What is this process called: Analog input, with a analog output with setpoint
It's just a control loop.  You can close the loop with a PID controller, but that is not the only choice.  What you described sounds most like a P controller that only uses the proportional (P) term.  That's basically the simplest possible control loop, and it can be sufficient for some applications.  When P control is not sufficient, usually some combination of I and D (integral and derivative) to improve the performance.  If that is  not enough, then you need to go study control theory.