A control strategy similar to ratio control is relation control. This is similar to ratio control in that a “wild” variable determines the setpoint for a captive variable, but with relation control the mathematical relationship between the wild and captive variables is one of addition (or subtraction) rather than multiplication (or division). In other words, a relation control system works to maintain a specific difference between wild and captive flow values, whereas a ratio control system works to maintain a specific ratio between wild and captive flow values.
An example of relation control appears here, where a temperature controller for a steam superheater on a boiler receives its setpoint from the biased output of a temperature transmitter sensing the temperature of saturated steam (that is, steam exactly at the boiling point of water) in the steam drum:
It is a basic principle of thermodynamics that the vapor emitted at the surface of a boiling liquid will be at the same temperature as that liquid. Furthermore, any heat lost from that vapor will cause at least some of that vapor to condense back into liquid. In order to ensure the vapor is “dry” (i.e. it may lose substantial heat energy without condensing), the vapor must be heated beyond the liquid’s boiling point at some later stage in the process.
Steam within the steam drum of a boiler is saturated steam: at the same temperature as the boiling water. Any heat lost from saturated steam causes at least some of it to immediately condense back into water. In order to ensure “dry” steam output from the boiler, the saturated steam taken from the steam drum must be further heated through a set of tubes called a superheater. The resulting “dry” steam is said to be superheated, and the difference between its temperature and the temperature of the boiling water (saturated steam) is called superheat.
This control system maintains a set amount of superheat by measuring the saturated steam’s temperature (within the steam drum), adding a “superheat setpoint” bias value to that signal, then passing the biased signal to the temperature indicating controller (TIC) where the superheated steam temperature is regulated by adding water (Note) to the superheated steam. With this system in place, the boiler operator may freely define how much superheat is desired, and the controller attempts to maintain the superheated steam at that much higher temperature than the saturated steam in the drum, over a wide range of saturated steam temperatures.
A ratio control system would not be appropriate here, since what we desire in this process is a controlled offset (rather than a controlled ratio) between two steam temperatures. The control strategy looks very much like a ratio control, except for the substitution of a summing function instead of a multiplying function.
Note : This mixing of superheated steam and cold water happens in a specially-designed device called a desuperheater. The basic concept is that the water will absorb heat from the superheated steam, turning that injected water completely into steam and also reducing the temperature of the superheated steam. The result is a greater volume of steam than before, at a reduced temperature. So long as some amount of superheat remains, the de-superheated steam will still be “dry” (above its condensing temperature). The desuperheater control merely adds the appropriate amount of water until it achieves the desired superheat value.