Mark, there's lots of ways to skin a cat, and I don't know the pump, valve and system curves, but I would tend to keep control variables localized and move them to the suction headers rather than introduce time lags with remote transmitters.
The way you have it now, assuming the first PT is maintaining a minimum suction pressure at pump group 2, there may be a couple of control limits you need to look at.
Suction pressures at pump group 1 could go below minimum suction pressure (NPSHR) as P1 goes moves to a higher RPM to supply increased pressure to P2
Assuming the group 2 PTs are maintaining minimum pressures on the process, they will increase P2 speed and reduce suction pressure at P2. If P1 can't keep up with its setting as before, once again P1 and now P2 will go below min NPSHR.
If the FCV setting is too high for any given flow the pumps and upstream portion of the system can supply at any time, according to their current RPMs, the system pressures will reduce until possibly minimum process pressure is lost. So a maximum FCV flow setting should be determined such that minimum process pressure is always maintained. That may require that you find a max FCV setting that is permissible for each combination of RPMs at group 1 and 2 pumps.
If PTs are set to maintain minimum pressures, maximum pipe pressures might be exceeded, if discharge pressures at pump's maximum rpm can do higher than the downstream allowable pressures. You may need to set max RPM limits.
Now I'll offer a suggestion as to how I would do this. The same control limits are needed, but everything is local and interaction between controls that might cause unstable looping is minimized.
Make a chart of pump rpms and flowrate delivered to the process. It may be a bit complicated, since the pumps are in series as you may need to establish system flows vs all combinations of RPM at pump group 1 and RPM at pump group 2, but I think its the best way to do it.
Now you can set your VSDs to control pump RPMs based on the flowrate you want to deliver to the process.
If you have a well designed system where pump flowrate, rpm, discharge pressures and system flow curves all correspond to your process requirements, you might be able to stop here and remove all the controls except for the pump RPM-Flow setting. But maybe you don't.
If not,
Then include min suction pressure overrides. With both groups of pumps on a local minimum suction pressure control, a PT in front of each overriding the flowrate set via the VSD, acting to slow down the pump rpm if suction pressure approaches a minimum suction pressure (the higher of either a minimum process pressure plus pipe losses, or the pump's NPSHR). That should cause suction pressures and all downstream system pressure levels to rise, as the slowing pumps reduce flow. With all pressures on the rise, but flow slowing, the FCV will try to maintain the set flowrate. If the set flowrate is too high for the pumps to maintain as they slow down, the FCV will start opening and all pressures will begin to drop.
So the trick to tuning and operating this system is finding the maximum flow setting you can have at the FCV while the pumps are at minimum RPM and the minimum flow you can have at the FCV while the pumps are at maximum RPM, so pressures are maintained below maximum pipe allowables, because if the FCV is set too low, the pumps will move to maximum rpm and highest discharge pressures. Limit the maximum pump RPMs so max disch pressures don't go over pipe pressures.
OK, I don't know eveything about this system, so you do it how you want.
"What gets us into trouble is not what we don't know, its what we know for sure" - Mark Twain