A latch module for controlling an opening and a closing of a door of an appliance includes a latch, a spring that applies an elastic force to the latch, a motor; and a cam that contacts a contact surface of the latch and is coupled to the motor to drive the cam to pivot the latch. The cam includes a first radius, a second radius, and a third radius in a circumferential direction at an outer circumference of the cam. The latch is positioned at a first basic position when the first radius of the cam contacts the contact surface of the latch, positioned at a second basic position when the second radius of the cam contacts the contact surface of the latch, and positioned at a third basic position when the third radius of the cam contacts the contact surface of the latch.