Inside angle on sine-driven

Oct. 1, 2002
An important step in designing with sine-driven brushless dc motors is choosing the alignment process and engineering around its shortcomings.

Electrical angle alignment of brushless dc (BLDC) motors is the process of determining how to apply electric current to the motor. In essence, it is determining where the magnets are with respect to the windings, not unlike determining the spark plug timing of an automobile engine.

In many precision positioning systems, particularly those that commutate in a sinusoidal fashion, alignment of the motor electrical angle is required – even when absolute position is available. The method used to accomplish this process affects system cost, complexity, and performance.


Before the advent of sinusoidally driven brushless dc (BLDC) motors, most servo-positioning systems relied on dc motors, employing brush-type commutators to channel electrical current to the appropriate winding to develop torque. Today, the job of commutation has moved from the mechanical realm (brushes and sliding contacts) to that of electronics.

Brushless motors, by definition, do not have an integral means of commutation. Instead, they must be commutated electronically; solidstate switches apply current to the motor windings in a manner that produces useful torque or force.

One way to commutate BLDC motors is with the “six-step” or “trapezoidal” technique, which relies on Hall-effect sensors. Inexpensive, the method is widely used in applications that don’t require smooth torque for positioning. For precision positioning, an alternative approach, sine drive commutation, is usually the method of choice.

Trapezoidal commutation lacks precision because of inaccuracies associated with Hall-effect sensors and torque disturbances stemming from the discontinuous nature of six-step drive currents. Sinusoidal commutation, on the other hand, is quite precise; but it has drawbacks too.

In addition to requiring more sophisticated electronics, sinusoidal commutation won’t work right if the electrical angle of the rotor with respect to the stator is unknown. In systems where the control and drive functions are performed in separate platforms, this can add a lot of needless complexity.


Torque T delivered by a sinedriven BLDC motor is:

T =IlineKt cosα

where α is the angle of misalignment between the magnets and the windings.

As long as the angle of misalignment is constant, output torque will remain smooth, without “ripple.” And although misalignment reduces torque (actually Kt), it is usually by very little (<2%) for reasonable values of α (<10°). Note: misalignment is usually specified in degrees “electrical.” To convert to mechanical degrees, the angle must be divided by the number of pole pairs.

Despite the fact that torque rolloff due to electrical angle misalignment is a cosine function – and therefore insignificant for small angles – it is still necessary to align the electrical angle with the motor angle. Any amount of misalignment wastes energy as motor heat, energy that would otherwise (in a properly aligned system) produce torque.

In perhaps the worst case (cosα<0), the motor will produce torque (or force in the case of a linear motor) in a direction opposite of that which is expected. This translates to positive feedback (in the position loop) and can have catastrophic consequences.

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Alignment methods

There are many ways to align the electrical angle in a sine-drive system. Perhaps the simplest procedure is pointing.

A voltage or current is applied to the motor for a random electrical angle. While current is held constant, the rotor is allowed to move (assuming it overcomes friction) and settle at a “null” position where force or torque is zero. Here, cos = 0, meaning that α is 90° from the applied electrical angle.

If current is applied at an angle of 270°, for example, and is 90°, then the total is 360 or 0°. So, once the rotor has completed its movement, the system is “pointed” at 0° electrical. The controller, then, uses this position as its reference for all future commutation.

The main benefit of using pointing to align a BLDC motor is its simplicity; it requires no additional sensors and employs system function blocks that already exist. What’s more, it’s quite accurate for systems with reasonably low friction.

What usually turns potential users away, however, is that pointing requires movement. Not just movement, but movement in a direction that cannot be predicted. In linear system, this can be disastrous because the motion may be into a hard stop. Some controllers get around this by minimizing movement to less than a quarter of an electrical cycle or so.

Hall sensing

Many motors used in sine-drive systems are actually built for trapezoidally commutated systems. The Hall-effect sensors incorporated in these motors lend themselves to electrical angle alignment.

Aligning with Hall sensors is a two-step process. First, the controller freezes the electrical angle (used to commutate the motor) at the “center” of the Hall transitions. After that, the controller monitors the Hall sensor, loading the appropriate electrical angle at the next transition. The electrical angle is then allowed to update using an incremental sensor.

Hall sensing is a good choice in a number of applications. But if the sensors and associated wiring are not already installed, it can get expensive. Also, despite published data to the contrary, Hall sensor alignment is often out of spec (typically by 9° electrical).

One thing to be aware of when using Halls for alignment is that the distance from a Hall state edge to the center is 30° electrical. Thus, the apparent motor Kt will drop to about 87% of its normal value just before the edge. Put another way, there will be a brief, one-time torque disturbance that occurs just as the new electrical angle is loaded – unless there’s some sort of mechanism to ramp the 30° error value down gradually.

Inductance measurement

In systems where cost is important (and alignment by pointing is not an option due to the random motion) rotor position may be determined by measuring the winding inductance.

This method yields position information that’s about as accurate as using Halls. However, the inductance measurement is nearly impossible to perform when the motor is being driven. For this reason, the method has limited use in positioning systems.

Inductance measurements are typically combined with back emf sensor data to provide commutation information for systems controlling velocity rather than position. Disk drives, fans, and pumps are classic examples.

Absolute alignment

Because of trade-offs involved with aligning a sine-commutated BLDC motor, many designers turn to absolute position sensors to dispense with the problem altogether. This is a good solution if the system already has a resolver or encoder on board. However, there are a couple of caveats.

First, the position sensor must be “electrically” aligned with the motor. Don’t assume anything because it must be specified.

If the sensor and motor are not aligned, then virgin systems will require a different alignment procedure (as well as nonvolatile memory to store an “offset angle”) than the one used in normal operation. This, in turn, can complicate field repairs and the replacement of system components.

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Another consideration has to do with multi-speed resolvers. Any combination of motor and multispeed resolver must meet the following criteria:

N (Number of resolver speeds) = Number of motor pole pairs

where N is an integer (1,2,3,4,5....).

The simplest case is where N = 1. The number of motor pole pairs matches the number of resolver speeds, making the electrical angle equal to the angle read by the resolver. Failing to comply with this condition necessitates the use of one of the other alignment schemes.

One final thing to remember about alignment using Hall sensors or absolute information is that the electrical angle of the motor is offset by 30° (electrical) from the (rising) zero-crossing of the phase A back emf.

System architecture

As with all start-up and initialization issues, electrical angle alignment can drive system design (or redesign).

When considering the options it is important to remember that with brushless dc motors in positioning systems, there are really three blocks in the system diagram that require position information: the position loop, the current loop, and the commutation controller. If, as with some “smart drives,” the position information comes to the drive as well as to an independent controller, the drive and the controller must be made to work together to determine the electrical angle, and then use it to commutate the motor correctly.

Brushless dc motors

Brushless dc motors are like their brush type counterparts, only inside out – with permanent magnets on the rotor and windings on the stator. Eliminating brushes (with electronic commutation) offers several advantages. For one, it improves system reliability. It also reduces EMI. Brushless motors also tend to run cooler because their windings, embedded in the stator, have a low thermal impedance path to ambient.

The simplest form of electronic commutation is called six-step or trapezoidal commutation. Trapezoidal is a reference to the ideal shape for the drive current. Six-step commutation timing is based on binary signals from three Hall-effect sensors. The sensors, equally spaced around the stator, change state each time they detect a passing rotor pole.

If the Hall sensors were perfectly placed and the back emf exactly trapezoidal, motor torque would be constant for a given drive current, independent of rotor position. But Hall sensors are never placed perfectly, nor do they provide perfectly timed switching signals because of hysteresis.

The resulting timing irregularities cause current discontinuities that produce torque disturbances. These unpredictable disturbances have a significant and negative effect on positioning systems. As a result, motors for precision positioning systems usually employ sinusoidal commutation driven by sinusoidal current waveforms.

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