If I were a city planner, I'd require that all new (or renovated) appartement buildings include a percentage of "affordable appartements", with fixed limits on the cost per square foot. That's how cities like Vienna keep rents affordable.
Isn't the majority of all housing in Vienna controlled by the state? It's probably easy to make rent controls work if you can bypass incentive problems by simply making all housing public.
How do you keep wealthy people from renting all the cheap apartments in the not-cheap buildings? I'm not sure I comprehend the plan.