[adrian_b]

You use "control" in the wide sense of "dependency", i.e. if two quantities are constrained by an equation, you say that one quantity controls the other, only because their values are not independent (which means that fixing the value of anyone of the two quantities also determines the value of the other quantity).

According to your usage, the voltage on a resistor is controlled by its current, because the voltage is proportional with the current (by the resistance of the resistor), and also the current is controlled by the voltage, because the current is proportional with the voltage (by the conductance of the resistor), exactly like in a transformer the input and output currents and voltages are bound by proportionality relationships.

It is true that this meaning of "control" is encountered in speech, but in engineering and physics "control" has a precise meaning, more restricted that how you use it.

In the engineering use of "control", it is always possible to distinguish which is the controller and which is the controlled in a control relationship.

When "control" is used like you use it, the "control" relationship is bidirectional and you cannot say which is the controller and which is the controlled, e.g. between the primary loop and the secondary loop of the transformer, or between the current and the voltage through a resistor.

For "control" in the engineering sense, unidirectionality is an essential property. Real control devices have some internal feedbacks that make them not completely unidirectional, but this is considered a defect and serious efforts are done to improve the unidirectionality of the control devices. A device with total feedback like a transformer cannot be used to implement any of the known control methods, i.e. you cannot make amplifiers or oscillators or logic gates with it.

[amelius]

But when electrical power is used to drive a simple DC motor, then that power "controls" the speed of that motor. When the power is removed and the motor keeps turning (by e.g. a flywheel) then the power is delivered back to the input. So in that example there is bidirectionality, where you still "control" the speed of the motor.

[adrian_b]

As I have said, some people, including you, are using the word "control" in this wider sense, where it is synonymous with "dependency".

Nevertheless, using "control" with this meaning in any engineering text would be a mistake, because there "control" must be used in its strict sense, to avoid confusions.

In any system there are many dependency relationships, corresponding to all the equations that are applicable to that system, but much fewer control relationships. The control relationships are quite important for the understanding of the system, so they must be identified clearly in a distinct way from other dependencies.

Etymologically, the right sense of "control" is the strict sense, because it has never been applied to a bidirectional relationship like that between the quantities connected by an equation, but it originally referred to a unidirectional relationship, between a dominant party, the controller, and a subordinate entity, the controlled, whose accounts were checked by the controller.

In proper engineering terms it is not the source of power which controls the speed of a motor, but the device that is used to vary the amount of that power. When there is no device to vary the input power, a DC motor works like a transformer, the input voltage is proportional with the output rotational speed and the input current is proportional with the output torque. The input quantities and the output quantities are dependent, so in the wide meaning of "control" you can say equally well that the input electric power is controlled by the output mechanical power or that the output mechanical power is controlled by the input electrical power. However the use of this phrases does not provide any advantage instead of just saying that you have a system of 2 equations that connect the 2 input quantities and the 2 output quantities, so given an appropriate pair of quantities the other 2 are provided by the equations. On the other hand, saying for instance that the motor speed can be controlled by the excitation current of the motor provides useful information by using the word "control", because it is implied that this method of varying the motor speed requires only a small power in comparison with the output power.