The Sizing Game

The sizing of simple feedback control systems with peak actuating power and sensor accuracy constraints, is a problem that theory has left to the designer by default, and he hasn´t done much with it. We find that a satisfactory sizing procedure must include the degredation in performance that arises when the sensor noise is large enough to absorb an appreciable part of the available actuating power. The solution proposed here is to size the power and noise constraints so that, in the absence of a signal, the mean square noise in the output of the actuator is less the 1/4 of the total actuating power available. These results have interesting implications for both the analysis and design of these constrained fbc systems.