The correct answer is: Series motor.
A series motor has the poorest speed control because the field winding and the armature winding are connected in series. This means that the current through both windings is the same, and the speed of the motor is proportional to the current. As the load on the motor increases, the current increases, and the speed of the motor decreases. This makes it difficult to control the speed of a series motor.
A differentially compounded motor has the field winding connected in series with the armature winding, and a second field winding connected in parallel with the armature winding. The second field winding has a smaller number of turns than the first field winding, so its effect on the speed of the motor is small. This type of motor has better speed control than a series motor, but not as good as a shunt motor or a cumulatively compounded motor.
A cumulatively compounded motor has the field winding connected in series with the armature winding, and a second field winding connected in parallel with the armature winding. The second field winding has the same number of turns as the first field winding, so its effect on the speed of the motor is equal to the effect of the first field winding. This type of motor has the best speed control of the three types of compound motors.
A shunt motor has the field winding connected in parallel with the armature winding. This means that the current through the field winding is independent of the current through the armature winding. The speed of a shunt motor is determined by the voltage applied to the motor and the resistance of the field winding. The speed of a shunt motor is relatively constant, regardless of the load on the motor.