I want to synthesize an $H_\infty$ tracking controller for a second-order system.
The system is subject to noise on position, velocity, and acceleration.
If we look at the typical framework with the generalized plant $P$
to me it looks that the noise signals, are part of the $w$ exogenous input, while the tracking error is the $z$ output. I measure position and velocity, which are corrupted by noise and form the output $v$, used as input to the controller $K$.
Inside the generalized plant "P" there are the corresponding weighting function indicating the frequency content of those noise signals.
Where does the reference signal go here? (is it another $w$ input?), and how can I fix the closed-loop bandwidth of this controller? e.g., such that I can track signals until 5 Hz, while the controller does not react to input signals with frequency larger than 100 Hz?
Thanks!