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# Reducing the cost of field-oriented motor control

Posted: 04 May 2015     Print Version

Keywords:Field-oriented control  FOC  motor control  motor shaft sensor  sensorless

Field-oriented control has permanently altered the way engineers think about motor control. But in order to work, it needs to know the angle of the rotor flux axis. If you are willing to pay the high cost of a motor shaft sensor, painstakingly mount that sensor on said motor shaft, connect the long cable between the sensor and the control electronics, and deal with the noise susceptibility and intermittent connections of said cable, then there's no problem. But, if like most people you prefer a more economical and robust solution, then we need to find another way to get flux angle information.

Most techniques to eliminate the shaft sensor depend on measuring other signals within the motor that are related to the flux signal. In some cases, these signals just naturally occur in a spinning motor and all we have to do is listen for them. Such algorithms fall into the category of passive techniques. Other signals only become visible if we actively stimulate the motor with higher-frequency signals.

Regardless of which technique you use, the signals of interest are often buried deep inside the motor and cannot be directly measured at the motor terminals. In such cases, we must employ a special algorithm called an observer to extract the desired signal(s) from other signals that we can observe outside the motor. There are far too many sensorless techniques to cover in one article, but we can investigate one of the most popular algorithms to provide an example of how sensorless control works. This technique is based on recreating the back-EMF signals inside the motor.

Consider the three-phase permanent magnet motor shown in figure 1. If we perform a forward Clarke transform on the three windings and write the voltage equations for the resulting alpha and beta windings, we get the equations in figure 1. This is simply the result of summing up the voltage drops across the windings' parametric elements and equating them to the applied voltage at the motor's terminals.

 Figure 1: Stationary frame voltage equations for permanent magnet synchronous motor.

From the expression in figure 1, can you find the angle information? Sure enough, it's hiding in the back-EMF signals. It would be great if we could somehow stick two voltage probes down inside the motor to measure these signals. Unfortunately, the back-EMF signals do not exist in a specific location within the motor. These signals are distributed throughout the stator coils and only appear on the motor terminals when the motor current is zero and isn't changing.

Using the differential voltage equations in figure 1, we can create block diagrams for calculating ialpha and ibeta, as shown in figure 2. The required inputs are the applied motor voltage, the back-EMF voltage, the stator resistance (Rs) and the stator inductance (Ls).

 Figure 2: Phase current estimator blocks.

Unfortunately, we don't have the back-EMF voltages. But we can measure the motor phase currents! Let's try to leverage this information to extract the missing back-EMF signals. Initially we will just assume the back-EMF voltages in figure 2 are zero. As a result, the estimates of ialpha and ibeta will likely be wrong. To determine the quality of these estimates, we compare them to the actual measurements of ialpha and ibeta, and generate error signals, as shown in figure 3.

 Figure 3: Comparing current estimates to actual values.

Now what we do with these error signals borders on magic! If there was a "Motor Control Wizard's Book of Spells," this neat little trick would certainly be in it. In figure 4, we supply the error signals to PI controllers and wrap the controller outputs around to the Back-EMF inputs.

 Figure 4: Stationary frame back EMF estimators.

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