Calculating Electrical Requirements for Direct Current Electric Actuators

February 1, 2020

Army Armament Research, Development and Engineering Center, Picatinny Arsenal, New Jersey

Servo control systems require accurate control of motion parameters such as acceleration, velocity, and position. This requires a controller that can apply current (torque) to accelerate a motor in a given direction, as well as provide an opposing current to decelerate it. When this application of aiding and opposing torque can be carried out in both directions, it is referred to as four quadrant motor control (Figure 1).

In four quadrant electric actuation systems, energy changes its form from electrical current flow to mechanical motion and vice versa. This conversion of energy is performed by an electric motor. An electric motor can be modeled electrically as a resistor, an inductor, and a voltage source. The resistor represents the resistance of the windings and internal wiring. The inductance is created from the turns of the wire that make up the windings. The voltage source is a result of the back electromotive force (EMF) created by the rotation of the motor shaft. When an electric motor shaft rotates, it produces an opposing voltage proportional to the motor’s angular velocity.

When the applied voltage exceeds the back EMF voltage, motoring occurs. When the back EMF voltage is greater than the applied voltage, braking occurs and the motor generates energy. In steady state, the difference between the applied voltage and the motor’s back EMF, divided by the circuit’s resistance, gives the current flowing in the motor windings. A motor’s current is directly proportional to its mechanical output torque.

Figure 2 depicts the conversion of energy from electrical input to mechanical output. Electrical energy is input to a power supply. The power supply converts the input energy into a form that can be used by the motor drivers [i.e., alternating current (AC) to direct current (DC)]. The motor driver applies the energy from the supply to the motor as necessary to obtain the intended motion. The electric motor then converts the electrical energy into mechanical energy. The output of the motor is typically mated with some form of mechanical actuator that converts the motor’s output to the intended motion. At each point in the conversion process, some energy is lost due to inefficiencies in the system.

A moving object possesses kinetic energy. When a motor decelerates a moving object, the energy returned to the system has to go somewhere. Similarly, potential energy in the form of gravitational forces, springs, etc., can be returned to the system as objects move. The energy is passed to the motor, which converts the mechanical energy back to electrical energy. The motor driver converts the electrical energy from the motor and returns it to the power bus between it and the power supply. At this point, something must be done with the remaining energy (Figure 3).

Similar to the motoring scenario, the conversion process is not 100% efficient, and a portion of the regenerated energy conversion energy is lost in the system as heat. There are several methods that can be used to handle the remaining energy. In some cases, it can be returned back to the power source (batteries, grid, etc.). If the energy is not removed from the system, the supply voltage will rise as the energy charges the bus capacitance. If the voltage rises too high, it could exceed voltage ratings of components and cause damage.

This work was done by Joshua Stapp for the Army Armament Research, Development and Engineering Center. ARDEC-0006

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Calculating Electrical Requirements for Direct Current Electric Actuators

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