Bob Moore writes:

Swept wing and some straight wing aircraft have independent Yaw Damper(s)
that control the rudder(s). Their primary function is to control (prevent)
dutch roll. They operate with the autopilot on or off.

I'm thinking along the lines of small aircraft such as a C172 or Baron. They
do not have AP control of the rudder, and yet the AP can still execute
coordinated turns.