I'm happy to see your channel, I'm just giving a suggestion so that you can also show the advantages of the circuit model you put forward, and don't forget to give an overview of the disadvantages of the circuit you are making, and make an alternative using other components for the same purpose in your circuit.
6:59 You have a bit of a misunderstanding here. Yes, that circuit is completely worthless because you should never build a differentiator, and real PID circuits use lead-lag filters. Your demonstration also doesn't make sense because this is SPICE, where noise is limited to the floating point quantization. That output is not because of noise, it's because you just added a low frequency pole in the feedback path of an op-amp. You have reduced the phase margin on your op-amp basically to 0, and you are seeing the poor stability as a highly underdamped response. Adding a feedback capacitor means that you form a capacitive voltage divider at high frequencies (near crossover) with little phase and a reasonable feedback factor, fixing the instability.
