Hmm no I had no decoupling capacitor. I had it on a breadboard and left it out. It should go between GND and VCC pins, right?
I will try it out later. Thanks for your help!
Edit: ShiftPWM works good now, I think I am going to stay with that.
But the output seems kind of flickering to me, even with 100Hz. Maybe it's too high for the Arduino and it is missing some interrupts (Which I think should not be the case, as the lib returns a load of 25% for the interrupts...) or I am hallucinating
Hopefully the guy in the laboratory allows me to use one of the logic analyzers so I can check this