Identifying and compensating force-ripple and side-forces produced by linear actuators

• US 20080067968A1
• Filed: 09/12/2007
• Published: 03/20/2008
• Est. Priority Date: 09/12/2006
• Status: Abandoned Application

• Current Assignee: Nikon Corporation
• Original Assignee: Nikon Corporation
• Inventors: Binnard, Michael, Coakley, Scott
• Application Number:
  US11/900,916
• Publication Number:
  US 20080067968A1
• Time in Patent Office: Days
• US Class Current: 318/687
• CPC Class Codes: H02P 25/06 Linear motors
• CPC Class Codes: H02P 25/064 of the synchronous type

Abstract

Methods are disclosed for operating at least one commutated actuator (generally termed a “linear actuator”) while compensating for error-inducing phenomena such as force-ripple and side-force. An exemplary method includes determining a set of commutation equations that substantially provide desired forces for the actuator in one or more directions. A map is generated of actual forces produced by the actuator in the one or more directions in proportion to coefficients of the commutation equations. Corrected commutation coefficients are determined from the desired forces and the map of actual forces. Electrical current is applied to the actuator using the commutation equations with the corrected coefficients. The methods are applicable to actuators having one degree of freedom (DOF) of motion or multi-DOF actuators, and are applicable to actuators that run on single-phase power or multi-phase power.

Claims

1. A method for operating a commutated actuator, comprising:

determining a set of commutation equations that substantially provide desired forces for the actuator in one or more directions;

generating a map of actual forces produced by the actuator in the one or more directions in proportion to coefficients of the commutation equations;

calculating corrected commutation coefficients determined from the desired forces and the map of actual forces; and

applying electrical current to the actuator using the commutation equations with the corrected coefficients.

2. The method of claim 1, wherein the actuator is a 1DOF linear actuator, a multi-DOF linear actuator, or a multi-DOF planar actuator.

3. The method of claim 1, wherein:

the actuator operates on multi-phase power; and

applying electrical current to the actuator comprises applying respective phase currents to the actuator.

4. The method of claim 1, wherein calculating corrected commutation coefficients is performed by a first-order method involving adding or subtracting compensation terms.

5. The method of claim 4, wherein the first-order method comprises:

determining nominal values for commutation current(s) according to one or more predetermined force constants such as motor constants;

obtaining corrected commutation currents by adding or subtracting, from the nominal values, at least one term involving a force constant; and

commutating the corrected commutation currents to the phase currents supplied to the actuator.

6. The method of claim 5, wherein:

the actuator is at least a 2DOF actuator providing controlled motions in at least the y-direction and z-direction;

adding or subtracting adjustment terms is performed according to;

$I_{y,\mathrm{corrected}}=I_{y,\mathrm{nom}}-\left(\frac{\mathrm{MapYY}}{K_{F_y}}-1\right)<br><br>I_{y,\mathrm{nom}}-\mathrm{MapZY}*\frac{I_{z,\mathrm{nom}}}{K_{F_y}}$$I_{z,\mathrm{corrected}}=I_{z,\mathrm{nom}}-\mathrm{MapYZ}*\frac{I_{y,\mathrm{nom}}}{K_{F_z}}-\left(\frac{\mathrm{MapZZ}}{K_{F_z}}-1\right)<br><br>I_{z,\mathrm{nom}}$

in which I_y corrected is a corrected commutation current for movement in the y-direction, I_z,corrected is a corrected commutation current for movement in the z-direction, I_y,nom is a nominal commutation current for movement in the y-direction, I_z,nom is a nominal commutation current for movement in the z-direction, MapYY is an influence function representing actuator force output along the y-direction in response to a unit commutation current I_y directed to produce a resultant force of the actuator along the y-direction, MapYZ is an influence function representing actuator force output along the z-direction in response to the unit commutation current I_y, MapZY is an influence function representing actuator force output along the y-direction in response to a unit commutation current I_z directed to produce a resultant force of the actuator along the z-direction, MapZZ is an influence function representing actuator force output along the z-direction in response the unit commutation current I_z, K_Fy is a force constant denoting a ratio of resultant force along the y-direction to a constant commutation force-command directed to produce a force substantially along the y-direction, and K_Fz is a force constant denoting a ratio of resultant force along the z-direction to a constant commutation force-command directed to produce a force substantially along the z-direction; and

$I_{y,\mathrm{nom}}=\frac{F_{y,\mathrm{desired}}}{K_{F_y}}$$I_{z,\mathrm{nom}}=\frac{F_{z,\mathrm{desired}}}{K_{F_z}}$

in which F_y,desired and F_z,desired are respective desired force components for achieving correction.

7. The method of claim 5, wherein the actuator is a 1DOF linear actuator, a multi-DOF linear actuator, or a multi-DOF planar actuator.

8. The method of claim 5, wherein the actuator operates on multi-phase power.

9. The method of claim 1, wherein calculating corrected commutation coefficients is performed by an iterative process of further refinement.

10. The method of claim 9, wherein the interative process comprises obtaining corrected commutation currents calculating a predetermined number of iterations of calculations used to determine the corrected coefficients, wherein each subsequent iteration is performed using the result of the previous iteration.

11. The method of claim 10, wherein:

the actuator is at least a 2DOF actuator providing controlled motions in at least the y-direction and z-direction;

the iterative process is performed according to;

$I_{y,j+1}=I_{y,j}-\left(\mathrm{MapYY}-K_{F_y}\right)*\frac{I_{y,j}-I_{y,j-1}}{K_{F_y}}-\mathrm{MapZY}*\frac{I_{z,j}-I_{z,j-1}}{K_{F_y}}$$I_{z,j+1}=I_{z,j}-\left(\mathrm{MapZZ}-K_{F_z}\right)*\frac{I_{z,j}-I_{z,j-1}}{K_{F_z}}-\mathrm{MapYZ}*\frac{I_{y,j}-I_{y,j-1}}{K_{F_z}}$$j=1,N$$I_{y,-1}=0;<br><br>$$I_{y,0}=\frac{{\mathrm{Fy}}_{\mathrm{desired}}}{K_{F_y}};<br><br>$$I_{z,-1}=0;<br><br>$$I_{z,0}=\frac{{\mathrm{Fz}}_{\mathrm{desired}}}{K_{F_z}}$

in which MapYY is an influence function representing actuator force output along the y-direction in response to a unit commutation current I_y directed to produce a resultant force of the actuator along the y-direction, MapYZ is an influence function representing actuator force output along the z-direction in response to the unit commutation current I_y, MapZY is an influence function representing actuator force output along the y-direction in response to a unit commutation current I_z directed to produce a resultant force of the actuator along the z-direction, MapZZ is an influence function representing actuator force output along the z-direction in response the unit commutation current I_z, K_Fy is a force constant denoting a ratio of resultant force along the y-direction to a constant commutation force-command directed to produce a force substantially along the y-direction, and K_Fz is a force constant denoting a ratio of resultant force along the z-direction to a constant commutation force-command directed to produce a force substantially along the z-direction, and F_y,desired and F_z,desired are respective desired force components for achieving correction.

12. The method of claim 10, wherein the actuator is a 1DOF linear actuator, a multi-DOF linear actuator, or a multi-DOF planar actuator.

13. The method of claim 10, wherein the actuator operates on multi-phase power.

14. The method of claim 1, wherein calculating corrected commutation coefficients is performed by a matrix method, in which the map comprises of a square matrix at each of a plurality of locations, and calculating corrected commutation coefficients comprises inverting the matrix.

15. The method of claim 14, wherein:

an actuator map is produced that reflects the number of commutation currents required by the actuator, the actuator map defining influence functions determined for a plurality of positions of the actuator, the influence functions describing force components of the actuator relative to respective commutation currents;

the functions are arranged in a square matrix at each of a plurality of positional locations produced by the actuator; and

calculating corrected commutation coefficients comprises inverting the matrix.

16. The method of claim 12, further comprising interpolating the calculated corrected commutation coefficients for respective positions between the plurality of locations.

17. A method for controllably operating a linear actuator, comprising:

producing a set of commutation force-commands for displacing a mover of the actuator;

commutating the mover along at least a first direction according to the commutation force-commands;

determining at least one force constant for the linear actuator being commutated according to the commutation force-commands, the at least one force constant relating, at least in part, position-dependent force variations to one or more of the commutation force-commands;

modulating the commutation force-commands according to the at least one force constant to produce modulated force-commands that compensate for position-dependent force variations along the first direction and for position-dependent force variations in a second direction orthogonal to the first direction; and

driving the linear actuator according to the modulated force-commands.

18. The method of claim 17, wherein the force constant incorporates a matrix including influence functions, including a first influence function that relates influence of the first commutation force-command to a force-component of the actuator along the first direction, a second influence function that relates influence of the first commutation force-command to a force-component of the actuator along the second direction, a third influence function that relates influence of the second commutation force-command to the force-component of the actuator along the first direction, and a fourth influence function that relates influence of the second commutation force-command to the force-component of the actuator along the second direction.

19. The method of claim 17, wherein:

determining the at least one force constant further comprises multiplying resultant forces, produced by the commutation force-commands, by an inversion of the matrix; and

modulating the commutation force-commands produces modulated force-commands that are functions of actuator position and a product of multiplying the desired resultant forces by the inversion of the matrix.

20. The method of claim 17, wherein the actuator is a 1DOF linear actuator, a multi-DOF linear actuator, or a multi-DOF planar actuator.

21. The method of claim 17, wherein the actuator operates on multi-phase power.

22. A method for controllably operating a linear actuator, comprising:

selecting multiple commutation equations for the linear actuator, including a first commutation equation for movement of the actuator along a first axis, and a second commutation equation for movement of the actuator along a second axis;

determining respective maps of position-dependent forces produced while commutating the linear actuator along the first axis according to the first commutation equation, the forces including a force along the force axis and a force along the second axis;

determining, from the maps, respective position-dependent influence functions;

from the influence functions, determining respective compensating force-commands;

determining position-dependent compensation currents to produce desired forces along the first axis and desired forces along the second axis; and

driving the linear actuator using the position-dependent compensation currents.

23. The method of claim 22, wherein:

the linear motor is a multi-phase linear motor; and

the method further comprises converting the force-commands to corresponding phase commands, and commutating the linear actuator, according to the phase commands.

24. A method for controllably operating a multi-DOF linear actuator, comprising:

selecting multiple commutation force-commands for the actuator, including a first commutation force-command being for movement of the linear actuator along a first axis and a second commutation force-command being for movement of the linear actuator along a second axis that is orthogonal to the first axis;

commutating the linear actuator according to the first and second force commands;

determining respective maps of position-dependent forces produced while commutating the linear actuator along the first and second axes, the forces including an output force along the first axis and an output force along the second axis;

determining, from the maps, respective force coefficients for multiple positions of the linear actuator along the first axis and second axis;

defining corrected commutation currents from the force coefficients; and

driving the actuator using the corrected commutation currents.

25. A method for controlling operation of a multi-DOF linear actuator including at least a primary magnet-coil array and a secondary magnet-coil array, the method comprising:

directing a force-command to the primary magnet-coil array to drive the linear actuator using the primary magnet-coil array;

causing the actuator to produce a resultant force including compensations for position-dependent force variations along a first axis and compensations for position-dependent force variations along a second axis orthogonal to the first axis; and

modulating a force-command to the secondary magnet-coil array to produce a force substantially along the second axis that is equal in magnitude and opposite in direction to a side-force resulting, at least in part, from the force-command to the primary magnet-coil array, to produce a force substantially along the first axis.

26. With respect to a selected at least one linear actuator in a set of actuators, a method for producing a predetermined force constant for compensation of at least one of force-ripple and side-force relative to a stroke-direction of the selected at least one actuator, the method comprising:

supplying a first commutation force-command directed to the selected at least one actuator to displace the selected at least one actuator through a first trajectory substantially along a first axis;

determining a component of a first resultant force of the selected at least one actuator in a direction along the principal axis and a component of the first resultant force along a second axis, that is orthogonal to the first axis, at each of a plurality of locations along the first axis;

supplying a second commutation force-command directed to the actuator to displace the linear actuator through a second trajectory, the second commutation force-command being linearly independent of the first commutation force-command;

determining a component of the second resultant force of the actuator along the first axis and a component of the second force of the actuator along the second axis at each of the plurality of locations;

determining, for each location, multiple force coefficients, including

a first force coefficient relating the influence of the first commutation force-command to the force component of the actuator along the first axis;

a second force coefficient relating the influence of the first commutation force-command to the force component of the actuator along the second axis;

a third force coefficient relating the influence of the second commutation force-command to the force component of the actuator along the first axis; and

a fourth force coefficient relating the influence of the second commutation force-command to the force component of the actuator along the second axis.

27. The method of claim 26, further comprising:

for each location, inverting a two-dimensional matrix defined at least by the four force coefficients; and

storing each inverted two-dimensional matrix.

28. The method of claim 27, further comprising:

determining a first principal influence coefficient as a ratio of a component of resultant force along the first axis to a constant commutation force-command directed to substantially produce a force along the first axis; and

determining a second principal influence coefficient as a ratio of a component of resultant force along the second axis to a constant commutation force-command directed to substantially produce a force along the second axis.

29. A commutated actuator system, comprising:

an actuator comprising a stator and a moving member magnetically coupled to the stator;

a driver coupled to one of the stator and moving member, the driver being configured to energized the one of the stator and moving member to which the driver is coupled, to cause movement of the moving member relative to the stator in one or more directions; and

a processor coupled to the driver, the processor being programmed with (a) corrected commutation equations by which forces are provided to the actuator for moving the moving member in a desired at least one direction, and (b) a calculation routine that, from a map of actual forces produced by the actuator in one or more directions and in proportion to coefficients of the commutation equations, calculates the corrected commutation coefficients for delivery to the driver.

30. The actuator system of claim 29, wherein the actuator is a 1DOF linear actuator, a multi-DOF linear actuator, or a multi-DOF planar actuator.

31. The actuator system of claim 29, wherein the actuator operates on multi-phase power.

32. The actuator system of claim 31, wherein the actuator is nominally symmetric with respect to an axis but includes a respective deliberate assymmetry.