Anaerobic sludge digesters are reactors in which waste water is treated with microbes to 'digest' the suspended solids. The reactor is essentially a CSTR. The reactor is intially charged with a microbial population. This is followed by the continuous addition of waste water feed and heat to the system. The use of methanogenic bacteria as the microbial population results in poor process stability. Hence, a good control system is necessary. A simple schematic of the setup is shown below.

The parameters affecting the process are the rate of heat addition and the flow rate of the influent waste water. Furthermore, there are environmental disturbances which affect the process. Chief among these are the concentration of suspended solids in the influent feed and the temperature of the feed. The important measured variables are the concentration of the suspended matter in the digester and the temperature of the digester.

You are required to model the process and derive the transfer functions relating the manipulated variables and the disturbances to the controlled variables. Furthermore, you should analyze the extent of interaction in the system and, based on the analysis, pair the appropriate manipulated and controlled variables. Finally, you are required to design a controller for the process.