At minimum, a VFD requires two control signals. One signal to tell it when to start, another to tell it how fast to go. Both of those signals can come from the PLC.
The run command is typically a contact closure. The speed command could be an analog signal. It could also be one or more contact closures which tell the VFD to select one of several preset speeds.
But, rereading your original post, I'm not sure I answered the question you asked. That's because I'm not sure what the question was. Do you want help on how to implement PLC control of a VFD or do you want reasons why PLC control of a VFD would be an improvement over the way the fan speed is currently controlled?