TWI494725B - Control device, control method and compensating method of position command - Google Patents

Description

Control device, control method and position command compensation method

The invention relates to a control device, a control method and a position command compensation method suitable for a gantry positioning platform.

The precision machinery industry is one of the key development industries in China, and the precision positioning technology is of considerable importance to the entire precision machinery industry. Precision positioning technology is one of the important technologies in the mechanical engineering of manufacturing products, measuring object size and operating various machines. With the continuous advancement of precision engineering, no matter in the semiconductor industry, precision machinery industry, biological cell field, photoelectric system, micro-structure, surface engineering, scanning probe microscope, etc., all are moving in the direction of miniaturization and precision, so The demand for positioning systems in the nanometer or micron range is increasing, and many precision positioning instruments have been used in the industry.

High speed and high precision have always been the development goals of the machine tool, but the machine tools used for different purposes have different problems to be overcome in different occasions. When the workpieces to be produced are getting bigger and bigger, The size of the machine tool is also larger. For example, in recent years, the production of large-size LCD panels and the manufacture of large-scale solar panels have led to the increasing use of Gantry design architectures in similar applications. In the past, in the control applications of XY platform or multi-axis machine, each axis was driven by a single motor. However, in order to meet the requirements of high acceleration, high thrust and high rigidity, the gantry precision motion control system uses a double parallel linear motor. A parallel system that drives a single axis, that is, a bilinear servo system with mechanical coupling, is born. In this architecture Under the above, the position error between the motors of each group, due to the coupling of the mechanism, can affect the coupling mechanism, cause damage to the controlled system, and even endanger the safety of the staff. Therefore, ensuring the synchronous motion of the dual parallel linear motor has also become a very important research topic.

Synchronous motion compensation for dual parallel linear motors is disclosed in U.S. Patent No. 7,531,981, U.S. Patent No. 5,646,495, and Taiwan Patent Publication No. TW 200729673.

The invention provides a control device for ensuring synchronous movement of a double parallel linear motor of a gantry positioning platform.

The present invention provides a control method for ensuring synchronized motion of a dual parallel linear motor of a gantry positioning platform.

The invention provides a position command compensation method for compensating a position command of a three-axis of a gantry type positioning platform.

The invention provides a control device suitable for a gantry type positioning platform. The gantry type positioning platform has a pair of load-bearing slide rails respectively extending along a pair of mutually parallel load-bearing axes, and two ends coupled to the pair of load-bearing slide rails respectively and extending along a load axis perpendicular to the pair of load-bearing axes a rail, a load slider coupled to the load rail, a pair of load carrying motors for driving the load rail to move on the pair of load rails, and a load motor for driving the load slider to move on the load rail . The control device includes the following components. a forward coordinate converter that converts a position command from a first coordinate space to a second coordinate space in accordance with a dynamic model to generate a transition position Command, where the dynamic model is built according to the physical parameters of the gantry positioning platform. A set of position controllers that convert the transition position command into a transition speed command. A first reverse coordinate converter converts a speed feedback from the pair of load carrying motors and load motors into a transient speed feedback in accordance with a dynamic model, wherein the transition speed feedback is compared to a transition speed command to produce a transition speed error. A set of speed controllers that convert the transition speed error into a transition torque command. A second reverse coordinate converter converts the transition torque command from the second coordinate space to the first coordinate space in accordance with the dynamic model to generate a torque command to drive the pair of load bearing motors and the load motor.

The invention provides a control method suitable for a gantry type positioning platform. The gantry type positioning platform has a pair of load-bearing slide rails respectively extending along a pair of mutually parallel bearing axes, and two ends respectively coupled to the pair of load-bearing slide rails and coupled along a load rail extending perpendicular to the pair of load-bearing axes A load slider for the load rail, a pair of load-bearing motors for driving the load rails to move on the pair of load-bearing rails, and a load motor for driving the load slider to move on the load rails. The control method includes the following steps. A dynamic model is established according to the physical parameters of the gantry positioning platform. A position command is converted from a first coordinate space to a second coordinate space in accordance with the dynamic model to generate a transition position command. Convert the transition position command to a transition speed command. A speed feedback from the pair of load bearing motors and load motors is converted to a transition speed feedback in accordance with a dynamic model, wherein the transition speed feedback is compared to a transition speed command to produce a transition speed error. Convert the transition speed error to a transition torque command. A transition torque command is converted from the second coordinate space to the first coordinate space in accordance with the dynamic model to generate a torque command. according to The torque command drives the pair of load bearing motors and load motors.

The invention provides a position command compensation method, which is suitable for a gantry type positioning platform. The gantry type positioning platform has a pair of load-bearing slide rails respectively extending along a pair of mutually parallel bearing axes, a load rail coupled to the pair of load-bearing rails at both ends, and a load slider coupled to the load rail. The position command compensation method includes the following steps. A dynamic model is established according to the physical parameters of the gantry positioning platform. A dynamic model is used to convert a position command from a first coordinate space to a second coordinate space to generate a transition position command. Convert the transition position command to a transition speed command. A speed feedback from the pair of load bearing motors and load motors is converted to a transition speed feedback in accordance with a dynamic model, wherein the transition speed feedback is compared to a transition speed command to produce a transition speed error. Convert the transition speed error to a transition torque command. A transition torque command is converted from the second coordinate space to the first coordinate space in accordance with the dynamic model to generate a torque command.

Based on the above, the present invention establishes a dynamic model of the gantry positioning platform according to the physical parameters of the gantry positioning platform, which can increase the convenience of the user in developing the control system.

The above described features and advantages of the present invention will be more apparent from the following description.

1 is a perspective view of a gantry type positioning platform to which the present invention is applied. Referring to FIG. 1 , the gantry positioning platform 10 of the present embodiment has a pair of load-bearing slide rails 11 , a load slide rail 12 , and a load slide 13 . This pair of bearers The slide rails 11 extend along a pair of mutually parallel bearing axes y1 and y2, respectively. Both ends of the load rail 12 are coupled to the pair of load rails 11 to move synchronously on the pair of load rails 11, respectively. Load slider 13 is coupled to load rail 12 for movement on load rail 12.

The gantry positioning platform 10 further has a pair of load bearing motors 14 and a load motor 15. The pair of load-bearing motors 14 are respectively disposed between the pair of load-bearing rails 11 and the load rails 12 to drive the two ends of the load rail 12 to move along the pair of load-bearing slide rails 11, respectively. The load motor 15 is disposed between the load rail 12 and the load slider 13. In the present embodiment, the pair of load motors 11 may be linear motors and respectively disposed at both ends of the load rail 12, and the load motor 15 may be a linear motor and directly disposed on the load slider 13. In another embodiment, the pair of load-bearing motors 11 can be respectively disposed on the pair of load-bearing slide rails, and the two ends of the load rail 12 are driven by a worm or a leather belt, and the load motor 15 can be disposed at the load. On the slide rail, the load slider 13 is driven by the leather belt. Based on the above, the gantry positioning platform 10 can be regarded as a servo system having three degrees of freedom of mechanism coupling (bearing axes y1, y2 and load axis x).

2 is a schematic view of a bearing axis and a load shaft of the gantry positioning platform of FIG. 1. Referring to FIG. 1 and FIG. 2, the pair of carrier motors 14 output d _y1 and d _y2 corresponding to the two positions on the pair of bearing axes y1 and y2, respectively. When the two positions are the same (i.e., d _y1 = d _y2 ), this represents the synchronous movement of the pair of load-bearing motors 14, that is, both ends of the load rail 12 move synchronously on the pair of load-bearing slides 11. However, in practical applications, due to the difference in assembly of the load bearing motor 14 and the load motor 15, the external force interference or the coupling effect between the travels, it is quite difficult to achieve the synchronous motion response of the pair of loader motors 14.

In the present embodiment, in addition to considering the linear motion of the respective axes, the both ends of the load rail 14 due to the asynchronous movement of the pair of carriers 14 are simultaneously considered, thereby generating a rotational motion. When the pair of carrier motors 14 are not synchronized, as shown in Fig. 2, there is a deviation value between d _y1 and d _y2 . The mechanism coupling causes the load rail 12 to have an angular offset relative to the load axis x, which causes the load slider 13 to move toward the load rail 12 with a center point C (ie, between the ends of the load rail 12) The center point) produces a moment of inertia which results in a time varying inertia and load variation on the pair of load bearing motors 14 on the pair of load bearing axes y1.

Therefore, in the present embodiment, a dynamic model is established to control the pair of carrier motor 14 and load motor 15. In addition to considering the linear response of the three axes, the concept of moment of inertia is simultaneously modeled into this dynamic model, that is, the dynamic model contains the inertia matrix.

Before deriving the dynamic model, define the parameters in Figure 2, where M ₁ is the mass of the load axis stator (ie load rail 12); M ₂ is the mass of the load axis mover (ie load slider 13); L is the length of the load axis stator (ie, the load rail 12); 2 w is the width of the load axis stator (ie, the load rail 12); I ₁ and I ₂ represent the inertia of the load axis stator (ie, the load rail 12), respectively. The inertial kinetic energy of the kinetic energy and the load axis mover (ie, the load slider 13) is expressed as follows:

I ₂ = M ₂ ( d _x ² +( w + v ) ² ) (2)

And the centroid position of the load axis stator (ie the load rail 12) Centroid position with the load axis mover (ie load slider 13) They are defined as follows:

Where d _y = d _y1 +( d _y2 - d _y1 )/2. The (3) and (4) are differentiated, the load axis of the stator (i.e. the load rail 12) of the center of mass velocity v _M1 mover and a load axis (i.e., the load of the slider 13) of the center of mass velocity v _M2 are defined as follows:

According to equations (5) and (6), the total kinetic energy of the centroid of the load axis stator (ie load rail 12) and the load axis mover (ie load slider 13), including the kinetic energy and rotation The kinetic energy can be expressed as follows:

Then the total kinetic energy of the entire gantry positioning platform 10 can be re-displayed as follows:

Then sort (9) into a matrix type as follows:

Where X = [ d _y θ d _x ] ^T ; D is the inertia matrix, defined as follows:

According to the derivation of the Lagrange equation, the Governing Equation of the gantry positioning platform 10 can be expressed as follows:

Where L = K - V ; K is the total kinetic energy of the gantry type positioning platform 10; V is the total potential energy of the gantry type positioning platform 10; U is the torque matrix of each axis motor of the gantry type positioning platform 10; F is the friction Force matrix. Next, the values of the elements in the Coriolis and Centrifugal Force matrix (ie, the C matrix) can be expressed as follows:

among them , with Representing the differential terms of d _y , θ, and d _x , respectively. The Christoffel Symbols c _ijk can be calculated by the following calculations:

Where d _{ij is} expressed as an element of the i-th row and the j-th column in the inertia matrix D. Then the inertia matrix I ₁ and I ₂ are substituted into (11) and re-derivation of formula (14), the matrix C can be obtained as follows:

Finally, the matrix is rearranged, and the gantry dynamic model with gantry-type positioning platform can be expressed as DX + CX + BF = BU .

F = [ F _{y 1} , F _{y 2} , F _x ] ^T (17)

U =[ u _{y 1} , u _{y 2} , u _x ] ^T (18)

B is a coordinate transformation matrix; F _y1 , F _y2 and F _x are the frictional forces of the three axes (y1, y2, x) of the gantry type platform 12; u _y1 , u _y2 and u _x are respectively the gantry positioning platform 10 The torque of the three axes (y1, y2, x).

3 is a control architecture of a control device and the gantry positioning platform of FIG. 1 in accordance with an embodiment of the present invention. Referring to FIG. 2 and FIG. 3, the control device 100 of the present embodiment is applied to the gantry positioning platform 10, in particular, a pair of load bearing motors for controlling the gantry positioning platform 10 (ie, the y1 carrying motor 14a and the y2 carrying motor 14b of FIG. 3). And a load motor (ie x load motor 15a of Figure 3). The control device 100 utilizes a dynamic model to calculate and compensate for the transition command to generate a torque command, and transmits the torque command to the pair of carrier motors (ie, the y1 carrier motor 14a and the y2 carrier motor 14b of FIG. 3) and a load motor ( That is, the x load motor 15a) drives them. The dynamic model is established in accordance with the physical parameters of the gantry positioning platform 10. These physical parameters include the width of the load rail of the gantry positioning platform 10, the length of the load rail, the mass of the load rail, the mass of the load slider, and the distance from the center of mass of the load slider to the boundary of the load rail. .

Control device 100 includes a forward coordinate converter 110a that converts position commands (position errors) from a first coordinate space (y1, y2, x) to a second coordinate space (y, θ, x) in accordance with a dynamic model. To generate a transition position command, wherein the first coordinate space (y1, y2, x) contains the position of the pair of bearing axes y1 and y2 and the position of the load axis x, and the second coordinate space (y, θ, x) contains the pair Geometric center position of load bearing axes y1 and y2, offset of load axis x The angle θ and the geometric center position of the load axis x.

The control device 100 includes a set of position controllers including a y position controller 120a, a θ position controller 120b, and an x position controller 120c for converting a transition position command into a transition speed command.

The control device 100 includes a first reverse coordinate converter 110b that converts the speed feedback from the y1 carrier motor 14a, the y2 carrier motor 14b and the x load motor 15a into a transient speed feedback in accordance with a dynamic model, wherein the transition speed feedback is The transition speed commands are compared to produce a transition speed error.

The control device 100 includes a set of speed controllers including a y speed controller 130a, a θ speed controller 130b, and an x speed controller 130c for converting the transition speed error into a transition torque command.

The control device 100 includes a second reverse coordinate converter 110c that converts the transition torque command from the second coordinate space (y, θ, x) to the first coordinate space (y1, y2, x) in accordance with the dynamic model to generate a The torque command drives the y1 carrying motor 14a, the y2 carrying motor 14b and the x load motor 15a.

In an embodiment, the first inverse coordinate converter 110b and the second inverse coordinate converter 110c may be combined into a single inverse coordinate converter.

In this embodiment, the gantry positioning platform 10 further includes a set of position detectors and a set of speed estimators. The set of position detectors includes the y1 position detector 16a, the y2 position detector 16b and the x position detector 16c of FIG. 3, and the set of speed estimators includes the y1 speed estimator 17a, y2 speed estimator of FIG. 17b and x speed estimator 17c.

The set of position detectors (y1 position detector 16a, y2 position detector 16b and x position detector 16c) respectively detect y1 carrying motors 14a, y2 The position of the motor 14b and the x load motor 15a is generated to generate a position command. The set of speed estimators (y1 speed estimator 17a, y2 speed estimator 17b and x-speed estimator 17c) converts the position feedback from the position detector into speed feedback and input to the second reverse coordinate conversion The device 110c.

In order to eliminate the effects of the moment of inertia, the dynamic model contains at least an inertia matrix, such as the inertia matrix D disclosed above. In addition, the dynamic model may also comprise a Coriolis force and centrifugal force matrix, such as the C matrix disclosed above. Additionally, the dynamic model may also include a friction matrix, such as the F matrix disclosed above. In order to position commands from a first coordinate space (y1, y2, x) into a second coordinate space (y, θ, x), the dynamic model may include coordinate transformation matrix is, for example disclosed above coordinate transformation matrix B. In order to obtain the torque of the three axes (y1, y2, and x), the dynamic model may further include a torque matrix, such as the torque matrix U of each of the shaft motors of the gantry positioning platform 10 disclosed above.

4 is a control method of an embodiment of the present invention. Referring to FIG. 2, FIG. 3 and FIG. 4, the control method of this embodiment is applicable to the gantry positioning platform disclosed in FIG. 1 to FIG. In step S210, a dynamic model is established according to the physical parameters of the gantry positioning platform 10. These physical parameters include the width of the load rail of the gantry positioning platform 10, the length of the load rail, the mass of the load rail, the mass of the load slider, and the distance from the center of mass of the load slider to the boundary of the load rail. .

In step S220, the position command (position error) is converted from the first coordinate space (y1, y2, x) to the second coordinate space (y, θ, x) in accordance with the dynamic model to generate a transition position command. In this embodiment, the first coordinate space includes The pair positions the positions of the bearing axes y1 and y2 and the load axis x, and the second coordinate space contains the geometric center position of the pair of bearing axes y1 and y2, the offset angle θ of the load axis x, and the geometric center position of the load axis x . Such an action can be achieved by the forward coordinate converter 110a of FIG.

In step S230, the transition position command is converted into a transition speed command. Such an action can be achieved by the set of position controllers (y position controller 120a, θ position controller 120b, and x position controller 120c) of FIG.

In step S240, the speed feedback from the y1 carrier motor 14a, the y2 carrier motor 14b and the x load motor 15a is converted into a transition speed feedback according to the dynamic model, and such an action can be performed by the first inverse coordinate of FIG. The converter 110b is achieved. The transition speed feedback is compared to the transition speed command to produce a transition speed error.

In step S250, the transition speed error is converted into a transition torque command. Such an action can be achieved by the set of speed controllers of FIG. 3 (y speed controller 120a, θ speed controller 120b, and x speed controller 120c).

In step S260, the transition torque command is converted from the second coordinate space (y, θ, x) to the first coordinate space (y1, y2, and x) in accordance with the dynamic model to generate a torque command. Such an action can be achieved by the second inverse coordinate converter 110c of FIG.

In step S270, the y1 carrying motor 14a, the y2 carrying motor 14b and the x load motor 15a are driven in accordance with the torque command.

Likewise, in order to eliminate the influence rotational inertia caused by the dynamic model includes at least the inertia matrix, for example, disclosed hereinabove inertia matrix D. In addition, the dynamic model may also comprise a Coriolis force and centrifugal force matrix, such as the C matrix disclosed above. Additionally, the dynamic model may also include a friction matrix, such as the F matrix disclosed above. In order to convert the position command from the first coordinate space to the second coordinate space, the dynamic model may comprise a coordinate transformation matrix, such as the coordinate transformation matrix B disclosed above. In order to obtain the torque of the three axes (y1, y2, and x), the dynamic model may further include a torque matrix, such as the torque matrix U of each of the shaft motors of the gantry positioning platform 10 disclosed above.

A position command compensation method according to an embodiment of the present invention includes steps S210 to S260 of the control method disclosed in FIG. 4, and does not include the driving action of step S270.

In summary, the present invention establishes a dynamic model of the gantry positioning platform according to the physical parameters of the gantry positioning platform through full digitization and modularization, thereby increasing the convenience of the user in developing the control system. The invention can effectively model the synchronous motion response and the linear dynamic response between the three axes, so that the tracking error of each axis or the synchronous motion error between the bearing motors can be well controlled.

Although the present invention has been disclosed in the above embodiments, it is not intended to limit the invention, and any one of ordinary skill in the art can make some modifications and refinements without departing from the spirit and scope of the invention. The scope of the invention is defined by the scope of the appended claims.

10‧‧‧ gantry positioning platform

11‧‧‧Loading rails

12‧‧‧Load rails

13‧‧‧Load slider

14‧‧‧Bearing motor

14a‧‧‧y1 carrying motor

14b‧‧‧y2 carrying motor

15‧‧‧Load motor

15a‧‧‧x load motor

16a‧‧‧y1 position detector

16b‧‧‧y2 position detector

16c‧‧‧x position detector

17a‧‧‧1 speed estimator

17b‧‧‧y2 speed estimator

17c‧‧‧x speed estimator

100‧‧‧Control device

110a‧‧‧ forward coordinate converter

110b‧‧‧First reverse coordinate converter

110c‧‧‧Second reverse coordinate converter

120a‧‧‧y position controller

120b‧‧ θ position controller

120c‧‧‧x position controller

130a‧‧‧y speed controller

130b‧‧ θ speed controller

130c‧‧‧x speed controller

1 is a perspective view of a gantry type positioning platform to which the present invention is applied.

2 is a schematic view of a bearing axis and a load shaft of the gantry positioning platform of FIG. 1.

3 is a control architecture of a control device and the gantry positioning platform of FIG. 1 in accordance with an embodiment of the present invention.

4 is a control method of an embodiment of the present invention.

14a‧‧‧y1 carrying motor

14b‧‧‧y2 carrying motor

15a‧‧‧x load motor

16a‧‧‧y1 position detector

16b‧‧‧y2 position detector

16c‧‧‧x position detector

17a‧‧‧1 speed estimator

17b‧‧‧y2 speed estimator

17c‧‧‧x speed estimator

100‧‧‧Control device

110a‧‧‧ forward coordinate converter

110b‧‧‧First reverse coordinate converter

110c‧‧‧Second reverse coordinate converter

120a‧‧‧y position controller

120b‧‧ θ position controller

120c‧‧‧x position controller

130a‧‧‧y speed controller

130b‧‧ θ speed controller

130c‧‧‧x speed controller

Claims (13)

A control device is applicable to a gantry type positioning platform having a pair of load-bearing slide rails respectively extending along a pair of mutually parallel bearing axes, the two ends being respectively coupled to the pair of load-bearing slide rails and along the vertical a load rail extending to the load axis of the load axis, a load slider coupled to the load rail, a pair of load motors for driving the load rail to move on the pair of load rails, and a load motor for driving the load slider to move on the load rail, the control device comprising: a forward coordinate converter for converting a position command from a first coordinate space to a second coordinate according to a dynamic model The space is configured to generate a transition position command, wherein the dynamic model is established according to physical parameters of the gantry positioning platform, and the dynamic model includes an inertia matrix; a set of position controllers, converting the transition position command into a transition speed command; a first reverse coordinate converter converts a speed feedback from the pair of load carrying motors and the load motor into a transient speed according to the dynamic model a feedback, wherein the transition speed feedback is compared with the transition speed command to generate a transition speed error; a set of speed controllers to convert the transition speed error into the transition torque command; and a second reverse coordinate converter, The transition torque command is converted from the second coordinate space to the first coordinate space in accordance with the dynamic model to generate a torque command to drive the pair of load bearing motors and the load motor. The control device according to claim 1, wherein the dragon The physical parameters of the portal positioning platform include the width of the load rail, the length of the load rail, the mass of the load rail, the mass of the load slider, and the distance from the center of mass of the load slider to the boundary of the load rail. The control device of claim 1, wherein the first coordinate space comprises a position of the pair of bearing axes and a position of the load axis, and the second coordinate space comprises a geometric center position relative to the pair of bearing axes The offset angle of the load axis and the geometric center position of the load axis. The control device of claim 1, wherein the dynamic model further comprises a Coriolis force and a centrifugal force matrix. The control device of claim 1, wherein the first inverse coordinate converter and the second reverse coordinate converter are combined into a single reverse coordinate converter. A control method is applicable to a gantry type positioning platform having a pair of load-bearing slide rails respectively extending along a pair of mutually parallel bearing axes, the two ends being respectively coupled to the pair of load-bearing slide rails and along the vertical a load rail extending from the pair of load-bearing axes, a load slider coupled to the load rail, a pair of load-bearing motors for driving the load rail to move on the pair of load-bearing rails, and for driving the load a load motor moving on the load rail, the control method comprising: establishing a dynamic model according to physical parameters of the gantry positioning platform, wherein the dynamic model includes an inertia matrix; and a position command is performed according to the dynamic model Converting from a first coordinate space to a second coordinate space to generate a transition position command; Converting the transition position command to the transition speed command; converting a speed feedback from the pair of load bearing motors and the load motor into a transition speed feedback according to the dynamic model, wherein the transition speed feedback and the transition speed command Comparing to generate a transition speed error; converting the transition speed error into the transition torque command; converting a transition torque command from the second coordinate space to the first coordinate space to generate a torque command according to the dynamic model And driving the pair of load bearing motors and the load motor in accordance with the torque command. The control method according to claim 6, wherein the physical parameters of the gantry positioning platform include the width of the load rail, the length of the load rail, the mass of the load rail, the mass of the load slider, and the sliding from the load. The distance from the center of mass of the block to the boundary of the load rail. The control method of claim 6, wherein the first coordinate space includes a position of the pair of bearing axes and a position of the load axis, and the second coordinate space includes a geometric center position relative to the pair of bearing axes The offset angle of the load axis and the geometric center position of the load axis. The control method of claim 6, wherein the dynamic model further comprises a Coriolis force and a centrifugal force matrix. A position command compensation method is applicable to a gantry type positioning platform having a pair of load-bearing slide rails respectively extending along a pair of mutually parallel bearing axes, and two ends coupled to the pair of load-bearing slide rails respectively a load rail and a load slider coupled to the load rail, the position command compensation method includes: Establishing a dynamic model according to physical parameters of the gantry positioning platform, wherein the dynamic model includes an inertia matrix; and using the dynamic model to convert a position command from a first coordinate space to a second coordinate space to generate a transition position command; Converting the transition position command to the transition speed command; converting a speed feedback from the pair of load bearing motors and the load motor into a transition speed feedback according to the dynamic model, wherein the transition speed feedback and the transition speed command Comparing to generate a transition speed error; converting the transition speed error to the transition torque command; and converting a transition torque command from the second coordinate space to the first coordinate space to generate a torque according to the dynamic model command. The position command compensation method according to claim 10, wherein the physical parameters of the gantry positioning platform include a width of the load rail, a length of the load rail, a quality of the load rail, a quality of the load slider, and a The distance from the center of mass of the load slider to the boundary of the load rail. The position command compensation method of claim 10, wherein the first coordinate space includes a position of the pair of bearing axes and a position of the load axis, and the second coordinate space includes a geometry with respect to the pair of bearing axes The center position, the offset angle of the load axis, and the geometric center position of the load axis. The position command compensation method according to claim 10, wherein the dynamic model further comprises a Coriolis force and a centrifugal force matrix.