Explicit characterization of all feedback-linearizing controllers for a general type brushless DC motor

In this note, we consider feedback-linearizing control of brushless DC motors which have been increasingly used in high-performance servo applications. We completely characterize the whole class of the feedback controllers that enable the brushless DC motors to behave like linear systems but without torque ripple. The whole class of the feedback-linearizing controllers is characterized in the explicit form which contains a function to be chosen freely. The previously known controllers correspond to either the particular ones in our whole class of the feedback-linearizing controllers or their truncated Fourier expansions. This free function can be used to achieve other control objectives as well as linear dynamic characteristics. Furthermore, our feedback-linearizing controllers can be easily determined from the measurement data of back EMF and can be used even for the case of asymmetric back EMF