Been brushing up on my control systems knowledge and I keep seeing that a P controller WILL NOT have 0 error and that doesn't make sense to me.
Imagine a tank problem, the setpoint is 50 cm, you open the drain valve and the level goes down to 49. Controller output goes up and you start putting water into the tank. Controller output does not go to 0 until the level is back to 50. So while this may take a while if your Kp is low, it will get there.
I understand that steady-state error is not measured at infinite time but the idea that a P controller will not reach the SP is odd to me.