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litwack@dccs.upenn.edu (Mark Litwack) writes:

>I've got some questions on micro-stepping
>a stepper motor.

>First, how is it accomplished?  My first guess
>is that you would step the current in the active phase
>down a little bit as you stepped up the current in
>the next phase.  This would make the armature sit
>rotationally between the two phases.  Is this right?

Yes.


>If so, is there a linear relationship between the current
>in the two phases and the rotational position?  I.e.,
>if I applied 2/3 the current to phase A and 1/3 the current
>to phase B, would the armature sit 1/3 step away from A?
>If not, I guess I would have to use some kind of rotational
>feedback.

No. The current applied to each winding varies cosinusoidally
with the intended position where torque is proportional to
phase current, and the phase torque varies sinusoidally with
rotor position. Here's more detailed explanation if you're
into math:
Assume that TA = peak static torque at phase A
	    TB = ........................... B
	    iA = current at phase A
	    iB = ................ B
	     p = rotor teeth the motor has
	     a = intended position
	 theta = rotor displacement from one step position

Then,		 TA = -k iA Sin(p*theta)
		        T
		 TB = -k iB Sin(p*theta - pi/2)
			T
Note: Positive and negative currents are used to give a step length of
      pi/(2p) on each excitation.


And,
		 iA = I Cos(a)
		 iB = I Cos(a - pi/2)

The total torque T, from TA + TB, is equal to -k I Sin(p*theta -a)
						T
and the equilibrium position where load torque=0 is theta = a/p.

Therefore, we can control the rotor position anywhere (depending on the
resolution of the microstep) between the full-step position.
One should be aware of the accuracy if both the resolution  and the
load torque are high. Then you must use position feedback sensors.
For example: A system having 50,000 steps/rev can have +/- 50 - 100
microstep position errors if load torque is large enough.

I'm trying to be as accurate as possible, but please correct me if something
is wrong.


>Any good suggestions for micro-stepping controllers
>(chips, hybrids, board level)?

Not that I know of. There are full / half-step controllers out there on a
chip, just add drivers. If you really want to build a microstepper,
you can design it yourself using any single-chip processor and use a
lookup table for each microstep current, and use chopper driver to get
an optimum current at any position.

If anybody knows of such controller, please let me know.
Thank you.

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