# Module 2: PMSM and FOC Theory

Discussion created by dumitru-daniel.popa on Dec 4, 2017
Latest reply on Apr 28, 2020 by AGUSTIN REY

INTRODUCTION

In this module of the, the focus is on the theory of the Permanent Magnet Synchronous Motor (PMSM) operation and Field Oriented Control (FOC) used to control the speed and position of PMSM's rotor.

From the beginning we need to point out that we will not go thru all the details of construction or mathematical models of the PMSM. If you look for specific details then the advice is to look for specific engineering handbooks.

The main goal of this article is to highlight only the specific details that represents the basics of PMSM motor control since we will use these aspects throughout the workshop. You can think about this as crash course that explains the key aspects of the theory behind PMSM and FOC.

Video training: How Permanent Magnet Synchronous Motors are built and what is Field Oriented Control

Please watch this video before going further. The rest of the article is a summary of the video.

PMSM MAIN COMPONENTS

A typical PMSM construction consists in a stator (Fig. 1) that supports three windings/coils connected in star or delta configuration which are energized with AC power. These windings/coils are placed around magnetic pole shoes that force the magnetic flux produced by the AC current passing the coil to take a specific path in order to maximize the motor efficiency.

 Fig. 1: The stator of the motor we are going to use for experiments in this workshop

The PMSM's rotor (Fig. 2) is usually made of permanent magnets mounted on the surface (SPM) or inside the rotor (IPM) and a steel shaft that transit the torque to various devices.

 Fig. 2: The rotor with surface mounted permanent magnets

The motor we are going to use thin this workshop was chosen to facilitate the development of the sensorless motor control. It has two pole pairs which are built in so called salient pole rotor type. This means that the stator flux path lengths varies in respect with the rotor position. This is a fancy way to say that the magnetic reactance is different between the motor flux and torque axes. This will helps us to build a magnetic salient tracking observer to estimate the rotor position and to eliminate the need for having a position sensor mounted on the motor shaft.

ROTATING MAGNETIC FIELDS

The key to rotate the motor's rotor is to be able to produce a rotating magnetic field in the stator like the one in Fig. 3. The most common way to produce a rotating magnetic field is to energized the coils with AC currents. If a three phase balanced current system is passed thru a system made of three windings/coils that are spatially distributed at 120 degrees apart, then the resulting magnetic field will rotate with the same frequency as the 3-phase AC current. The "guy" that figured this out was Mr. Tesla

 Fig. 3: Producing a rotating magnetic field in the stator

If we oversimplify the physical processes that happens inside the stator coils and yoke, and instead of a continuous AC current waveforms we conveniently choose only 6 strategic interest points then you can easily see how the resulting magnetic flux vector is shifting its direction in sync with the AC current systems.

Controlling the position and strength of the magnetic field produced in the stator is the first step towards the Field Oriented Control.

FIELD ORIENTED CONTROL SECRETS

The ESSENCE of Field Oriented Control is to align the stator current vector (Is) that produces the rotating magnetic field (red dotted line arrow in Fig. 4.) with the rotor torque-axis. To have the motor to perform at its peek efficiency the magnetic flux produced by the stator windings must be at 90 electrical degrees compared to the magnetic flux produced by the rotor.

 Fig. 4: Field Oriented Control Goals

To align the stator flux vector with the rotor torque axis a the key aspect of Field Oriented Control technique is to know the position of the rotor at any moment (the angle between the rotor flux axis and the stator phase A magnetic axis). Without this critical piece of information the whole mechanism will fail to perform.

The Field Oriented Control gives us a the possibility to simplify the entire control structure of the synchronous machines using a series of mathematical transformations that allows us to think and act as in a linear domain rather that in a complex one where quantities varies in time and space. In other words, by using the FOC and the concepts derived from it we can transforms a 3-phase AC motor into a simple 1-phase DC motor where magnetic field and motor torque can be controlled separately and this mechanism is described in Fig. 5.

 Fig. 5: Clarke and Park transformation used for Field Oriented Control

Starting from a 3-phase PMSM standard mathematical model that is described by 3 differential equations in a fixed reference system, we can perform a simple Clark transformation to reduce the number of equations and then have them translated using Park transformation from a time domain into a Laplace domain where the model can be described by 2 simple linear algebraic equations as shown in Fig. 6.

 Fig. 6: PMSM mathematical model simplified with Clarke and Park transformations

That's the beauty of Field Oriented Control.

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