Actually, all of that is probably irrelevant, although it might provide rough guidance. Peter Nachtwey's answer, that it is linear enough, is the best. I think the suggestion behind that is that you can set up your process to a stable state, with the pump running on manual at a speed that maintains the DP at, say, 18PSI. Take note of the speed setting. Then change the speed up manually and gradually until the DP is 22 PSI, and take note of that speed setting. Now drop the speed back to the setting that yielded 18PSI in a single step, and log how the DP responds. That is your characteristic response, and, though very rough, from there you should be to able apply any of several algorithms* to set some initial PID parameters.
Because without knowing the process, none of us can "explain [... the] relation [between] DP and pump speed."
Also, controlling pressure with pump speed is, as parky suggested, rare, even for a VFD.
* The best would be to send Peter or someone similar a purchase order
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