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.
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