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"High-power brushless motors must be controlled by PWM, requiring a microcontroller to provide start-up and control functions. Do you understand the role of PWM in brushless DC motor control?"
Motion control system designers often face challenges when selecting or developing electronic devices that use pulse-width modulation (PWM) to drive brushless DC motors. Paying attention to some basic physics can help avoid unexpected performance issues. This article provides general guidance for using PWM drivers with brushless DC motors.
Commutation of brushless DC motors
Brushed DC motors use mechanical commutation, while brushless DC motors, unlike brushless DC motors, employ electronic commutation. This means that the motor's phases are energized and de-energized sequentially according to the rotor's position relative to the stator. For a three-phase brushless DC motor, the driver consists of six electronic switches (usually transistors), commonly referred to as a three-phase H-bridge (Figure 1). This configuration allows for three bidirectional outputs, energizing all three phases of the motor.
Figure 1: A three-phase motor H-bridge consisting of six transistors, connected to the three motor phases.
By turning transistors on and off in a specific sequence, each phase of the motor is energized to ensure that the magnetic field induced by the stator and rotor magnets remains in the optimal direction (Figure 2).
Figure 2: Cross-sectional schematic of a slotless brushless DC motor. The blue area is the rotor with two permanent magnets. The magnetic field generated by the magnets is indicated by the blue arrows. The orange area is the three-phase winding. A magnetic field is generated when current flows from phase A to phase C, indicated by the orange arrows for simplicity. When the two arrows are aligned, the rotor will rotate. The driver changes the phase (rotating the stator magnetic field, orange arrows) to ensure that the stator and rotor magnetic fields are kept as close to 90 degrees as possible (to generate maximum torque).
The motor can be driven by the widely used six-step trapezoidal commutation drive (Figure 3), or it can be controlled by more advanced vector control, also known as field-oriented control (FOC), depending on the complexity of the electronic equipment (Figure 4).
Figure 3: Six-step commutation phase current and Hall sensor status.
Figure 4: Phase current using FOC amplifier.
PWM regulation of brushless DC motors
In brushed or brushless DC motors, the operating points (speed and torque) of the application may differ. The role of the amplifier is to change the supply voltage or current, or both, to achieve the desired motion output (Figure 5).
Figure 5: Comparison of motion control architectures between brushed DC motors and brushless DC motors.
There are generally two different ways to change voltage or current:
• Linear amplifier;
• Chopper amplifier.
Linear amplifiers adjust the power delivered to the motor by changing the voltage or current. Power not delivered to the motor is dissipated (Figure 6). Therefore, a large heat sink is required to dissipate the power, which increases the size of the amplifier and makes it more difficult to integrate into the application.
Figure 6: Example of a linear amplifier for powering a motor.
A chopper amplifier regulates voltage (and current) by turning power transistors on and off. Its main advantage is the power saving when the transistors are off. This helps conserve battery life in applications, reduces heat generation in electronic devices, and allows for the use of smaller electronic components. In most cases, chopper amplifiers use the PWM (Pulse Width Modulation) method.
The PWM method involves varying the duty cycle at a fixed frequency (Figure 7) to adjust the voltage or current to a desired target value. Note that one advantage of PWM chopping current compared to other methods is that the switching frequency is a fixed parameter. This makes it easier for electronics designers to filter electromagnetic noise. When the PWM transistor duty cycle is 100%, the voltage applied to the motor is the bus voltage. When the transistor duty cycle is 50%, the average voltage applied to the motor is half the bus voltage. When the transistor duty cycle is 0%, no voltage is applied to the motor.
Figure 7: Different PWM duty cycles. The frequency is the same under all operating conditions, and the average voltage (dashed line) is proportional to the duty cycle.
Inductive effect of brushless DC motor
A DC motor is characterized by an inductor L, a resistor R, and a back electromotive force (EMF) E connected in series. The back EMF is a voltage generated by magnetic induction (Faraday-Lenz's law of induction), which is opposite to the applied voltage and proportional to the motor speed. Figure 8 shows the motor with PWM on and off.
Figure 8: Simplified equivalent circuit diagram of a DC motor with PWM on (left) and off (right). For simplicity, the circuit on the right corresponds to the slow decay mode (current recirculation in the motor).
For simplicity, we will now disregard the back electromotive force. When a voltage is applied to or removed from the RL circuit, the inductor will resist changes in current. When a voltage U is applied to the RL circuit, the current will rise exponentially, its dynamics depending on the electrical time constant τ determined by the L/R ratio (Figure 9). After five times the time constant, it will gradually reach a steady-state value, i.e., 99.7% of U/R.
▎Figure 9: The current in the RL circuit increases exponentially.
When the RL circuit discharges, the same exponential behavior will be observed. In fact, brushless DC amplifiers have fairly high PWM frequencies, making it difficult for the current to reach a steady state. This frequency is typically above 50 kHz, thus providing sufficient cycles for proper current modulation during each commutation step. For a PWM frequency of 50 kHz, the cycle time for turning the transistor on and off is equal to 20 μs. Considering a six-step commutation, the commutation time for a single-pole motor operating at 40,000 rpm (667 Hz) requires 250 μs. Thus, during one commutation step, there are at least 250/20 = 12.5 PWM cycles.
The electrical time constant τ of a brushless DC motor is several hundred microseconds. Therefore, the current has time to react within each PWM cycle. However, the mechanical time constant is in the range of milliseconds, so the coefficient between the mechanical and electrical time constants is 10. Therefore, when the voltage switches at a typical PWM frequency, the motor rotor itself does not have sufficient time to respond. Low PWM frequencies of several kiloHz can cause rotor vibration and audible noise. It is recommended to use a frequency spectrum above the audible frequency range, i.e., at least above 20 kHz.
Limitations of PWM in brushless DC motors
PWM causes the current to rise and fall each cycle. The variation between the minimum and maximum current values is called current ripple. High current ripple can cause problems. It is recommended to keep it as low as possible. Motor torque needs to take the average current into account. The average current depends on the duty cycle and is independent of current ripple.
Unlike brushed DC motors, brushless DC motors do not have brushes. High current ripple does not affect the lifespan itself. Current fluctuations, however, significantly impact motor losses and generate unnecessary heat. Current ripple introduces two types of losses:
Joule losses. Current ripple will increase the root mean square (RMS) current value, which is taken into account in Joule loss calculations. Ripple will generate additional heat but will not increase the average current, and therefore will not increase torque. Note that it is the square of the change in the RMS current function.
Iron loss. According to Faraday's law of electromagnetic induction, a change in the magnetic field in a conductive material will generate a voltage, which in turn creates a current loop called eddy current. Iron loss is proportional to the square of the motor speed and the square of the motor current. Actual measurements show that when the current ripple is large, the additional iron loss increases significantly. Therefore, keeping the current ripple as low as possible is crucial.
Recommendations for minimizing current ripple
We can develop some recommendations to minimize ripple:
Reduce or adjust the supply voltage. Current ripple is proportional to the supply voltage. Higher voltages help reach extreme operating points requiring high speeds or higher power. However, if the application does not require high speeds or high power, a lower supply voltage will help reduce current ripple. Operating at a lower voltage at the same load point also increases the duty cycle, which will further reduce current ripple. Always keep the PWM duty cycle below 50% whenever possible, as this is the worst-case scenario.
Increase the PWM frequency. The higher the frequency, the shorter the PWM period; therefore, the current rise time is shorter. It is recommended that the PWM frequency for brushless DC motors be no less than 50 kHz. PWM frequencies of 80 kHz or higher are more suitable for motors with very small electrical time constants.
Increase the inductance. Brushless DC motors have very small inductance values. Increasing the external inductor is a good idea because it slows down the rise and fall of current, thus reducing current ripple. Furthermore, a specified inductance value is given for a PWM frequency of 1 kHz. Since the motor inductance varies with the PWM frequency, at a typical PWM frequency of 50 kHz, the inductance may decrease to 70% of the specified value.
The optimal inductance value is usually determined experimentally. An additional inductor is needed, as shown in Figure 10. While this solution addresses the current ripple problem, integrating the additional inductor can be challenging, especially in space-constrained situations. Therefore, exploring the other two solutions first is often a wise choice.
Figure 10: Brushless motor with additional line inductance.
PWM offers numerous advantages and is the most widely used solution in brushless DC motors. Setting an appropriate PWM voltage and using a higher PWM frequency helps reduce ripple and eliminates the need for additional inductors. Thanks to the current low cost of electronic components, employing a high PWM frequency has become a simple solution.
When it comes to the size and weight of electronic devices (such as portable devices with embedded electronic components), or when battery life is a critical metric (the extra energy consumed by Joule losses due to additional inductor resistance), electrical designers should consider these parameters when developing motion control systems.
Key concepts:
■ Review the PWM regulation of the brushless DC motor.
■ Understand the limitations of PWM in brushless DC motors.
Think about it:
Are you tackling the challenges of selecting or developing electronics that use PWM to drive brushless DC motors?
