Here is a graphic of the supply and demand curves and the distortion caused by rent control. By holding down the price (from P0 to Pmax, the artificial maximum price) the demand is increased to Q2 - more demand at the lower price - but the supply is diminished to Q1 from the equilibrium Qe. Both, of course, cause an imbalance which is to say a shortage of housing is caused by pushing down the rent charged.
(Since I wrote the post on rent control on my IPhone it’s not easy to modify it now.)
Graphic found at Passion for Liberty.com blog.