The majority of single-engine helicopters do not have autopilots installed. The few that do have autopilots (not counting experimental designs) use a series-parallel model. Even a simple two-axis system without a flight director can be somewhat complicated as it will have a series actuator and a parallel actuator for both pitch and roll.
In the case of the Sagem autopilot, the series actuator is known as a SEMA (Smart Electro Mechanical Actuator), the flight control tube is cut and the actuator inserted. SEMAs are fast moving with limited authority (plus or minus 3.5 mm). The parallel actuator is called a trim actuator and is normally attached to one end of the flight control tube.
When the pilot engages the pitch-and-roll switch, the two SEMA actuators (one for pitch, one for roll) provide a SAS (Stability Augmentation System) by making very small rapid movements that enhance stability through rate dampening. When the force trim switch is engaged, the two trim actuators will hold the cyclic control in that position. The trim actuator contains a spring-and-clutch mechanism that provides the force trim. If the pilot moves the cyclic control it will want to return to its original position.
The autopilot’s upper modes allow it to hold heading, a navigational course, altitude, and indicated airspeed. Heading and course are controlled by roll and only one of these can be active at a time. Altitude and airspeed are controlled by pitch and only one of these can be active at a time as well. In both of these modes it is normally the SEMA actuator that controls the rotor system while the trim actuator anchors the flight controls. When a SEMA is operating off its midpoint, the trim motor is activated to move the cyclic in the appropriate direction and amount to cause the SEMA to return to its center position, restoring full authority.
The autopilot computer receives data on airspeed, altitude, heading, and course and compares it to the value selected by the pilot. If there is a deviation, the autopilot computer sends the appropriate signal to the actuators which moves the rotor system in a direction to cancel the deviation. This allows the autopilot to maintain heading or course and altitude or airspeed.
This describes a very basic system. More advanced helicopter autopilots have flight directors, yaw servo actuators, and servo actuators that control the collective. There are also systems that will auto hover.