Contributions to the Theory of Automatic Controllers and Followers
D G Prinz · Journal of Scientific Instruments · 1944
The similarity is pointed out between (continuous) automatic controllers, self-balancing instruments (`followers') and negative feed-back amplifiers. Systems of this type can be represented by a closed chain of variables in such a manner that two adjacent variables are connected either by a factor of proportionality or a differential operator. This representation leads immediately to the differential equation of the system from which criteria of stability and data about accuracy and speed of response can be derived in terms of time constants and `amplification factors'. Each component element of the system is represented by an elementary operator, and the physical relations between these elements are reflected in mathematical relations between the operators which in turn lead to conclusions about the performance of the system; for instance, the cancelling-out of one operator by another may indicate the elimination of a process time lag by the controller mechanism. The operators are closely related to the complex output/input ratios of equivalent electrical networks and can be calculated by routine methods of circuit theory. In particular, the action of certain stabilizing systems is shown to be a consequence of elementary electrical facts.