Stepper Mid-band stabilization, formerly: Gecho 210 step multiplier

Interesting, Mariss. I thought I read somewhere that half- and microstepping
eliminated or reduced exciting the system into mid-band resonance. Thanks
for the great technical description. I still find this stuff fascinating.
I've done disk servo PID loops, and industrial PMAC servo systems years ago,
but nothing with steppers.

I'll leave the (stepper) driving to you!

Regards,

Paul R. Hvidston, N6MGN
ACKSYS Engineering
Upland, CA

----- Original Message -----
From: "mariss92705" <mariss92705@...>
To: <CAD_CAM_EDM_DRO@yahoogroups.com>
Sent: Monday, February 25, 2002 7:14 PM
Subject: Gecho 210 step multiplier, was Re: [CAD_CAM_EDM_DRO] Stepper Math


> Paul,
>
> Mid-band stabilization (parametric resonance) is an entirely
> different animal. Here's the cause and the cure:
>
> THE CAUSE:
>
> A step motor is a first-order resonant system, also called a mass-
> spring system. What characterizes first-order systems is (in
> mechanical systems) a 90 degree phase lag between force and velocity.
> Velocity is at maximum when force is zero and visa versa in a
> resonating mass-spring system.
>
> Now enter the drive. At low speeds the drive is a current source
> (infinite impedence) and effectively is an open circuit to the
> winding back EMF. The drive contributes 0 degrees phase shift to the
> system.
>
> Above some speed (corner speed), the drive transitions from a current
> source to a voltage source. A voltage source has (ideally) 0
> impedence and effectively shorts the winding back EMF. This adds an
> additional 90 degree phase shift, making the total 180 degrees now.
> This is a setup for undamped oscillation and that is exactly what
> happens. The motor will break out into an oscillation that builds in
> amplitude until the motor stalls (+/- 2 full steps mechanical).
>
> THE CURE:
>
> Reduce the system phase lag by adding a phase lead component.
> Everyone has seen what a car does with bad/missing shock absorbers.
> More properly called rate or viscous dampers, they introduce second-
> order damping to quickly damp out oscillation. Adding a phase lead
> requires a derivative component and "rate" is the derivative of
> position. A rate damper provides a resistive force proportional to
> velocity.
>
> A cheaper way to the same goal is to do it electronically. The rate
> of motor load change (acceleration) is sensed and bandpass amplified.
> This signal then phase modulates the step pulses by retarding or
> advancing their timing in the drive. This prevents the motor from
> resonating, so all of its torque is now available for the load.
>
> Mariss