Quasi-optimization of relay servos by use of discontinuous damping

A NUMBER of articles1―6 have been written which deal with the optimum response of a relay servo to a step input, with some mention of a ramp input. If optimum response is defined as that response which regains position correspondence in minimum time and without overshoot, then it has been shown that an ideal relay servo with second order motor-load combination may be optimized. The optimized relay servo has one period of acceleration with maximum torque, an instantaneous torque reversal (ideal relay) at an appropriate point, and one period of deceleration with maximum torque. The system attains zero error and zero error-rate simultaneously, the torque is removed, and the system is stationary at zero error. For the second order motor-load, with a maximum torque specification, this represents the fastest possible response. For higher order motor-load units, more switching operations5 are required.