Design discrete controller for zero steady state error I have the following system 

where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$ 

How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero?

I know that this has to do with the system type and in this case we have to deal with a type 0 system which for a step input will give a finite steady state error. Adding an integrator we make the type 1 getting the desired result. Now how would we deal with this in a discrete system? Do I get my constant time controller and convert it to a discrete controller?
You can obtain the steady state error using Finite value theorem (http://www.engr.iupui.edu/~skoskie/ECE595_f05/handouts/fvt_proof.pdf) and then you can compute your controller to make it zero.
or if you have sampling fast enough, you can just discretize your continous version of controller.