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That's from the manual. The UCBB should be more than able to drive the inputs to the VFD. Connecting the DCM to the main controller ground (/UCBB ground input) is perhaps something to be avoided if possible, but it's not the end of the world to connect them (arguably, less noise immunity). If there is a problem then you know you have a solution that is to provide true galvanic isolation with a relay. It might be worth examining your system - you *might* find you have a lightly coupled 0v reference in any case through any EMI capacitors in any SMPS you have, negating any advantage and the connecting of 0V to DCM may actually be beneficial.

Exec summary: It'll work, go into this with eyes open for noise immunity.