To achieve better dynamic performance, a more complex control scheme needs to be applied to control the motor. With the mathematical processing power offered by microcontrollers, advanced control strategies which use mathematical transformations to decouple the torque generation and the magnetization functions in PM motors can be implemented. Such de-coupled torque and magnetization control is commonly called rotor flux oriented control, vector control, or simply Field-Oriented Control (FOC).

In a direct current (DC) motor, the excitation for the stator and rotor is independently controlled, the produced torque and the flux can be independently tuned as shown in Figure 3-2. The strength of the field excitation (for example, the magnitude of the field excitation current) sets the value of the flux. The current through the rotor windings determines how much torque is produced. The commutator on the rotor plays an interesting part in the torque production. The commutator is in contact with the brushes, and the mechanical construction is designed to switch into the circuit the windings that are mechanically aligned to produce the maximum torque. This arrangement then means that the torque production of the machine is fairly near exceptional all the time. The key point here is that the windings are managed to keep the flux produced by the rotor windings orthogonal to the stator field.

Figure 3-2 Flux and Torque are Independently Controlled in DC Motor Model

The goal of FOC on synchronous and asynchronous machines is to be able to separately control the torque-producing and magnetizing flux components. FOC algorithms allows decoupling of the torque and of the magnetizing flux components of stator current. With decoupled control of the magnetization, the torque producing component of the stator flux can now be thought of as independent torque control. To decouple the torque and flux, it is necessary to engage several mathematical transforms, and this is where a microcontroller adds the most value. The processing capability provided by a microcontroller enables these mathematical transformations to be carried out very quickly. This, in turn, means that the entire algorithm controlling the motor can be executed at a fast rate, enabling higher dynamic performance. In addition to the decoupling, a dynamic model of the motor can also be used for the computation of many values such as rotor flux angle and rotor speed, improving overall quality of control.

According to the laws of electromagnetism, the torque produced in a synchronous machine is equal to the vector cross product of the two existing magnetic fields as in Equation 15 .

This expression shows that the torque is maximum if stator and rotor magnetic fields are orthogonal, meaning 90 degrees apart. If this condition can be maintained all the time and if the flux can be oriented correctly, the torque ripple is reduced and a better dynamic response is provided. However, for this to be true, the rotor position must be known: this can be achieved either with a physical position sensor (such as an incremental encoder) or a sensorless rotor position observer.

In order to achieve the goal of aligning the stator flux orthogonally to the rotor flux, the d-axis component of the stator current in the (direct, quadrature) rotating reference frame is set to zero. The (d, q) rotating reference frame is explained more fully in Section 3.1.1.1.2. When this condition is true, the stator flux and the rotor flux are orthogonally aligned. The d-axis component of the stator current can also be used in some cases for Field Weakening, which allows for reduction of back- emf and for the motor to operate at higher speeds.

FOC consists of controlling the stator currents represented by a vector. This control is based on projections which transform a three-phase time and speed dependent system into a two coordinate (d and q coordinates) time invariant system. These projections lead to a structure similar to that of a DC machine control. FOC machines need two constants as input references: the torque component (aligned with the q coordinate) and the flux component (aligned with d coordinate). As FOC is simply based on projections, the control structure handles instantaneous electrical quantities. This makes the control accurate in every working operation (steady state and transient) and independent of the limited bandwidth mathematical model. The FOC thus solves the problems of classical motor control schemes, in the following ways:

• The ease of reaching constant reference (torque component and flux component of the stator current)
• The ease of applying direct torque control because in the (d, q) reference frame the expression of the torque is defined in Equation 16.
  Equation 16. ${\tau }_{\mathrm{e}\mathrm{m}}\propto {\psi }_{\mathrm{R}}\times {\mathrm{i}}_{\mathrm{s}\mathrm{q}}$

By maintaining the amplitude of the rotor flux (ψ_R) at a fixed value, a linear relationship between torque and torque component (i_Sq) is obtained. Therefore, the torque can be controlled by controlling the torque component of the stator current vector.