Stoping PID for stepper motor

Hello. Im working in my DIY 120x60 co2 laser (tube is moving with head).
What I have now is 2 stepper motors on Y axis and have problem here. When Y axis moving stopping there is kind of oscilation and head goes a bit more behind the desired position. You can see on the photo here:
10mm/sec
(green arrows is start point and direction, red arrow the problem)


When it is 20mm/sec you can see it is better, and also the tail of oscilation when it goes X axis.

Is it possible to fix it by some kind of PID, so it reduce speed slowly before the stop, and not stop with the like a bump like it is now.

You are asking if you should fix a mechanical problem with software. Mechanical has to be right so the software can do its job.

Fix this first. Make sure the head is rigidly mounted. One of my lasers has a Zaxis adjuster. On a fine positioning stress test, I see wiggles, but it does not show in the everyday work. You need to get to this point in your mounting.

Then fine tune everything with the software.

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