Coulomb Friction Damping

In a servomechanism with no frictional forces, all the torque developed, which is proportional to the error is used to accelerate the load.  However, when friction damping is introduced, the torque developed must first overcome the frictional force before the system can be set in motion. 

  If d represents the error that must exist before the system can develop sufficient torque to overcome the frictional torque, then if the error is less than d when the system is not in motion, the system will remain at rest with that amount of error.  The response to a step function input of a servomechanism with coulomb friction damping is shown below; the response curve of an undamped system is also given so that a direct comparison can be made. 

From Figure it can be seen that each successive oscillation of the output shaft is reduced in amplitude by the retarding effect of the friction damping until a point is reached when, with the output shaft velocity at zero, the error is less than d; at this point the output shaft will come to rest.  However, as shown in Fig 8, the output shaft may not be at its correct position and a permanent error may exist; this error is known as positional error.   

The response curve given in Figure indicates two overshoots before the system finally comes to rest, but the number of overshoots for a given degree of damping will depend upon the size of the initial error in relation to the amount of error required to overcome the friction torque; an initial error of 2d would produce no overshoot, whilst a large initial error compared with 2d would produce several overshoots.  In practice, coulomb friction damping is not used and, although always present, it is kept to a minimum.

Aircraft Servomechanisms

Servomechanisms can be classified according to two main categories:

• Open loop systems.

• Closed loop systems.

OPEN LOOP

In an open loop system, the input demand generates an electrical equivalent of the demand position. This signal is amplified to the required power level and applied to a motor to position the load. The speed of response and the final position of the load depend on the following factors:

• Any variations in load conditions.

• Frictional forces within the motor and its load, and any mechanical interconnections.

• Variations in power supplies.

• The value of the demand voltage.

• Variations in amplifier gain.

As the open loop system suffers from the variable factors shown above, the output is unlikely to follow the input precisely and cannot provide the close tolerance required.

CLOSED LOOP

If the errors in the output of a system are detected and fed back to the input so that the necessary corrections can be made to eliminate the error, the system is said to be a closed loop system. A Closed loop system is shown below.

The essential features of a closed loop system are:

• Information concerning the behaviour of the load is fed back to the input. This is called feedback.

• The position of the output (feedback) is compared to that demanded by the input. Typically in a summing amplifier.

• The production of an error signal proportional to the difference between the demand and feedback signals.

• Power amplification of the error signal to control the load.

• Movement of the load in such a direction as to reduce the error signal to zero, at which point the output is the same as that demanded by the input.