Methods and systems for controlling a multiphase electromagnetic machine

1. A method for controlling a multiphase electromagnetic machine, the method comprising:

determining, using processing equipment, a position of a translator relative to a stator, wherein the translator is configured to translate relative to the stator, and wherein the stator comprises a plurality of windings forming a plurality of phases;

determining, using processing equipment, a set of force constants corresponding to the phases based at least in part on the position;

determining, using processing equipment, a set of current values applied to the phases based at least in part on the force constants, on a desired electromagnetic force, and on at least one objective function and at least one constraint; and

applying the set of current values to the phases.

2. The method of claim 1 , wherein the determining the set of current values further comprises optimizing the at least one objective function subject to the at least one constraint.

3. The method of claim 1 , wherein the at least one objective function is selected from the group consisting of a sum of ohmic losses, a sum of the absolute values of the set of current values, a difference between the desired electromagnetic force and an actual electromagnetic force, and a combination thereof.

4. The method of claim 1 , wherein the at least one constraint is selected from the group consisting of a predetermined value of the sum of the set of current values, a predetermined value of at least one current value of the set of current values, an allowable range of at least one current value of the set of current values, an allowable range of temporal change values for a temporal change in at least one current value of the set of current values, and a combination thereof.

5. The method of claim 1 , wherein the plurality of phases comprises at least four phases, and wherein the set of force constants comprises at least four force constants corresponding to the at least four phases.

6. The method of claim 1 , wherein the plurality of phases comprises at least three phases, and wherein the set of force constants comprises at least three force constants corresponding to the at least three phases, the method further comprising determining a current value corresponding to a directly controlled virtual phase, wherein the virtual phase has an associated force constant of substantially zero.

7. The method of claim 1 , wherein the plurality of phases comprises at least three phases, and wherein the set of force constants comprises at least three force constants corresponding to the at least three phases, the method further comprising determining a current value corresponding to an indirectly controlled virtual phase, wherein the virtual phase has an associated force constant of substantially zero.

8. The method of claim 1 , further comprising determining the desired electromagnetic force based at least in part on the position.

9. The method of claim 1 , further comprising determining, with the processing equipment, a magnetic flux in the translator, wherein the determining the set of current values is further based at least in part on the magnetic flux.

10. A method for controlling a multiphase electromagnetic machine, the method comprising:

determining a position of the translator relative to the stator,

wherein the stator comprises a plurality of windings forming a plurality of phases;

determining, using processing equipment, a set of force constants corresponding to the phases based at least in part on the position;

selecting at least one objective function;

selecting at least one constraint;

determining, using processing equipment, a set of current values based at least in part on the set of force constants, a desired electromagnetic force, the at least one objective function, and the at least one constraint; and

applying the set of current values to the phases.

11. The method of claim 10 , further comprising determining, using the processing equipment, whether the set of current values is acceptable.

12. The method of claim 11 , further comprising selecting, using the processing equipment, at least one of a new objective function and a new constraint if it is determined that the set of current values is not acceptable.

13. The method of claim 11 , further comprising adjusting one constraint of the at least one constraint if it is determined that the set of current values is not acceptable.

14. The method of claim 11 , further comprising adjusting the desired electromagnetic force if it is determined that the set of current values is not acceptable.

15. The method of claim 11 , further comprising removing a constraint of the at least one constraint if it is determined that the set of current values is not acceptable.

16. A system for controlling a multiphase electromagnetic machine, the system comprising:

a power subsystem configured to apply current to a plurality of windings forming a plurality of phases of a stator;

a position sensor coupled to the electromagnetic machine, the position sensor configured to sense a position of the translator relative to the stator; and

processing equipment coupled to the power electronics and the position sensor, the processing equipment configured to:

determine a position of a translator relative to the stator based on output of the position sensor,

determine a set of force constants corresponding to the phases based at least in part on the position, and

determine a set of current values to be applied by the power subsystem to the phases based at least in part on the set of force constants, on a desired electromagnetic force, and on at least one objective function and at least one constraint.

17. The system of claim 16 , wherein the plurality of phases comprises at least four phases, and wherein the set of force constants comprises at least four force constants corresponding to the at least four phases.

18. The system of claim 16 , wherein the plurality of phases comprises at least three phases, and wherein the set of force constants comprises at least three force constants corresponding to the at least three phases, and wherein the power subsystem further comprises a directly controlled virtual phase, and wherein the processing equipment is further configured to determine a current value corresponding to the directly controlled virtual phase, wherein the virtual phase has an associated force constant of substantially zero.

19. The system of claim 16 , wherein the plurality of phases comprises at least three phases, and wherein the set of force constants comprises at least three force constants corresponding to the at least three phases, and wherein the power subsystem further comprises an indirectly controlled virtual phase, and wherein the processing equipment is further configured to determine a current value corresponding to an indirectly controlled virtual phase, wherein the virtual phase has an associated force constant of substantially zero.

20. The system of claim 16 , wherein the processing equipment is further configured to determine the desired electromagnetic force based at least in part on the position.

21. The system of claim 16 , wherein the at least one objective function is selected from the group consisting of a sum of ohmic losses, a sum of the absolute values of the set of current values, a difference between the desired electromagnetic force and an actual electromagnetic force, and a combination thereof.

22. The system of claim 16 , wherein the at least one constraint is selected from the group consisting of a predetermined value of the sum of the set of current values, a predetermined value of at least one current value of the set of current values, an allowable range of values of at least one current value of the set of current values, an allowable range of temporal change values of a temporal change in at least one current value of the set of current values, and a combination thereof.

23. The system of claim 16 , wherein the processing equipment is further configured to perform an optimization of the at least one objective function subject to the at least one constraint to determine the set of current values.

24. The system of claim 16 , wherein the processing equipment is further configured to determine a set of pulse width modulation values corresponding to the plurality of phases based at least in part on the set of current values.

25. A non-transitory computer readable medium storing computer executable instructions that, when executed by at least one processor, cause a computer system to carry out a method for controlling a multiphase electromagnetic machine, the method comprising the steps of:

determining, using processing equipment, a position of a translator relative to a stator, wherein the translator is configured to translate relative to the stator, and wherein the stator comprises a plurality of windings forming a plurality of phases;

determining, using processing equipment, a set of force constants corresponding to the phases based at least in part on the position; and

determining, using the processing equipment, a set of current values applied to the phases based at least in part on the set of force constants, on a desired electromagnetic force, and on at least one objective function and at least one constraint.