I will copy your code into IDE and study it to see what sense I can make of it. Although I am not educated in this area, I do obsess over things till i understand them (or at least to a point that gets me what I need).
At first I found both 'p' and 'd' values to be too sensitive to use and focused on the 'i' value. At first setting it to 5-10 and leaving p&d at zero, gave me the smoothest increase in pressure with the least pulsing. The issue is though that I need to produce up to 4200psi and currently am only able to steadily produce 1000psi at best before it starts slamming the valve.
I am now running p=10, i=75, and d=0.001 with probably the smoothest operation yet, but still only able to reach just over 1000psi before the valve starts slamming and the pressure fluctuates massively. Below is a link to a short video of the pressure banging and the machine that this pressure system is used in.
As you can see in the video, the end result is firing a HEUI diesel injector. HEUI injectors use an intensifier piston (using oil pressure) to mechanically increase the fuel pressure by 7 times. The intensifier piston has 7 times greater surface area than the fuel plunger. So at full oil pressure (4200psi) fuel pressure at the nozzle is approximately 29,400psi before losses.
To answer your question of how fast can it build pressure; I do not have a means to measure it, but I can say the pilot valve responds so fast I can peg out the 5000psi gauge instantly with the wrong PID settings. The oil pump (hydraulic pump) moves 0.37 In^3 per revolution and we are running at approximately 1440RPM, moving roughly 532 in^3 or 2.3 gallons per minute. When the injector fires it obviously consumes a small amount of oil, depending on the size of injector it can consume as much as 0.35in^3 per injection which the maximum injection event is 2.3 miliseconds. Our goal is to fire 4 injectors in sequence.
Hopefully I explained everything well enough, if anyone needs clarification, just ask.
-Jon