Abstract :
For a relay-controlled servo mechanism represented by an nth-order differential equation it is shown that one change-over and one only, at a unique time, is necessary to bring error and error rate to zero in the least possible time. Previous workers have used the sign of a non-linear function to control change-over, but such methods are suitable only for simple second-order systems with step inputs. To satisfy the need of a technique capable of wider application, e.g. random inputs, prediction of switching by means of a high-speed repetitive analogue computer has been demonstrated with a model experiment. Such a scheme has been shown to be practicable; its use is not limited to simple systems. In the specific example of a 10 kW control system the responses are compared of the on-off control using predicted change-over to those obtained (by simulation) of an orthodox servo mechanism, a linear but saturating servo. The optimized on-off control is always better for all amplitudes of step, ramp and parabolic function inputs, and on the average the same performance would be obtained with both systems using only about half the torque with the on-off control.
