Gantry synchronization control method based on inertia equivalence and disturbance estimation

Abstract

The invention relates to the technical field of industrial automatic motion control, in particular to a gantry synchronous control method based on inertia equivalence and disturbance estimation. According to the technical scheme, the method comprises the following steps that dynamic modeling is conducted on a double-drive gantry system based on a Lagrange equation, the system is described as a generalized coordinate system with cross beam midpoint displacement, workbench offset and a cross beam rotation angle, a nonlinear dynamic equation is derived, the equivalent mass of each drive shaft is calculated in real time according to the model, and the equivalent mass of each drive shaft is calculated. According to the calculated real-time equivalent mass and an expected acceleration instruction given by the system, dynamic feed-forward compensation force is generated and used for pre-compensating inertia force, changed due to load movement, of the system. According to the method, the problem that the synchronization precision is reduced due to inertia time variation caused by load change and unknown disturbance is solved, and the response speed, the steady-state precision and the anti-interference capability are jointly improved.

Description

Technical Field

[0001] This invention relates to the field of industrial automation motion control technology, and in particular to a gantry synchronization control method based on inertia equivalence and disturbance estimation. Background Technology

[0002] As a core component of high-end equipment such as high-end CNC machine tools, laser processing equipment, and precision measuring instruments, the motion control performance of the dual-drive gantry platform, especially the synchronization accuracy between the two axes, directly determines the overall machining quality, efficiency, and dynamic performance. Ideally, the servo motors on both sides of the gantry platform should maintain absolute synchronous movement, meaning that the crossbeam remains parallel to the preset guide rail reference throughout its movement.

[0003] However, in practical industrial applications, dual-drive gantry systems face two long-standing and interconnected core technical challenges that severely restrict their development towards higher precision and higher speed.

[0004] 1. The problem of time-varying inertia: The position of the load (such as the machining head, measuring sensors, etc.) on the crossbeam of the gantry platform is dynamically changing. This change in load distribution causes the total rotational inertia of the entire system and the proportion of this inertia distributed on the two drive shafts to constantly change. Traditional control strategies, such as the conventional "PID controller + fixed parameter feedforward" method, design their feedforward compensation model based on fixed nominal parameters of the system (such as mass and inertia). When the dynamic parameters of the actual system change due to load movement, this fixed feedforward model becomes mismatched with the actual model. Mismatched feedforward compensation is no longer accurate, which not only fails to effectively improve the dynamic response performance of the system, but also introduces additional overshoot, oscillation, and even system instability, seriously affecting the dynamic accuracy and stability during high-speed start-stop and commutation processes.

[0005] 2. Disturbance Suppression: During operation, the system is subject to various internal and external disturbances, including but not limited to: resistance changes caused by guide rail unevenness, nonlinear changes in friction between the slider and guide rail, complex mechanical coupling effects between the two drive shafts, and sudden changes in external load. These disturbances directly disrupt the force balance and speed synchronization between the two shafts. Traditional PID control heavily relies on error feedback, which is a form of "post-event adjustment." Its disturbance rejection response has inherent hysteresis, and the phase lag of the integral element easily leads to continuous, slowly decaying oscillations during disturbance recovery, resulting in long recovery times and making it difficult to meet the stringent stability requirements of high-precision machining.

[0006] To address these challenges, Active Disturbance Rejection Control (ADRC) technology has been introduced into such systems due to its independence from precise object models and its powerful disturbance estimation and compensation capabilities. ADRC estimates and compensates for both internal and external disturbances through an Extended State Observer (ESO), exhibiting good robustness. However, simulations and practical applications show that the dynamic response speed of pure ADRC control (without feedforward) (e.g., approximately 0.03 seconds) is still slower than that of schemes incorporating feedforward compensation. On the other hand, simply combining ADRC with a feedforward model based on fixed parameters, while improving the response speed, fails to fundamentally solve the feedforward model mismatch problem caused by load movement. This mismatch itself constitutes a disturbance, increasing the estimation burden on the ESO and failing to fully realize the synergistic effectiveness and maximum potential of the integrated control of "model feedforward" and "disturbance estimation."

[0007] In summary, those skilled in the art have long sought a high-precision synchronization control strategy capable of adapting to load changes, achieving real-time accurate compensation, and possessing strong suppression capabilities against various unknown disturbances, in order to overcome the performance bottlenecks of existing technologies and meet the stringent requirements of modern high-end equipment for nanometer-level synchronization accuracy. Therefore, this application proposes a gantry synchronization control method based on inertia equivalence and disturbance estimation. Summary of the Invention

[0008] The purpose of this invention is to address the problem in the background art of needing a high-precision synchronous control strategy that can adapt to load changes, achieve real-time accurate compensation, and have a strong ability to suppress various unknown disturbances. The invention proposes a gantry synchronous control method based on inertia equivalence and disturbance estimation.

[0009] The technical solution of this invention: a gantry synchronization control method based on inertia equivalence and disturbance estimation, comprising the following steps:

[0010] S1. Based on the Lagrange equation, the dynamic model of the dual-drive gantry system is performed. The system is described as a generalized coordinate system with the displacement of the midpoint of the crossbeam, the offset of the worktable, and the rotation angle of the crossbeam. The nonlinear dynamic equation is derived. The equivalent mass of each drive shaft is calculated in real time according to the model.

[0011] S2 generates a dynamic feedforward compensation force based on the calculated real-time equivalent mass and the desired acceleration command given by the system, which is used to pre-compensate for the inertial force of the system that changes due to the load motion.

[0012] S3. Design an extended state observer to unify the inaccuracies of the system model and external disturbances into a total disturbance, and extend it into state variables for real-time estimation. In each servo cycle, use the discretized state update equation to estimate the position, velocity and total disturbance state in real time based on the system control input and position feedback.

[0013] S4 uses a linear state error feedback control law to generate a nominal control quantity, and combines the nominal control quantity, dynamic feedforward compensation force, and the estimated value of total disturbance to generate a final control signal, which is output to the servo driver to drive the motor.

[0014] Optionally, in step S1, the equivalent mass includes a translational equivalent mass independent of the load position and a rotational equivalent mass related to the square of the load position, wherein the translational equivalent mass... The calculation formula is:

[0015]

[0016] in, For the mass of the beam, For the mass of the slide block.

[0017] Optionally, in step S1, the rotational equivalent mass The calculation formula is:

[0018]

[0019] in, The distance between the two drive motors Let the moment of inertia of the beam be... This represents the offset of the worktable along the direction of the crossbeam.

[0020] Optionally, the dynamic feedforward compensation force described in step S2 The calculation formula is:

[0021]

[0022] in, For real-time equivalent quality, The desired acceleration command.

[0023] Optionally, the extended state observer in step S3 is a linear extended state observer, and its gain is determined by setting the observer bandwidth. Adjustment, including:

[0024]

[0025] in, , , These are the observer gains for position, velocity, and total disturbance state, respectively.

[0026] Optionally, the discretized state update equation in step S3 is as follows:

[0027]

[0028]

[0029]

[0030] in, Sampling time, At the current sampling time, for Position estimation at time, for Velocity estimation at time, for Total disturbance estimate at time 1 for The actual position measurement at any given time (from the encoder or grating ruler). for Control input at any time (torque command). The estimated gain of the controlled object.

[0031] Optionally, the final control signal mentioned in step S4 The calculation formula is:

[0032]

[0033] in, For nominal control quantity, This is the estimated total disturbance. To control the gain, It is a dynamic feedforward compensation force.

[0034] Optionally, the parameters of the linear state error feedback control law are determined by the controller bandwidth. Tuning, in which the proportional gain Differential gain .

[0035] Compared with the prior art, this application includes at least one of the following beneficial technical effects:

[0036] Through dynamic inertia allocation, the feedforward parameters can be adjusted in real time according to the load position, so that the feedforward compensation force is matched with the current dynamic state of the system, which improves the dynamic response speed of the system and reduces overshoot during startup and commutation.

[0037] By using an extended state observer to perform closed-loop observation and compensation of the total disturbance, the mismatch of the feedforward model is also estimated and offset in real time as a disturbance, enabling the system to suppress inertia calculation errors, model inaccuracies and external disturbances, and shortening the recovery time after being disturbed.

[0038] By integrating dynamic feedforward and closed-loop disturbance compensation, the advantages of feedforward control speed and disturbance compensation immunity are combined, enabling the system to achieve rapid dynamic response while maintaining extremely high steady-state synchronization accuracy.

[0039] This invention solves the problem of decreased synchronization accuracy caused by time-varying inertia due to load changes and unknown disturbances, and achieves a combined improvement in response speed, steady-state accuracy and anti-interference capability. Attached Figure Description

[0040] Figure 1 This is a structural principle block diagram of the dual-drive gantry synchronous control system provided in an embodiment of the present invention;

[0041] Figure 2 This is a simplified schematic diagram of the gantry frame movement;

[0042] Figure 3 This is a Simulink simulation model diagram of the method described in this invention;

[0043] Figure 4-a , Figure 4-b and Figure 4-c This is a simulation comparison curve of the method of this invention and the conventional control method in terms of steady-state synchronization error, wherein:

[0044] Figure 4-a Amplification of steady-state error range Figure 1 , Figure 4-b Amplification of steady-state error range Figure 2 , Figure 4-c This is an enlarged view of the error segment after adding the disturbance;

[0045] The red line represents ADRC with feedforward, the black line represents ADRC without feedforward, the blue line represents PID with feedforward, and the green line represents PID without feedforward.

[0046] Figure 5 This is a flowchart of the gantry synchronization control method based on inertia equivalence and disturbance estimation of the present invention. Detailed Implementation

[0047] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0048] Example

[0049] like Figure 1The accompanying drawings further illustrate the dual-drive gantry synchronous control system provided in this embodiment. The control system mainly consists of a feedforward compensation module, a PD feedback controller, an extended state observer (ESO), and a disturbance compensation module, forming a complete control loop. The reference position signal is first input to the feedforward compensation module. This module calculates the equivalent mass of the mechanical system based on the real-time position y of the slide block and generates a feedforward compensation force based on the acceleration information of the reference trajectory. This force is specifically used to counteract the changes in system inertia caused by changes in the slide block position. The feedforward output and the feedback output of the PD controller are superimposed to form the total control quantity. The PD controller is responsible for handling position tracking errors and ensuring the basic stability of the system. The extended state observer (ESO) monitors the system output and control quantity input to estimate the total disturbance of the system in real time, including model uncertainties, external disturbances, and the coupling effect between the two motors. The estimated disturbance is compensated for by the 1 / b gain module, achieving forward-looking suppression of various disturbances and significantly improving the robustness of the system.

[0050] like Figure 5 As shown, the gantry synchronization control method based on inertia equivalence and disturbance estimation proposed in this invention will be described in detail below for each step.

[0051] Step S1, based on the Lagrange equation ,in, Let be the i-th generalized coordinate, which in this system is , Let L be the derivative of the i-th generalized coordinate with respect to time, i.e., the generalized velocity. Let L be the Lagrangian function, defined as the difference between the system's kinetic energy T and potential energy V, i.e., L = T − V. In this system, the potential energy V is negligible. For corresponding to generalized coordinates The generalized force.

[0052] The dual-drive gantry system is modeled and described as having three generalized coordinates (crossbeam midpoint displacement x, table offset y, and crossbeam rotation angle). The dynamic system of [system name] is described, and its nonlinear dynamic equations are derived. Based on this model, the real-time equivalent mass of each drive shaft is calculated. This value is determined by the translational equivalent mass, which is independent of the load location. and rotational equivalent mass related to the square of the load position It consists of two parts, and updates in real time with the position y of the worktable. The mass of the gantry beam is m1, the mass of the slide is m2, and the distance between the two grating rulers on the beam is L. It is the moment of inertia of the beam and the slide. Let be the moment of inertia of the beam about its own center of mass (center point).

[0053] Step S2, based on the real-time equivalent mass calculated in step S1 With respect to the desired acceleration command given by the system Generate precise dynamic feedforward compensation force.

[0054]

[0055] This is to pre-compensate for the inertial forces that change due to the movement of the load.

[0056] Step S3: Design a second-order linear extended state observer (ESO). Define the inaccuracies of the system model (including equivalent mass calculation errors, friction, external disturbances, etc.) as a unified "total disturbance" z3, and extend it as a new state variable for real-time observation. In practical digital control systems, a discretized ESO is required: in each servo cycle, based on the sampling time Ts, using the current control input u(k) and position feedback y(k), the position, velocity, and total disturbance state are estimated in real-time through discrete state update equations. The ESO estimates the observed value of the total disturbance in real-time using the system's control input and position output. Its observer gain is determined by setting the observer bandwidth. Adjustment ( This gain is also used for the calculation of discrete ESO.

[0057] Step S4: Generate initial control input using a linear state error feedback (LSEF) control law. The feedforward control signal, feedback control signal, and disturbance compensation signal are combined to generate the final control signal. ,in This is to control the gain. The control signal is output to the servo driver, which drives the motor to move, thus achieving extremely fast dynamic response while possessing strong anti-interference capability.

[0058] To verify the effectiveness of the method described in this invention, this embodiment was simulated and verified in the MATLAB / Simulink R2018a environment using a specific dual-drive gantry platform as the object. The key parameters of the platform are as follows: The X-axis motion system of the platform adopts a symmetrical layout design, with two motion platforms configured on two parallel X-axises, forming two corresponding support structures. The two corresponding motion platforms are guided by linear guide pairs and synchronously driven by a flat linear motor to jointly support a crossbeam.

[0059] The simulation object in this embodiment is based on a real dual-drive gantry platform, which is parametrically modeled. The key mechanical structural parameters of the platform are as follows:

[0060] The distance between the two drive motors is L=0.97 m, the mass of the crossbeam is m1=18.526 kg, and the mass of the slide is m2=3.923 kg.

[0061] The specific implementation steps are as follows:

[0062] Step S1: Establish a nonlinear dynamic model of the system based on the Lagrange equations, abstracting the system into a dynamic system with three generalized coordinates and deriving the system's dynamic equations. For each driving axis, calculate its equivalent mass in real time, where the translational equivalent mass... The total mass is calculated to be 13.186 kg through amortization, and the equivalent mass during rotation is... The final real-time equivalent mass is obtained by converting the total rotational inertia of the system. The sum of the two values ​​is dynamically updated based on the worktable position y. A dynamic feedforward compensation force is generated based on the real-time equivalent mass. Its value is With desired acceleration command The product of is used to pre-compensate for the main inertial forces of the system.

[0063] Step S2: Design a linearly extended state observer to estimate the total disturbance in real time, and set the observer bandwidth. =500rad / s, and calculate the ESO gain parameter accordingly. =1500、 =750000、 =125000000.

[0064] The continuous-time ESO equations are as follows:

[0065]

[0066] Since the actual servo system uses digital control, the continuous-time ESO needs to be discretized. Let the sampling time be... (In this embodiment) =0.01s), the update equation for the discrete-time ESO is as follows:

[0067]

[0068]

[0069]

[0070] in,

[0071] The sampling time is consistent with the sampling period of the simulation system;

[0072] Index of the current sampling time;

[0073] for Position estimation at a given time;

[0074] for Velocity estimation at time;

[0075] for Total disturbance estimate at time;

[0076] for The actual position measurement at any given time (from encoder feedback);

[0077] for Time-based control input;

[0078] To control the gain, it is consistent with the continuous-time model;

[0079] , , The observer gain parameter is determined by the observer bandwidth. Calculated.

[0080] Discrete ESO updates the state estimate in each sampling period and is used for real-time disturbance compensation. This discretization method is easy to implement in embedded processors, avoiding the computational delay problem of continuous-time models in digital control.

[0081] An ESO observation equation is established to estimate the position, velocity, and total disturbance state in real time through system control inputs and position outputs. A linear state error feedback control law is employed, and the controller bandwidth is set accordingly. The LSEF parameters were calculated. , Generate nominal control quantity Final control quantity By subtracting the disturbance estimate from the nominal control quantity and dividing by the nominal control gain This is obtained by combining the feedforward compensation amount.

[0082] Step S3: Build a simulation model in the MATLAB / Simulink environment to verify performance, such as... Figure 3 The table's position y-speed is 50 mm / s, and it is excited using a 10 ms stepped input method to better reflect the discrete trajectory characteristics in actual operation. The sampling time is 0.01 s, and step perturbations of 10 and -10 are applied at t=3s and t=4s, respectively.

[0083] Simulation results show that the method of the present invention has a dynamic response adjustment time of approximately 0.015 s and an overshoot of 0.5 mm; it exhibits the smallest synchronization error amplitude and the shortest recovery time after disturbance; and it stabilizes the synchronization error within ±1 nm in steady state. Compared with PID control and pure ADRC control, the present invention demonstrates significant advantages in dynamic response, disturbance rejection, and steady-state accuracy, effectively verifying the superiority and practicality of the method.

[0084] Simulation results are as follows Figure 4-a , Figure 4-b and Figure 4-c As shown.

[0085] Dynamic response: The method of this invention (corresponding to the red line in the figure) has the fastest response (about 0.015s) and the smallest overshoot, below 0.12mm.

[0086] Disturbance immunity: When a step disturbance is added at 4s, the method of this invention has the smallest error amplitude, the fastest recovery speed, and the best oscillation suppression effect.

[0087] Steady-state accuracy: The steady-state error of the method of the present invention is kept at an extremely small nanometer level (±1nm), and the curve is smooth with no obvious oscillation.

[0088] The above embodiments fully demonstrate that the method of the present invention is superior to traditional control strategies in terms of dynamic performance, steady-state accuracy and disturbance rejection robustness, and is particularly suitable for high-precision, complex dual-drive gantry synchronous control scenarios.

[0089] It should be noted that this invention proposes a gantry synchronization control method based on inertia equivalence and disturbance estimation. The method uses the Lagrange equation to derive the control of the inertia distribution of the underlying platform caused by the change in the mass displacement of the crossbeam, and performs acceleration feedforward compensation. Disturbances caused by model parameter deviations are estimated and compensated using an extended observer of the active disturbance rejection control method. Through this method, the underlying platform can achieve full feedforward, thereby realizing high-precision synchronization control.

[0090] like Figure 2 As shown, the equivalent mass formula is: the mass of the gantry beam is m1, the mass of the slide is m2, and the distance between the two grating rulers on the beam is L. The motion of the gantry-type dual-drive platform can be determined by... , , It is fully described by three independent degrees of freedom, where x represents the midpoint o of the gantry beam along... The displacement in the axial direction, y, represents the displacement of the center of mass of the worktable on the crossbeam from o along the crossbeam direction. The rotation angle of the gantry frame.

[0091] Equivalent mass of each motor shaft It consists of two parts:

[0092] Translation: The average mass of the slide and the beam is distributed (independent of y).

[0093] Rotation: The additional inertia caused by the position y of the slide (proportional to y2).

[0094] The system's translational equivalent mass is due to the two motors moving in the same direction, each bearing half of the mass; therefore, the translational equivalent mass is:

[0095]

[0096] The derivation of the equivalent mass of the system in pure rotational mode is as follows:

[0097] When the slide is at position y, the total moment of inertia of the system is:

[0098]

[0099] The motor applies forces F1 and F2, generating a net torque:

[0100]

[0101] Symmetric driving ): LF, The net torque generated by the motor force;

[0102] Torque balance equation:

[0103]

[0104] in It is angular acceleration. It is the total moment of inertia of the system, representing the moment of inertia of the system about the center of rotation (the midpoint of the beam).

[0105] linear acceleration 'a' and angular acceleration at the motor mounting point The relationship is:

[0106]

[0107] Substituting into the torque balance equation, we get:

[0108]

[0109] The solution is:

[0110]

[0111] According to Newton's second law The rotational equivalent mass is obtained as

[0112]

[0113] Therefore, the formula for the equivalent mass of the motor shafts at both ends of the crossbeam is:

[0114]

[0115] in, The translational term represents the total mass of the system when both motors jointly drive it in translational motion. Distributed evenly across each motor shaft. For rotation terms, It is the moment of inertia of the beam and the slide, with a coefficient. It converts the moment of inertia into an equivalent mass on the motor shaft.

[0116] Disturbance estimation compensation:

[0117] For any axis of motion of the gantry platform, let the mass...

[0118] The dynamic equation of the system model is The second-order system defines the total disturbance (including model uncertainty and external disturbance) as the third state:

[0119]

[0120] in, is a nonlinear function, related to state x, external disturbance d, and time t. b is the actual control gain, representing the actual influence coefficient of the control input u on the system dynamics. The nominal control gain represents the estimate of the system dynamics by the control input u.

[0121] The expanded state-space model is then:

[0122]

[0123] in: , , Let z1 be the system output position, z2 be the first derivative velocity of z1, and z3 be the total disturbance. u is the control input. Let be the nominal control gain, representing the estimate of the system dynamics by the control input u. h(t) is the disturbance rate function, representing the rate of change of the total disturbance z3 over time. y is the measured output.

[0124] The linear ESO equation in continuous time is:

[0125]

[0126] in: , , Positions ,speed Total disturbance The estimated value; u is the control input; The nominal control gain represents the estimate of the system dynamics by the control input u. , , Here are the observer gain parameters, and their values ​​are as follows:

[0127] (in, (observer bandwidth)

[0128] use Feedforward compensation disturbance

[0129]

[0130] in, This is the nominal control law.

[0131] After compensation, the system approximates an ideal second-order integrator.

[0132] (Ideal Second-Order Integrator)

[0133] Since the controller ultimately needs to be implemented on a digital processor, the continuous-time ESO needs to be discretized. Let the sampling period be... Then the discrete ESO update formula is:

[0134]

[0135]

[0136]

[0137] in:

[0138] for Position estimation at a given time;

[0139] for Velocity estimation at time;

[0140] for Total disturbance estimate at time;

[0141] for The actual position measurement at any given time (from the encoder or grating ruler).

[0142] for Control input at any time (torque command).

[0143] The estimated gain of the controlled object.

[0144] , , The observer gain parameter is determined by the observer bandwidth. The calculation is consistent with continuous time:

[0145]

[0146] in The observer bandwidth (rad / s) needs to be adjusted according to the dynamic characteristics of the system, and is usually taken as 3-5 times the system bandwidth.

[0147] Discrete ESO updates the state estimate in each sampling period and is used for real-time disturbance compensation. This method is easy to implement in embedded systems and avoids the latency problem of continuous-time models in digital control.

[0148] The synchronous control method sets the servo drive to torque mode, calculates the position and velocity deviations based on the desired position, velocity, and acceleration curves, and multiplies them by proportional and differential factors, respectively. These deviations are then added to the inertial force feedforward and disturbance estimates as control variables. This method compensates for deviations in advance based on changes in inertia and disturbances, achieving better control performance than existing synchronous control algorithms that compensate based on deviations.

[0149] The above specific embodiments are merely several optional embodiments of the present invention. Based on the technical solutions of the present invention and the relevant teachings of the above embodiments, those skilled in the art can make various alternative improvements and combinations to the above specific embodiments.

Claims

1. A gantry synchronization control method based on inertia equivalence and disturbance estimation, characterized in that, Includes the following steps: S1. Based on the Lagrange equation, the dynamic model of the dual-drive gantry system is performed. The dual-drive gantry system includes the displacement x of the midpoint of the beam, the offset y of the worktable, and the rotation angle θ of the beam. The nonlinear dynamic equation is derived, and the equivalent mass of each drive shaft is calculated in real time according to the model. S2, Based on the calculated real-time equivalent mass and the desired acceleration command given by the dual-drive gantry system, a dynamic feedforward compensation force is generated to pre-compensate the inertial force of the dual-drive gantry system that changes due to load movement. S3. Design an extended state observer to unify the model's inaccuracies and external disturbances into a total disturbance and extend it into state variables for real-time estimation. In each servo cycle, the position, velocity, and total disturbance state are estimated in real time based on the system control input and position feedback using the discretized state update equation. S4 uses a linear state error feedback control law to generate a nominal control quantity, and combines the nominal control quantity, dynamic feedforward compensation force, and the estimated value of total disturbance to generate a final control signal, which is output to the servo driver to drive the motor.

2. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 1, characterized in that, In step S1, the equivalent mass includes a translational equivalent mass independent of the load position and a rotational equivalent mass related to the square of the load position. The translational equivalent mass... The calculation formula is: in, For the mass of the beam, For the mass of the slide block.

3. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 2, characterized in that, In step S1, the rotational equivalent mass The calculation formula is: in, The distance between the two drive motors Let the moment of inertia of the beam be... This represents the offset of the worktable along the direction of the crossbeam.

4. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 1, characterized in that, The dynamic feedforward compensation force mentioned in step S2 The calculation formula is: in, For real-time equivalent quality, This is the desired acceleration command.

5. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 1, characterized in that, The extended state observer mentioned in step S3 is a linear extended state observer, and its gain is determined by setting the observer bandwidth. Adjustment, including: in, , , These are the observer gains for position, velocity, and total disturbance state, respectively.

6. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 5, characterized in that, The discretized state update equation described in step S3 is as follows: ， ， ,in, Sampling time, At the current sampling time, for Position estimation at time, for Velocity estimation at time, for Total disturbance estimate at time 1 for The actual position measurement at any given time (from the encoder or grating ruler). for Control input at any time (torque command). The estimated gain of the controlled object.

7. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 1, characterized in that, The final control signal mentioned in step S4 The calculation formula is: in, For nominal control quantity, This is the estimated total disturbance. To control the gain, It is a dynamic feedforward compensation force.

8. The gantry synchronization control method based on inertia equivalence and disturbance estimation according to claim 1, characterized in that, The parameters of the linear state error feedback control law are controlled by the controller bandwidth. Tuning, in which the proportional gain Differential gain .

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