Process Control Task Assignment ideas

Hi everyone,
has been a long time I've been reading interesting threads here sometimes but today I may need to start a new one! I have an interesting Assignment for school and my knowledge is quite restricted so I have to ask here for input, ideas or explanations from more experienced people..
The idea is to think about a chemical process ( can be a flash separation, a distillation column, an heater or whatever) that needs to have 2 inputs and 2 outputs. I thought about a cracking furnace. ( but take this in mind please, if you think about an easier process just tell me).Then I should draw a block diagram for this and until this point I can do it without big problems. Then, I should say if the system is linear, non linear or piecewise linear. How can I do that? If I don't find any transfer function for a cracking furnace in literature, how can I say if it's linear or not? And in case I find a transfer function,is just the nature of this function to say if the system is linear? Then also asks for dynamic and static characteristic, but I don't know what's meant by dynamic or static. Ok for dynamic I think when you change time constant but, again, without transfer function how can I say that?And, if I have a transfer function, is there anyway to relate it to the time constant and say without softwares the dynamic change?
I know are several doubts but I am also afraid I just thought at a more difficult process, indeed already to think about two manipulated and controlled variables for the cracking furnaces makes me think for hours and hours.. Any suggestion or further explanation for this are really welcome! Thanks, I'll also attache a file with the main doubts.