[Answer] Does Omron have a PLC that can control 15 servo motors?

I haven’t used Omron products in recent years, so I’m not very familiar with their current lineup. However, even without knowing the specific Omron models, I can say with confidence that their products should be able to achieve what you are asking for.

If an integrated PLC does not have enough built-in I/O to control that many motors, you can also expand the system by adding dedicated modules.