Demonstrating Repercussions of Torque Ripple in a Brushless Motor

Author: Pat Gipper

A virtual model of a brushless DC motor


I am going to give a quick demonstration that shows how controlling a brushless DC motor using standard 6-step commutation can cause undesirable excitation of system resonance. But I also encounter unexpected results. Read on!


I have recently moved from a project using Field-Oriented Control (FOC) for positioning a three phase brushless DC motor to using the standard 6-step positioning that switches the six FET bridge using Hall effect devices. One of the main arguments for using FOC is that it provides smoother movement of the motor. This makes a lot of sense when you consider the ripple torque produced by the 6-step motor rotating the motor with a fixed current. Figure 1 shows the ripple torque of a motor that will be repeated at each electrical revolution. Notice the six ripples that occur in the torque every 360 electrical degrees. I emphasize “electrical” revolution of the motor because it won’t necessarily be the same as mechanical revolution except in the case of a two pole motor.

Figure 1

I was simplifying the six step model by eliminating the high frequency pulse width modulation of the bridge transistors by using them only to commutate the motor and using the average voltage produced by the PWM as the overall voltage supply to the bridge. Not only does this allow for faster results but it also takes out all the noise on the phase currents. I thought this would be a great opportunity to demonstrate how the 6-step positioning results in oscillatory movement of the motor.

Figure 2 shows the motor speed with a small DC voltage step applied to the bridge. The interesting thing to note is that the speed is at a maximum at the motor rotation where the torque is at a minimum. That seems counter-intuitive at first until you consider that the back EMF of the motor is also at a minimum at those positions. This means that the motor speed can increase such that the back EMF voltage is equal to the bridge voltage.

Figure 2

I then connected a load inertia to the motor that had a resonance of 95 Hertz and ran the same step response, with results shown in Figure 3. As expected, the resonance is large at first and then decays to a small residual amount. This is because the motor torque ripple frequency is only about half the load resonant frequency.

Figure 3

To really see some action, I increased the voltage of the step such that the torque ripple frequency is the same as the load resonant frequency, with results shown in Figure 4. Now you can understand the argument for using Field-Oriented Control, the torque/speed ripple can excite natural resonant frequencies of your system!

Figure 4

My goals for demonstrating the benefits of Field-Oriented Control were complete, so I proceeded with some further work on this model for my next project. I wanted to de-couple the external power supply from the motor control by isolating with a series diode and a capacitor to ground in front of the bridge. Re-running the last step response I was surprised to find that the oscillation nearly vanished. What the heck? I realized the diode voltage drop was changing the speed of the motor and changed the ripple frequency. No problem, this is a simulation where diodes can have zero drop. Once I made this change, the motor speed increased. But still the oscillation decays! See Figure 5.

Figure 5

Examining Figure 5 you can see that the motor speed ripple has nearly vanished, providing very little excitation to the load resonance. A plot of the voltage on the bridge capacitor is shown in Figure 6. You can see that the voltage now changes in phase with the motor back EMF, which means that motor speed can stay constant with rotation.

Figure 6


I demonstrated how the torque ripple of a brushless DC motor using standard six-step commutation can cause undesirable reactions from your system. I also discovered an unexpected result where the resonance is damped out. Does this mean that field oriented control is unnecessary? The answer is no. Further investigation found that the phenomenon only occurs when the motor load is extremely low, so impractical in most use-cases.


Pat Gipper is a chief system engineer at Array of Engineers, where he performs modeling and simulation and supports system level design requirements. Pat has over 35 years of engineering experience in the aerospace industry.

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