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 shows the conversion of energy from electrical input to mechanical output. Electrical energy is input to a power supply that 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 (see Figure 3).

Similar to the motoring scenario, the conversion process is not 100% efficient, and a portion of the regenerated 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.

There are several considerations when designing/selecting a power supply for an electrically actuated system. The most basic parameters to consider are voltage and current. For a given motor, a minimum voltage value is required to obtain a given maximum angular velocity, and a minimum current value is required to obtain a given maximum torque.

While the voltage requirements are fixed, a high-power stored energy system can be used to reduce the peak current loads on the power supply by storing energy at a lower power and delivering high power to the system momentarily as needed. One means of accomplishing this is by adding additional capacitance to the power bus. This has the added benefit that the capacitance can also store regenerative energy. If power is consumed by the actuators at a rate higher than the power supply is providing, the bus voltage will drop as the net energy in the capacitors is reduced. This voltage drop must be taken into account when determining the nominal bus voltage to ensure the minimum voltage required to operate the system is never reached. Another important consideration when adding capacitance is the fact that a discharged capacitor, when connected to a voltage source, appears as a short. The power supply must be capable of charging the capacitance to the nominal bus voltage in a controlled manner (i.e., constant current or constant power). The supply must also be tolerant of bus voltages exceeding its set value due to regenerative charging.

One approach to managing regenerative energy is to reduce the amount of energy produced. By reducing the maximum velocity, the total kinetic energy of the system is reduced, resulting in less net energy returned to the system when decelerating. Reducing the deceleration rate while maintaining the same initial velocity will actually result in a net increase in energy returned to the system due to reduced resistive losses; however, that energy will be returned to the system over a greater period of time and at a lower maximum power. If there are predictable loads on the power bus that could absorb this lower-power energy, this could also be a suitable approach.

Another approach is to manage the voltage increase that results from energy being added to the power bus. Using a given capacitance, one could lower the bus voltage, thus requiring more energy to get to the same peak voltage. This approach requires that the voltage does not drop below the minimum required voltage. Another option that maintains a given bus capacitance is to use components with a higher voltage rating, thus allowing the regenerated energy to increase bus voltage to a higher value without damage. However, the voltage ratings required to achieve this may result in components that are expensive, difficult to source, and/or much larger in size.

As with any engineering design, a factor of safety should be applied. This would include components rated higher than the expected peak voltage, additional capacitance, load resistors that dissipate more power with a higher wattage than calculated, and a supply that has additional voltage and current headroom.

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