Effects of friction in an optimum relay servomechanism

A recently proposed relay servo-mechanism employs maximum torque at all times, with the sense of the torque determined by a comparison of the error and the square of the error rate. With correct switching and no friction, this system gives the minimum possible response time for a step input with the specified inertia and maximum torque. A theoretical study of the effects of Coulomb or viscous friction is described in this paper. The degradation of the step-function response as a result of friction is measured by the change in response time, integrated absolute error, and integrated squared error. It is found that moderate amounts of friction can be tolerated with only a small loss in performance, if a slight change is made in the switching device.