1 Field Oriented Control (FOC)

In case of the PMSM, the rotor field speed must be equal to the stator (armature) field speed (i.e., synchronous). The loss of synchronization between the rotor and stator fields causes the motor to stall.

FOC represents the method by which one of the fluxes (rotor, stator or air gap) is considered as a basis for creating a reference frame for one of the other fluxes, with the purpose of decoupling the torque and flux-producing components of the stator current. This decoupling assures the ease of control for complex three-phase motors in the same manner as DC motors with separate excitation. This means the armature current is responsible for the torque generation, and the excitation current is responsible for the flux generation. In this application note, the rotor flux is considered as a reference frame for the stator and air gap flux.

The particularity of the FOC in the case of a Surface Mounted Permanent Magnet type PMSM (SPM) is that the d-axis current reference of the stator i_dref (corresponding to the armature reaction flux on d-axis) is set to zero. The magnets in the rotor produce the rotor flux linkage, Λ_m, unlike AC Induction Motor (ACIM), which needs a constant reference value, i_dref, for the magnetizing current, thereby producing the rotor flux linkage. The d-axis current reference for Interior Permanent Magnet type PMSM (IPM) motors is explained later in this section.

The air gap flux is equal to the sum of the flux linkage of the rotor. This is generated by the permanent magnets and the armature reaction flux linkage generated by the stator current. For the constant torque mode in FOC, the d-axis air gap flux is solely equal to Λ_m, and the d-axis armature reaction flux is zero.

Conversely, in constant power operation, the flux generating component of the stator current, negative i_d, is used for air gap field weakening to achieve higher speed.

In sensorless control, where no position or speed sensors are needed, the challenge is to implement a robust speed estimator that is able to reject perturbations such as temperature, switching noise, electromagnetic noise, and so on. Sensorless control is usually required when applications are cost sensitive, where moving parts are not allowed. For example, when position sensors are used, or when the motor is operated in an electrically hostile environment. However, requests for precision control, especially at low speeds, should not be considered a critical matter for the given application.

The position and speed estimation is based on the mathematical model of the motor. Therefore, the closer the model is to the real hardware, the better the estimator will perform. The PMSM mathematical modeling depends on its topology, differentiating mainly two types: surface-mounted motor and interior permanent magnet (IPM) motor. Each motor type has its own advantages and disadvantages with respect to the application needs.

The proposed control scheme has been developed for both surface-mounted and interior permanent magnet synchronous motors. The surface mounted motor is shown in the following figure, which has the advantage of low torque ripple and is lower in price when compared with an interior PMSM. The air gap flux for the motor type considered is smooth therefore, the inductance value of the stator, L_d = L_q (non salient PMSM), and the Back Electromagnetic Force (BEMF) is sinusoidal.

The IPM motor shown in the following figure, exhibits additional reluctance torque in addition to the permanent magnet torque. It provides higher torque at a given operating current compared to the SPM type. In an Interior PM motor, the reluctance of the magnetic flux path varies according to the rotor position. This magnetic saliency results in the variation of the inductance at the motor terminal according to the rotor position. Therefore, the effective flux length of L_d and L_q are different, L_d ≠ L_q (salient), because of PM in the flux path. Therefore an IPM motor has inductance saliency, and it utilizes both reluctance torque and permanent magnet torque.

The torque generation of IPM motors can be expressed, as shown in the following equation.

$T=\frac{3}{2}p({\mathrm{\Lambda }}_m+(L_d-L_q\left)i_d\right)i_q$

Where,

p is the number of pole pairs

L_d, L_q are the d-axis and q-axis inductances respectively

i_d, i_q are the d-axis and q-axis currents respectively

Λ_m is the magnetic flux linkage

The generated torque consists of both permanent magnet torque and the reluctance torque components. The PM torque is produced by the interaction between PM and torque current of stator windings. The reluctance torque is produced by the force acting on the magnetic material that tends to align with the main flux to minimize reluctance. Reluctance torque is independent of permanent magnet excitation.

In case of SPM motors, L_d = L_q and the above equation simplifies to

$T=\frac{3}{2}p{\mathrm{\Lambda }}_m{i}_q$

Therefore, the generated torque consists of only the permanent magnet torque component.