So I got a reply back from Alicat about what those control registers mean. Turns out the documentation is spotty for a reason, the algorithm they use to control the valve is proprietary so they cannot reveal the details. However, they could describe things roughly by an analogy:
"Address 21 (or the P value) can be considered as the gas pedal in a car, the harder you push it (raise its value) the faster the valve will operate.
Address 22 (the D value) can be considered the brakes, the more the brakes are applied (raise its value) the faster the valve will stop at its set point.
Finding a balance between these two values is crucial when trying to achieve an optimal response and accuracy from the valve.
Address 23 ( the integral value) is a bit undefined…and rarely used. It’s a value completely unique to the valve on the device, I guess to keep the analogy alive you can say that the I value is like the gear ratios within a gear box. The farther spread out the ratios are, (the larger the I value) the overall stability is increased, but the acceleration suffers. Conversely, the closer together the ratios become (the smaller the I value) acceleration is increased but overshoot and instability can become a major issue.
Keep in mind that too high a value in any of these categories can and will cause overshoot/undershoot/oscillation, so when tuning start at a base number, write those base values down and increase and decrease in small increments."
I guess I will just play with the settings to get the performance that I need! Thanks Alicat!