I am working in a control project in which I need to control two variables \$x\$ and \$y\$ according to their reference values.
Since I don't have an advanced knowledge in modern control theory, I usually tackle these problems using PI, PID, lead/lag controllers.
I have simplified my problem in the following image. My system has a matrix with time varying coefficients (and it adds coupling to the variables), and I am not being able to write the open-loop transfer function to find the good parameters of my PI controllers.
Do I need to use a fancier control structure than PI control or can I obtain an approximation of the transfer function and keep the topology of this solution?