Consider the transfer function of a PT2 system:
Various technical systems can be approximated by a PT2-System, for example
a damped mass-spring oscillator. Here the natural frequency
is 20 [rad/s] and the damping factor is 0.05.
The plant is stable and minimum-phase.
Your mission, should you decide to accept it, is to design an H∞
controller that renders the closed loop stable and satisfies the control targets below.
In a first step, you have only one degree of freedom in choosing the weights
and one control objective (the steady-state offset).
When that goal is achieved, in a second step two
additional degrees of freedom become available, and all control objectives
have to be achieved.