Commutating optical encoder: 100 to 10,000 line-count incremental optical Hall encoders are used for Hall commutation signaling to sixstep drives. They eliminate position and phasing inaccuracy, holding them to within ±0.5 electrical degrees.

In the last installment of this two-part series, we explored how permanent-magnet brushless dc servomotors (PMBDCs) provide the highest continuous torque density and efficiency of any electric motors.

To actually get top performance from these motors, though, and keep each phase-current input coordinated with the motor's corresponding back emf/torque function, proper feedback is required.

Real PMBDC motors

It is impossible to supply switched dc current to each phase pair that perfectly follows the input commutation signal. The phaseneutral output here is more realistic than other modeled trapezoidal output. The fl at sections are at 90°.
Select figure to enlarge.

Until now, we have assumed that our motor is an ideal three-phase, wye connected PMBDC motor, with perfect back emf/torque functions. In reality, it is difficult (if not impossible) to construct a motor with ideal back emf. Manufacturers can only construct motors that produce phase-neutral back emf that, when plotted, looks trapezoidal — but not with 120 electrical-degree flat areas at the top and bottom.

Instead, real PMBDC motor plots have 60 to 90 electrical-degree flats at top and bottom — and when two phases are combined, the resulting line-line back emf looks more sinusoidal than trapezoidal. See Figs. 4 and 5. This type of PMBDC motor output is often called quasi-sinusoidal K_E.

In addition to quasi-sinusoidal motors, it is quite simple to construct motors that output true sinusoidal back emf with less than 1% total harmonic distortion. Today, the majority of commercially available PMBDC motors output this sinusoidal K_E — shown in Fig. 6.

Both sinusoidal and quasi-sinusoidal motors can be operated using a six-step drive. However, this doesn't output normalized, constant torque output. Instead, the output includes what's called drive-induced torque ripple, shown at the bottom of Figs. 4, 5, and 6. If an application can tolerate torque ripple, then a six-step drive may be most suitable — as they are less costly than other options.

True sinusoidal K_E motors

This output includes 60° fl ats that are phase-neutral.
Select images to enlarge.

Most commercially available PMBDC drives are sinusoidal - not six step. Traditionally, Hall switches provide commutation signals to these drives. However, by the 1980s, commutating optical encoders proliferated; now, their incorporated Hall signals are generally used for motor startup only. Why?

Until a drive senses an index pulse, it doesn't know exact rotor position. For this reason, optical Halls are still used for initial startup information.

Once a PMBDC motor is up and running, its drive servo electronics only need an encoder's line count per revolution and index pulse to control motor position and velocity. As with ideal trapezoidal motors (theoretically) driven by a six-step drive, true sinusoidally driven K_E motors output maximum continuous torque and efficiency when each phase current is kept in phase with the motor's corresponding back emf/torque function.

Let us explore this mathematically.

As with all PMBDC motors, K_E(θ) (in V/rad/sec) equals K_T(θ) (in Nm/A) — so that the three line-neutral back emf/torque functions R, S, and T for a true sinusoidal K_E motor are:

With these three line-neutral torque functions, three corresponding phase currents supplied to the motor by the sinusoidal drive are:

As is customary in sinusoidal ac circuit analysis, each phase current is allowed to have a different phasing ϕ with respect to the corresponding back emf/torque function.

Multiplying each phase current by its corresponding back emf/torque function and then adding all three gives the total torque produced by a true sinusoidal motor/drive combination:

T_R +T_S +T_T