A steady state approach to the theory of saturable servo systems

It is shown that simple saturable servo systems can have two modes of response to a given input signal -- one a linear mode as predicted by linear feedback theory, and the other a saturated mode predictable from a large signal analysis presented here. This dual mode of response theory provides a reasonable explanation for premature saturation, hysteresis in the input-output characteristics, jump resonance and similar anomalous effects that so often degrade the steady state performance of saturable servo systems. Furthermore, systems which exhibit a large degree of anomalous steady state behavior can be expected to exhibit a correspondingly poor transient response under large signal conditions such as obtained when the system is coming out of saturation. Demonstration of the existence of this dual mode of response and prediction of the range of signal amplitude and frequencies for which it exists are both built around the "saturated" transfer characteristics of the control loop. This analysis is quantitatively useful only in certain simple cases where the necessary saturated transfer characteristics can readily be found. Its chief value lies in the insight it provides to the cause of anomalous behavior. In this respect it is particularly useful to the designer because it relates this behavior to the loop gain and phase characteristics of the saturated transfer characteristics. The analysis is applied here to two simple examples, and the results are verified by an analog computer study on simulations of these systems.