Using LQR on a third order model

Hi Everyone,
I am currently working on a project where I have been asked to optimise a third order model representing the transport network using the LQR with regards to fuel economy and emissions. I have linearised the state model and developed the LQR controller in mathlab Simulink. Having not studied optimal control before, I am stuck in terms of how to interpret and use the model. I understand that manipulating the Q and R matrices regulate the penalties on the excursion in the trajectories of the state variables and control input. Is simply using trial and error sufficient to optimise the model? What does it really mean to select parameters that make the system reach plateau more quickly? I am struggling to interpret my general understanding of LQR to the problem at hand. in terms of the fuel saved, I could have extracted that from the third order model by the number of vehicles and thus the emissions. Do I need the LQR?
Many thanks for your time.