Quasi-optimization of relay servomechanisms by use of stored energy for braking

IN A PREVIOUS PAPER1 the authors show that a relay servomechanism can be made to have a deadbeat response to a step displacement input by using proper combinations of linear derivative switching and discontinuously applied viscous damping. In brief, viscous damping is applied to the motor or load when the relay enters its dead zone. The resultant phase trajectory in the dead zone is a straight line for many cases, and derivative controlled relay operation can be adjusted to make the locus of points at which the relay opens parallel to the deadzone trajectory. The relay cannot reverse under these conditions and the system gain can be raised until the dead zone is quite narrow.