Instrument servomechanisms with backlash, coulomb friction, and stiction

AN INSTRUMENT servomechanism is normally thought of as a small positioning device with low power consumption. A typical block diagram is shown in Fig. 1. A gear ratio of 1 to 1 is used in this paper for convenience. The load is shown as an inertia with coulomb friction but no viscous friction. It is further assumed that JL = 0. This might correspond to the common case in which the output member is just the wiper arm of a potentiometer. When there is backlash in the gear train the following sequence of events is normal. The motor drives (with backlash taken up), reducing the error: as the motor velocity decreases the load velocity also decreases, and continuous mechanical contact is maintained because JL = 0, and the coluomb friction C provides adequate drag on the output. When the motor velocity becomes zero, the load velocity also becomes zero. If the error is not zero, the motor reverses but the load does not move because of the backlash. Thus, the error does not change and the motor is driven open-loop with a constant driving torque, or voltage, until the backlash is taken up. The load is then “picked up” by the drive and both the output velocity and the error rate jump from zero to the instantaneous drive shaft velocity. This sequence is usually repeated a number of times.