An investigation of the switching criteria for higher order contactor servomechanisms

The use of a linear anticipatory switching network in an on-off servomechanism, while improving system stability, does not result in optimum response. Mathematical analysis of second order systems indicates that the network should be a nonlinear function of error and error rate. This paper describes a method for deriving the switching criterion for a “piecewise” linear on-off servo of order greater than two, when the input variable is limited to a step function of position and velocity. The switching criterion results in system error and in derivatives of error reducing to zero in a minimum time. System behavior is described in the principal co-ordinate phase space. Starting at a point in the phase space corresponding to the initial conditions, the representative point moves in a series of discontinuous trajectories determined by the sign of the controlled variable, eventually reaching the origin. The sequence of sign reversals represents the desired switching criterion.