Power is seldom controlled. Power has two components. Electrical power from a battery is voltage multiplied by current. You can control voltage or current relatively easily, but it is difficult and generally not desirable to control both at the same time.
Mechanical power from a motor is speed multiplied by torque. Here again, you can control one or the other relatively easily, but controlling both is neither easy nor desirable.
In general, motor torque is controlled by controlling the supply current. If you control the torque, the motor run as fast as the necessary to get to the speed where that torque will no longer accelerate the load.
Motor speed is controlled by controlling the supply voltage. If you control the speed, the motor will supply as much torque as it can to get to the speed that is set. At that point, the torque will be whatever is required to sustain that speed.
From the standpoint of controlling the load, speed control is often desirable, but it also necessary to limit the current. The controller can be designed to allow a set maximum current, but reduce that current when the desired speed is reached. That is similar to the way we drive a car. We press the accelerator down to produce a comfortable rate of acceleration then back off the acceleration when the desired speed is reached and modulate the accelerator to maintain an even speed.
From the standpoint of electronically controlling a commutator-type DC motor, pulse width modulation of the battery voltage sets the voltage applied to the motor. The motor will draw current depending on the operating speed and the characteristics of the load. The controller needs to monitor the current and adjust the voltage modulation to keep the current within a safe limit.