PID: how to deal with delay between controller and a process?
You need to incorporate the delay in your transfer function \$H(z)\$. If the delay is a multiple of the sampling period, then the delayed transfer function is simply
$$H(z) z^{-m}.$$

If the delay is not a multiple of the sampling period, you can do a couple of things. Firstly, it is probably a good approximation to select the closest multiple of the sampling period. Secondly, you can use the advanced z-transform, which is given by
$$F(z, m) = \sum_{k = 0}^\infty f(Tk + m) z^{-k}.$$
If the delay \$m\$ is a constant, which it will be in your case, then the advanced z-transform has the same properties as the z-transform.

It is important to check the controllability matrix when you have a significant delay. It can render the system uncontrollable in certain situations.