Sunday, May 26, 2013

Smooth Feedrate Envelopes for Motion Control, Part II

In the previous post, I derived equations for smooth feedrate control of stepper motors, claiming that by using a smoother feedrate envelope that the motors could be driven faster with less chance of skipping steps and losing position.

In this post, I demonstrate this with a real stepper motor and show that it actually does work: using the envelopes does actually prevent the motors from losing steps.  My test setup is a single NEMA 17 stepper, driven by one of my A4988 driver breakouts, which is controlled by an Arduino sketch running on the Arduino Due.  I'm using half-stepping on the motors, driven by a 200KHz timer interrupt step callback which decides whether or not to step based on the interpolated supplied delays for the start and end of each move.  The move itself approximates a square wave, first accelerating from a slow feedrate, then performing a constant speed portion, then decelerating back to the initial feedrate.

The video below shows the stepper being driven using a constant acceleration profile, which causes the kinks in the feedrate graph in my previous post. You can clearly see it moving around on the table and stalling frequently before it reaches the top speed.

In contrast, here is the result using the third-order cubic feedrate envelope for the same set of moves. The stepper is easily able to handle the top speed and jerks around considerably less on the table.  Of course this comes at a price, a higher pulse-frequency must be used to resolve the acceleration profile.

You can get the code I used for this from following link:, it includes a multi-axis DDA implementation suitable for use with timer-interrupts as well as the code for evaluating the feedrate envelopes.

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