Does H infinity control have to be limited to a simple 1Dof feedback architecture?

Question

So I understand how H infinity control can be used to synthesize a controller that is in the standard error-feedback framework shown here:

https://www.researchgate.net/figure/1-DOF-feedback-control-system_fig1_313128407

but I was wondering can it be used for different architectures like a "2 dof" controller where the reference and the output are passed in separately to the controller:

https://www.researchgate.net/figure/General-2DOF-PID-controller-structure_fig3_327690406

or can it be used to design a feedforward controller like shown here:

https://apmonitor.com/pdc/index.php/Main/FeedforwardControl

As I understand it, the only requirement for the synthesis of an H infinity controller is that the weighted system must be representable by a linear fractional transform with the controller being connected to a generalized plant like so:

https://www.researchgate.net/figure/Closed-loop-system-TzwK-LF-T-P-K-formed-via-lower-linear-fractional-transformation_fig1_251939874

It seems like for all of the other controller frameworks we can specify the system as this linear fractional transformation, so is it safe to assume that we can apply standard H infinity control synthesis to these other frameworks (like 2 dof or feedforward)? I thought it would be but I cannot find any examples doing this and I was wondering if there were any aspects to these systems that made the synthesis infeasible. Sorry for the links, I don't know how to directly link picture diagrams, and thanks!

Answer 1

You can use H-infinity design to optimize any control system that can take the form

     ┌─────────┐
z◄───┤         │◄────w
     │    P    │
y┌───┤         │◄───┐u
 │   └─────────┘    │
 │                  │
 │      ┌───┐       │
 │      │   │       │
 └─────►│ K ├───────┘
        │   │
        └───┘

If you include your references in the signal w, and the error between the reference and the output in z, you are designing a tracking controller.

All the H-infinity optimization does is to minimize the H-inf norm of the transfer function between w and z with respect to K. The generalized plant P can also be designed such that the reference is fed straight into K through y, thus allowing K to contain a reference filter. If you have other external signals that are known, you can do the same for those in order to have K include feedforward also from those.