PID gains from a Transfer Function of a mass-spring-damper system

I am looking to calculate the PID gains (Kp, Ki -> Ti, Kd -> Td) of a PID controller in Matlab. From the state-space model, I calculated the transfer function to be:

I tried doing this tutorial but I am having trouble using the feedback function since the numerator of the transfer function doesn't match the other parameter.

Does anyone have any advice?

For reference, my system model is:

Thank you!

Answer 1

[Arkadiy Turevskiy]

Well, your system has 1 input (force) and 2 outputs (x1,x2), so it is a single input - multi output system. The tutorial you tried to follow is showing how to design a PID Controller for a single-input single-output system.

What do you need to control in your system, is it x2? That would be most reasonable thing to do.

If that is the case, then the transfer function you should be looking at is F to x2.