How to use the future measurements of the disturbance in the H_inf control framework?

I am using the function hinfstruct to implement an H_inf controller for a disturbance rejection problem.

So far, I have successfully implemented the controller using output measurements only. However, I would like now to also add the future measurements of the disturbance that are provided by a LIDAR. Unfortunately, the controller that I get using also future measurements is not behaving better with respect to the one that is using only output measurements and I did not find out why yet.

I am using SIMULINK to represent the Generalized Tunable Plant, and the scheme is the following:

where dg is the scaled disturbance, u_sym is the control signal, z is the output I am interested to minimize (z=0 for dg=0) and y_tilde is containing both the output measured (from the plant) and the future measurements of the disturbance dg. Finally, Wg, Wz, Wu and Wu_dot are the weighting functions.

The Generalized Plant block looks like follows. Note that since it is not possible to use a filter of the form e^(s*T) (because the resulting system would not be causal), I am using an equivalent formulation (at least I think it is equivalent) by feeding the "present disturbance" to the controller through y_tilde and, instead, feeding the plant with a delayed disturbance, filtering it through e^(-s*T).

here P_sym is simply the real plant.

Finally, for what concerns the controller, the Controller block looks like this:

here K_LID is a tunable gain matrix, C_LID is a tunable PI and CFF is a tunable filter with 2 zeros and 2 poles. The idea is to use the same architecture that I have used for the controller computed using only the measurements of the output y (with no future measuremnts of the disturbance) consisting of a series of C_LID and K_LID and adding to it a feed-forward filter CFF. Note that the reason why I use a gain K_LID in series with the PI controller C_LID is because y has dimension 1, instead I have several actuators to control the system and therefore I wanted a flexible tunable gain for each of them after the output of the PID that has dimension 1.

Does anyone have any suggestions about the Generalized Plant/Controller schemes?