In many control schemes some type of computation using process variable or controller output signals is performed. For instance, a flow rate may be compensated for temperature, pressure or density effects, a required air-to-fuel ratio may be multiplied by a fuel rate to determine an air flow controller set point, or two temperatures may be subtracted in order to control from a differential temperature. The implementation of these computations is straightforward if the signals have been digitized, converted to engineering units and made available in floating-point format to a high-level software program. If, however, the computation is to be done with analog hardware, say by combining two or more 3 15 psig or 4 20 mA signals using discrete devices called adding relays, multipliers, etc., then the signals must be properly scaled so that the resultant signal has the correct range in engineering units. The same problem exists if the computation is performed in a digital device in which all signals are represented by a integer value within a common range. In both of these cases, we can consider that the signal has a range of 0 100%, or a normalized range of 0 to 1.

Quite often, the proper signal scaling values are obvious. At other times, a more formal methodology for signal scaling will be very beneficial. This appendix presents such a method which will work in all cases, although for simple scaling problems, it is perhaps an overkill.

Every analog signal has both a signal value and an interpretation in...