*4.1.1. Speed/torque vector control*

The concept of vector control was first proposed by Siemens' F. Blaschke in the early 1970s, which is also named as field-oriented control (FOC). In this method, the stator current of a three-phase AC motor is transformed into two orthogonal components [18]. One component can control the magnetic flux; the other can control the torque.

In a typical FOC block diagram for a permanent magnet synchronous motor (PMSM), the control system first transforms the command speed or torque into the corresponding current command *i d* \*, *i q* \*. Then, proportional-integral (PI) controllers are used as current regulator to generate the reference d–q axis reference voltage. The transistor switching is defined by the pulse-width modulation signal according to the stator references voltage.

For the FOC system, the most important thing is to realize the Clarke and Park transformation. It is these transformations that connect the three-phase coordinate system to the *d* −*q* axis coordinate system. The Clarke transformation converts three-phase currents to a two-axis plot to create time-varying quadrature-current values *i <sup>α</sup>* and *i <sup>β</sup>*. And the Park transformation is between the stationary coordinates *α* −*β* and the *d* −*q* coordinate reference frame rotated to align with the rotor flux. As the *d* axis is always in the direction of magnet flux linkage and *q* axis in the quadrature direction, the values of *i <sup>d</sup>* and *i <sup>q</sup>* remain constant. The flux and torque are separately controlled by stator direct-axis current *i <sup>d</sup>* and quadrature-axis current *i q*.

FOC is used to control the AC synchronous and induction motors by transforming their dynamic structure into that of DC machines. Unfortunately, the scheme requires many electronic components such as sensors, amplifiers, or multipliers which increase the cost and more calculations are needed to realize the control strategy. This situation is changed due to the availability of microelectronics, with the cost of control hardware being no longer a major consideration [19].
