The effect of speed-dependent friction and backlash on the stability of automatic control systems

A control system is considered which employs a motor driving a load through gearing having backlash. It is assumed that linear speed-dependent friction is applied to both the motor and the load. The effect of backlash and friction on the stability of the control system is investigated using the describing function technique. A method of deriving the describing function is given and it is shown that the presence of friction modifies the application of the describing function as presented by Tustin.1 In particular it is shown that although the positional reset may be divided in the ratio of the inertias, the system may still exhibit sustained oscillations, and the choice of system parameters to eliminate these oscillations is discussed. To illustrate the effect of backlash and friction quantitatively a second-order control system is considered. The oscillations predicted by the theory are measured on an electronic analog of the system. By a correct choice of the system parameters the oscillations are removed.