I have done a number of vfd control loops/systems from Opto22. The best way is to use serial or preferrably ethernet comm to do so. This way you have complete access to the variables you might need. Otherwise, you have to connect a number of disceets to the VFD in order to control what mode the vfd is in at a given part of the process. I have done so both ways. The biggest problem is that many manufacturers of VFD's have their own ways of doing things in their VFD CPU and that is not always friendly to connecting a controller. Most of the japanese VFD's will have Modbus RTU available as standard. Keep in mind that, using the VFD's PID loop might prove to work the best, however, that will require having to connect and range the feedback sensor as well as using digital IO to control the mode of the VFD (PID mode versus speed reference mode). By using comms, you can do all of it including using the PID template in Pac and feed the speed reference into the VFD via Modbus. A Pac controller can use the serial module to do this many times per second while running the rest of the process with no sweat.
In so far as your oven burner goes, be sure to check that the burner input regulator has the approprate input pressure required, I did one where no one checked this, not even the contractor who installed 200' of 2" pipe to the burner. The VFD in this case controls the air input pressure of the manifold which in turn controls the proportional burner regulator to maintain the gas/air ratio inspite of the changes of air flow. Therefore you need to use the oven air temp to control the VFD speed using a PID to do so. Now this gets a little tricky becuase the VFD speed is not linear with respect to air flow, in fact, fans ad pumps are anything but linear in that respect. The problem I have encountered is that once the oven is up to temp, controlling the temp is difficult since apparently some builders do not provide a means of cooling. Once the oven is hot, it has no means of cooling except for load or insulation losses. This can take forever, so if your oven overshoots, then it stays there for maybe 10-15 minutes. The solution for this is simple, you need a set of 4-20ma vent louvers. Next you need to intgrate the vent louvers with the heating PID. I did this using 2 PID's, one heat and one for cooling. The two PIDs is not necessarily the best design, however it was able to hold +/- 2 degs at 250 deg F on both the soak time as well as the ramps. The only real problem with this is to keep the 2 pids from fighting each other and to keep the cooling PID at fully closed postion as much as possible. The other way is to use 1 PID and do some math to produce the cooling vent outputs as a product of the heating PID. The biggest problem becomes getting the PID to be sensitve enough for decent control at 250 degrees as well as unsensitive enough to control at 150 degress. This can be done by using math to change the gain at various temp levels or even proportionally. Another set of variables that comes into play is the ambient temperature and initial heat loading of the oven structure itself. If you have a means of measureing the amount of BTU's the oven is producing such as a mass air flow meter on the burner fan intakes, then you can correlate that to BTUs and then measure how much BTU load it takes to heat the oven up with no product load at a particalur ambient and likewise the same for a hot oven with product and a different temp.