It takes half a century, but after that duration the nation leading a personal union can inherit or integrate their subject nation so long as the leading nation has more provinces than the subject country.
Inheritance can occur when a ruler dies. See the hovertip over the king in the diplomacy screen to see the probability statistic. Main influences are Diplomatic Reputation, Stability, and whether the countries share a culture group.
Another option, if the leader in the union has 190+ relations with the subordinate partner, then "Integrate" is a diplomatic process that will get the ball rolling on the integration and is similar to annexation.