Yaw damping is achieved by using the rudder to generate a yawing moment that opposes any yawing motion. Also, rudder is used to correct sideslip by applying a rudder input in the opposite direction of the sideslip. My question is how to simultaneously fulfill yaw damping and zero side-slip/yaw acceleration requirements? More specifically, should both requirements be controlled independently and resultant rudder is the sum of two or yaw damping should be made inner loop to sideslip/yaw acceleration control?
It's all a single activity. Yaw dampers provide a single function; provide an active automatic rudder input to keep the airplane aligned in the airflow when the airplane's static yaw stability, its "weathervaning" tendency provided by the vertical fin, is insufficient.
The system detects sideslip for any reason and applies rudder to take out the side slip, within its range of authority (usually around 1/3 of rudder travel). It's normally a separate always-on channel, not connected to the autopilot.
Think of it as a separate person you hired to sit with his own set of rudder pedals, and instructions to watch the slip/skid ball and do whatever it takes to keep the ball centered at all times.
This means that displacements in yaw from turbulence or gusts are automatically controlled, as well as adverse yaw induced by aileron displacement.
When an airplane turns, the turn is generated by the bank created by aileron, which causes sideslip toward the low wing. The vertical fin provides the yawing action to coordinate the turn; a big weathervane (as the bank steepens, more and more of the turn rate is coming from elevator, but for simplicity we'll assume very shallow turns where that is minimal). Rudder inputs are only required for turns because of adverse yaw from aileron displacement, or gusts that excite yawing movements.
On an airplane with a yaw damper, you put your feet on the floor after takeoff and never touch the rudder pedals during normal maneuvering in the air. The yaw damper does all the corrective inputs to keep the ball centered for you. Outside the take off and landing phases, you only need to get on the pedals for situations that require more input than the yaw damper has authority to correct. Namely, engine failures.
the resultant rudder is the sum of the two.
If you want to fly a straight path, yes.
Sideslip is the result of an uncoordinated yaw. A yaw damper is required when the aircraft's natural damping ability is insufficient.
Exacerbating factors are high altitudes, high weight to surface area ratio, and swept wings. A paper airplane does not need a yaw damper, a 747 flying at high altitudes does.
In design the vertical stabilizer and fuselage surface area behind the center of gravity control yaw. This is known as longitudinal stability.
The need to actively apply rudder to eliminate unwanted sideslip and/or damp yawing oscillations indicates the aircraft is more unstable in the regime it is flying.
Interestingly, in the design of very large aircraft, a yaw damping system may prove more economical than an extremely large tail fin. However, larger fins are virtually foolproof safety insurance.
More specifically, should both requirements be controlled independently and resultant rudder is the sum of two or yaw damping should be made inner loop to sideslip/yaw acceleration control?
Except when operating near the stall -- and striving to avoid a spin-- applying rudder inputs as needed to keep the ball centered will always give satisfactory results. Assuming that the pilot (or the automatic flight control system) is able to keep the ball truly centered, this statement holds true even in parts of the flight envelope where an aircraft (typically a swept-wing aircraft) has a self-sustaining (undamped) "Dutch roll" yaw-roll oscillation mode.