Re: mill threading, Acceleration, Axis

Mariss,

Again, very infighting! Looks like Door #3. "S-shaped curve (sine from
-pi/2 to pi/2 + 1)" gives the Sigmoid curve then? And this should be
the least likely to loose steps? I've used linear ramps before, seems
like they run out too fast.

I generated v/t from my acceleration calc routine, and generated PLC
code which I "pasted" into Vector. And yep, if I take it to the max
velocity, it's an 'S'. But, for my limited "top end", it's fairly
abrupt on the top! The 'S' shape is cut off (truncated) for slower
terminal velocities. And if I understand what I'm reading in the CY-545
doc's, It's true there too! So perhaps Dave's comment about generating
Sigmoid curves on the fly are the only way to fix it. Oh well.

I like the car analogy, except, don't you just HIT THE GAS? Oops! that
would be a REAL JERK!

Thanks,
Alan

Mariss Freimanis wrote:

>
> Hi,
>
> My 2 cents on the acceleration debate. To paraphrase an unamed
> notable who made this argument famous, "It depends on what your
> definition of 'best is' is."
>
> 1) Best for simplicity: Linear ramp
> 2) Best for shortest time to speed: First integral of the speed-
> torque curve.
> 3) Best for minimum "jerk factor": S-shaped ramp.
>
> 1) The best time to speed using a constant rate of acceleration is
> based on using 100% of the motor's available torque at the terminal
> speed. Since motor torque is much higher at the beginning of
> acceleration, this available torque goes unused.
>
> 2) A step motor speed-torque curve is a two-part curve; constant
> torque from zero speed to the motor's corner speed. The corner speed
> is where the motor's natural load-line is intersected. The motor's
> natural speed-torque curve is the 1/x function.
>
> Suffice it to say the motor torque is high at low speeds and low at
> high speeds. For the shortest time to speed, accelerate rapidly at
> first, then more gradually with increasing speed as torque falls off.
>
> The best fitting rate of acceleration is the speed-torque curve. The
> resultant velocity with time (velocity profile) will be the first
> integral of this curve.
>
> 3) Abrupt changes in acceleration induce ringing in the load. This is
> called the "jerk factor". Stated differently, the second derivative
> of the velocity is an infinate-impulse function.
>
> The best function for the acceleration ramp is the definate integral
> of sine from 0 to pi. The result is an S-shaped curve (sine from -
> pi/2 to pi/2 + 1). Since all higher order derivatives of the sine
> function are finite, the second derivative is also.
>
> By analogy, we unconsciously use S shaped acceleration curves to keep
> the second derivative finite in our everyday lives. Consider what you
> do when you see the traffic light turn red as you approach an
> intersection.
>
> The brakes are applied gradually at first, then harder to establish a
> constant rate of deceleration. As speed diminishes, the pressure on
> the brake pedal is gradually released until brake action and speed
> simultaneously arrive at zero.
>
> If the brakes are applied abruptly, (linear ramp) your head bobs
> forward until you adjust to force of deceleration. When the car comes
> to a stop, deceleration ceases and your head bobs backward because it
> was tensed against the suddenly absent deceleration.
>
> This is the "jerk" factor in action, 2nd derivative as well as the
> driver.
>
> Mariss