It all depends on how it's implemented. The usual method of controlling rent is to cap only a subset of properties in an area - for example, leaving new builds or new tenancies exempt. Which tends to create a two-tier system that benefits one set of tenants at the expense of the other, while discouraging reallocation for downsizing and suchlike. And as you allude to, without further restrictions on tenancy contract terms, the private landlords will attempt to extract their pound of flesh in other ways.
On the other hand, if rent controls are used as part of a wider strategy to gradually convert private rental stock over to social housing - that is, as a stick to encourage private landlords to sell up to the public sector - along with other measures including more state investment in building such housing, large fines for private landlords leaving their rental properties unoccupied, and so on, then this can be a long-term positive on the overall housing situation.
The end goal should be to remove this wholly unnecessary parasitic landlord class from the housing provision entirely, rather than tinkering around the edges of the problem, as this Berlin measure was doing.