Devices with different power supplies will have different ground levels. This means that the potential of their ground levels is not equal. Their grounds are "floating".
This typically causes problems when a 0-10 Volt control signal generated by a device with it's own power supply (e.g. HVAC controller) is connected to a fan speed controller. If the ground terminals of both devices are not connected, fan speed might vary at random due to the floating grounds of both devices.
To avoid this, connect the ground terminals of both devices to create a "common ground" level and to avoid floating of both grounds.
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