Degrees of freedom

Degrees of freedom 

The degrees of freedom of a process define the maximum number of independently acting automatic controllers that can be placed on a process

Degrees of freedom = number of variables – number of equations

• Steam heater
• Liquid to liquid heat exchanger
• Reboiler

Steam heater

• In this case there are four process variables and one defining equation which is that of the conservation of energy based on the first low of thermodynamics [ HsWs= CpW(T2-T1)]
• In a steam heater there are four process variables are two flow and two temperatures
• The number of degrees of freedom of that process is three thus, a maximum of three automation controller can be placed on it .

Liquid to liquid heat exchanger

• In this case there are six process variables and one defining equation is [ CpF(Th1-Th2) = CpcFc(T2c-T1c)]
• Six process variables are four temperature and and two flow variable
• The number of degrees of freedom of that process is five thus, a maximum of five automation controller can be placed on it.

Reboiler

• In this case there are only two process variables and one defining equation is [HsWs =H1W1]
• Two process variables are two flow variables
• In this cases there is only a single degree of freedom, and therefore on these processes only one automatic controller can be used.