplitude limiting mechanism ensures the smoothness of the control signal, effectively suppressing system oscillation caused by signal mutation. It synthesizes the control signal before amplitude limiting with the disturbance compensation signal, and then performs amplitude constraint, so that the final output signal has both anti-interference ability and stability. This processing method is particularly suitable for sudden disturbances or system parameter mutations, and provides reliable output guarantee for multi-axis cooperative control.

[0053] By controlling the signal amplitude within a reasonable range at all times, amplitude limiting processing also improves the response consistency of the system. Even in the presence of large disturbances or rapid dynamic changes, each servo axis can maintain coordinated operation, and the overall cooperative performance will not be affected by the signal overload of individual axes. This design enhances the adaptability and reliability of the system under various working conditions.

[0054] The introduction of the clipping process aims at the driver saturation problem commonly seen in multi-axis servo systems. Its technical effect lies in preventing the control signal from exceeding the hardware tolerance limit, thereby protecting the driver from damage and maintaining the continuous and stable operation of the system. The application of the saturation function simplifies the implementation logic, realizes real-time clipping without complex calculations, and improves the practicality and efficiency of the method.

[0055] Step S5 and its clipping process significantly improve the overall robustness and adaptability of the multi-axis servo system. By combining disturbance compensation and signal clipping, the system can maintain collaborative performance under various working conditions and reduce the risk of failure caused by disturbances or abnormal signals.

[0056] The clipping process ensures the smoothness and boundedness of the control signal, further optimizes the dynamic response, and prevents oscillation or overshoot. This feature addresses the safety and stability requirements of the control system, provides reliable output protection for multi-axis collaborative control through integrated compensation and constraint mechanisms, and ultimately enhances the feasibility and effectiveness of the method in industrial applications.

[0057] Further, the parameters of the proportional gain matrix , the derivative gain matrix , and the observer gain matrix are determined by an offline optimization algorithm based on system identification data to minimize collaborative errors and disturbance effects.

[0058] The parameters of the proportional gain matrix, the derivative gain matrix, and the observer gain matrix are determined by an offline optimization algorithm based on system identification data to minimize collaborative errors and disturbance effects. The purpose of setting this feature is to pre-optimize the key parameters of the control system to avoid the uncertainty of online adjustment, thereby improving the control accuracy and stability of the multi-axis servo system.

[0059] By utilizing system identification data, the offline optimization algorithm can accurately model the dynamic characteristics of the system and minimize the objective function for collaborative errors and disturbance effects, ensuring that the gain parameters are optimally configured before system operation. This offline approach reduces real-time calculation burden, enabling the control system to respond quickly to dynamic changes while reducing performance fluctuations caused by improper parameters.

[0060] The offline optimization algorithm adjusts the numerical values of the proportional gain matrix, the derivative gain matrix, and the observer gain matrix through mathematical optimization methods such as gradient descent or genetic algorithms to balance the response speed, stability, and anti-interference ability of the system. The proportional gain matrix affects the direct compensation effect of the error, the derivative gain matrix suppresses oscillation and overshoot, and the observer gain matrix optimizes the accuracy of disturbance estimation.

[0061] By minimizing the coordination error and disturbance influence, this feature directly addresses the control performance degradation caused by parameter drift or external disturbances in multi-axis servo systems, enhancing the robustness and adaptability of the system. The optimization process is based on actual system data, ensuring that the parameter settings match the real working conditions, improving the practicality and reliability of the method.

[0062] Offline optimization of gain parameters significantly improves the overall performance of multi-axis coordination control. The system can maintain high-precision synchronous motion under various load and disturbance conditions, reducing steady-state error and dynamic deviation. In addition, offline optimization reduces the complexity of online adaptive adjustment, making the control system easier to implement and maintain. This feature provides the basis for parameter optimization for the entire method, ensuring the effective integration of coordination control and disturbance suppression, ultimately enhancing the efficiency and durability of multi-axis servo systems in industrial applications.

[0063] Further, the method further comprises a real-time adaptive adjustment step, wherein the proportional gain matrix , the derivative gain matrix , and the observer gain matrix are dynamically updated according to the online estimated system parameters to adapt to load changes, and the adaptive adjustment is based on the following formula: .

[0064] wherein is the initial gain, is the adjustment amount that changes with the system parameters , which is calculated online by the gradient descent method.

[0065] The real-time adaptive adjustment step allows the proportional gain matrix, the derivative gain matrix, and the observer gain matrix to be dynamically updated according to the online estimated system parameters to adapt to load changes and other dynamic conditions, allowing the control system to respond in real time to changes in system parameters such as load fluctuations or environmental disturbances, thereby maintaining the coordination performance and stability of the multi-axis servo system.

[0066] By dynamically adjusting the gain parameters, the system can compensate for performance degradation caused by parameter drift or internal changes, ensuring that the control algorithm is always in an optimized state and reducing dependence on offline preset parameters. This step addresses the control accuracy degradation caused by uncertain factors in multi-axis servo systems, enhancing the adaptability and robustness of the system through online optimization.

[0067] is the adjustment amount that changes with the system parameters , which is calculated online by the gradient descent method. The gradient descent method iteratively minimizes the objective function, such as the coordination error or disturbance influence, to calculate the gain adjustment amount in real time, allowing the proportional, derivative, and observer gains to be automatically corrected according to the current system state.

[0068] The gain parameters are continuously optimized during operation, improving the accuracy and speed of the control response. This feature addresses the problem of non-linear changes and disturbance sensitivity in multi-axis environments, reducing steady-state errors and oscillation phenomena through adaptive updates, and improving overall control efficiency.

[0069] Real-time adaptive adjustment significantly improves the performance of multi-axis servo systems in dynamic conditions. It enables the system to automatically adapt to load changes, reduces collaborative deviations caused by external disturbances, and improves motion synchronization and stability. In addition, the adaptive step reduces the need for manual parameter tuning, improves system autonomy and maintainability, enhances the practicality and reliability of the control method through online optimization of gain parameters, and ensures long-term stable operation of multi-axis servo systems in industrial applications.

[0070] A collaborative error calculation mechanism based on graph theory model is used to convert the topological relationship of multi-axis systems into mathematical representation through Laplacian matrix, and to quantize the deviation of each axis from the expected trajectory in real time. This error signal is processed through a control algorithm containing proportional-derivative-integral terms to generate preliminary control instructions with feedforward characteristics, effectively improving multi-axis synchronization accuracy. A disturbance estimation system based on an observer is constructed to extract disturbance characteristics using integral operation by comparing the difference between actual output and model predicted output. The estimated disturbance vector is added as a compensation signal to the feedforward control quantity to form the final control instruction with anti-interference capability. A special amplitude limiting mechanism is introduced to constrain the amplitude of the control signal through a saturation function to prevent driver saturation.

[0071] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including instruction devices that implement the functions specified in the flow Figure 1 one or more flows and / or blocks Figure 1 one or more blocks or multiple blocks.

[0072] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are performed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the flow Figure 1 one or more flows and / or blocks Figure 1 one or more blocks or multiple blocks.

[0073] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application also intends to include these modifications and variations.

Claims

1. A method for coordinated control and disturbance rejection for a multi-axis servo system, the multi-axis servo system comprising a plurality of servo axes, each of the servo axes having a driver, a motor and a feedback sensor, characterized in that, The method comprises the following steps: Step S1: Real-time acquisition of current state information of each servo axis, including position signal and speed signal; Step S2: Based on the current state information, the collaborative error vector between multiple axes is calculated, wherein the collaborative error vector is determined by the deviation between the state of each axis and the expected collaborative trajectory; Step S3: generating a preliminary control signal from a cooperative control calculation formula defined as: ; wherein, is a preliminary control signal vector, is a cooperative error vector, is a derivative of the cooperative error vector, and is a preset proportional gain matrix and a derivative gain matrix; Step S4: determining a disturbance estimation vector based on a disturbance calculation formula, the disturbance calculation formula being: ; wherein, is a disturbance estimation vector, is a system measurement output vector, is an observer output vector, is an observer gain matrix; Step S5: Add the preliminary control signal and the disturbance compensation signal to generate a control signal, and output the control signal to the driver of each servo axis.

2. The method for coordinated control and disturbance rejection of a multi-axis servo system according to claim 1, wherein, In step S2, the calculation of the collaborative error vector is based on a graph theory model, in which each servo axis is a node and the inter-axis connection relationship is defined by an adjacency matrix, and the collaborative error vector is calculated by the following formula: ; wherein is a graph Laplacian matrix, is a multi-axis state vector.

3. The method for coordinated control and disturbance rejection of a multi-axis servo system of claim 1, wherein, In step S3, the coordinated control calculation formula further comprises an integral term to eliminate steady-state error, and the coordinated control calculation formula comprising the integral term is: ; wherein, is the integral gain matrix.

4. The method for coordinated control and disturbance rejection of a multi-axis servo system of claim 1, wherein, In step S5, the generation of the control signal further comprises a clipping process to constrain the control signal amplitude to prevent driver saturation, the clipping process being defined by the following equation: ; is a saturation function, whose upper and lower limits are preset based on the allowed input range of the servo drive.

5. The method for coordinated control and disturbance rejection of a multi-axis servo system of claim 1, wherein, The expected collaborative trajectory is generated in real time by a task planning module and is subjected to coordinate transformation based on a kinematics model to ensure synchronous movement of each axis.

6. The method for coordinated control and disturbance rejection of a multi-axis servo system of claim 1, wherein, the parameters of the proportional gain matrix , the derivative gain matrix and the observer gain matrix are determined by an off-line optimization algorithm based on system identification data, targeting the minimization of the cooperative error and disturbance influence.

7. The method for coordinated control and disturbance rejection of a multi-axis servo system of claim 1, wherein, The method further comprises a real-time adaptive adjustment step, wherein the proportional gain matrix , the derivative gain matrix , and the observer gain matrix are dynamically updated according to the online estimated system parameters to adapt to load variations, the adaptive adjustment is based on the following formula: ; wherein, is the initial gain, is the adjustment amount that varies with the system parameters is calculated online by the gradient descent method.

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