accurate control

:? im trying to build a circuit that can convert 100rpm to 600rpm (taken of a rollera)into 0 to 10 volts dc this will be used to set the reference signal for a vfd, this in turn will drive another roller yhis second roller will also produce a 0 to 10 voltage to be compared to the original to see if both are same speed. going to use a frequency producing sensor and frequency to voltage converters but unsure how to produce error voltage if rollers are at different speeds.

Do you need to apply feedback to force both rollers to be at the same speed?

Your description sounds too complicated. I am not sure I could give you a good answer but here goes:

If both rollers' sensor circuits produce a 0-10V signal, then you can simply use an op-amp to calculate the difference and produce an error signal. This error signal can be input to an analog PID circuit which can output a 0-10V that canl be fed into the vfd.

BTW, what's a vfd?

Maybe there are easier ways like dividing down the frequency out from the 600rpm roller by 6 and comparing the frequency after division to the 100rpm roller. This works like a phase locked loop.

BTW, what's a vfd?

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Variable Frequency Drive