Pressure control is already an integrating process. You should need little if any integrator. A little may be required to adjust for offset.
Feed forwards should be proportional to the rate of change in the pressure, not the pressure itself because pressure control is an integrating process.
DON'T USE ZN TUNING FOR THIS!!! If ZN is tuned right it will overshoot and oscillate a few times.
I think you are expecting to change the pressure faster than what is possible. It takes time to get the air into and out of the cylinder. During this time the integrator winds up and then must overshoot to wind down. You should turn the integrator down or off unless you plan to ramp the pressure slowly so the integrator will not see the huge error and over react.
Feed forwards should be proportional to the rate of change in the pressure, not the pressure itself because pressure control is an integrating process.
Shane called it feed forward but it really is a bias needed to get the SLC PID to operate 'bipolar'. I don't think he is really doing true feed forward control.
I'm still trying to get a full handle on all the components Shane has here and where they all are. But I think he has two small flow valves that are controlling the pressure in the pilot cavity of an air piloted regulator. He has no actual feedback of this pressure. The air piloted regulator feeds his tank. He has actual feedback from the tank. So, Peter, depending on where you stop looking, this may or may not be an integrating processs from the standpoint of the control signal. Between the small valves and the pilot operated regulator it is an integrating process. Between the regulator and the tank it is a first order non-integratng process as the output pressure in the tank will stop climbing once the tank pressure reaches the regulator pilot pressure (within the accuracy of the regulator). It looks like an integrating process to the PI controller but it will have an additional delay element in it. I suspect the regulator pilot chamber can charge much faster than than the tank.
As I said before I would have changed out to a straight flow valve and directly controlled that. It removes one control element and lets you directly control what you are really trying to control.