A positioning servomechanism with a finite time delay and a signal limiter

An idealization of a servomechanism which is used in a digital positioning circuit is analyzed. The loop consists of an ideal integrator, a finite time delay and a nonlinear signal limiting element. An exact solution is derived. Also, a simple approximate solution and an error term are obtained. Finally, curves are given which express the time necessary to zero in on the final position from a given initial position as a function of the loop parameters.