Are you looking at replacing just the control box or the pump & motor also?
If you just want to replace the controller, you need to understand the following things. The Franklin system is 240 volt 1 phase input. It is 240 volt 3 phsase output. It runs the motor at up to 80 hertz rather than 60 hertz. It uses a 2 psi pressure switch to ramp the motor faster or slower.
You can go to
www.driveswarehouse.com and purchase a Hitachi vfd controller to do this for about $250. I have retro fitted the hitachi drive before. I haven't tried to run the hitachi with the Franklin pressure switch system. It can probably be done. The hitachi can be programmed to stair step speeds. The easier option is to just use the hitachi as a phase converter and turn it on and off with a pressure switch. You would need to add a cycle stop or a larger pressure tank also. The third option would be to control the vfd with a 4-20 milliamp pressure transducer. A transducer will run 100-200 dollars.
If you replace the motor also you can go to a conventional system.
Here is the biggest problem I have with vfd systems. They work fantastic, until they don't. When the vfd goes out, and hopefully it doesn't take out the wire and motor also, if it's out of warranty, I have to tell my customer well that box on the wall is $1000-2500 instead of $150-500.