A non-linear analysis technique for an on-off servo with velocity inputs

Optimum transient response can theoretically be obtained with a servo system operated in an on-off mode. Although phase plane techniques can produce an optimum system for positional inputs, it is shown that a phase plane analysis is invalid for velocity inputs for a type 1 control servo. A novel approach to the problem is presented which permits an optimum switching procedure to be obtained for velocity inputs, while validity is retained for positional inputs. The resulting system has the properties that the steady state error for both velocity and positional inputs is zero, and no more than two switching cycles are ever needed to return the error to zero.