App note from Littelfuse on solution to control split-phase motor using logic devices and triacs. Link here (PDF)
In the huge variety of the AC motors, one-phase motors are an excellent option when only the single-phase power is available to supply electrical energy which motors require to operate. One of the most common single-phase motors is the split-phase motor which is used in many applications, such as pumps, bench drills, compressors, vacuum cleaners, electrical sewing machines, etc.
In some if these applications it is necessary to reverse the motor which requires two conditions. The first condition is the removal of power to the motor in order to stop it. The second condition is to change the electrical connections between the mainand the start winding.