The type of learning in which voluntary responses come to be controlled by their consequences is: observational learning

The type of learning in which voluntary responses come to be controlled by their consequences is: Operant Conditioning (not obseravational learning).
Operant conditioning is a method of learning  and a learning process that occurs through rewards and punishments for behavior.
It is also called "instrumental conditioning".

The correct answer is operant conditioning.

Operant conditioning (OC) refers to a behavioral learning process in which desired behaviors are rewarded and reinforced, and undesirable or unwanted behaviors are punished in an attempt to extinguish them. Through OC, individuals come to realize that their voluntary behavior leads to either positive or negative consequences.