Field Oriented Control (FOC) Algorithm Introduction

1.Introduction

Motor control is a highly powerful yet challenging field that must consider constraints such as product cost, power consumption reduction, power factor correction (PFC), and EMI reduction.

Due to their advantages of high reliability, stability, low cost, and high efficiency (>80%), induction motors are widely used in industrial DC motor controllers and HVAC variable refrigerant flow systems.

However, the complex mathematical model of motors, nonlinearity during saturation, and parameter oscillations caused by physical temperature make AC induction (ACI) motors difficult to control. This led to the introduction of “Vector Control”.

This article focuses on one particular method: Field Oriented Control (FOC), primarily based on three aspects:

1. The current and voltage space vectors of the machine
2. The transformation from a three-phase speed and time-dependent system to a two-coordinate time-invariant system
3. The generation of effective space vector PWM patterns
4. Induction Motors

As introduced in previous articles, induction motors derive from the way the rotor magnetic field is generated. The rotating stator magnetic field induces currents in the short-circuited rotor, which produce the rotor magnetic field that then interacts with the stator field to generate torque for mechanical applications.

When the rotor begins to accelerate and approaches the synchronous speed of the stator field, the speed difference between rotor and stator flux decreases, reducing the induced voltage in the stator and the energy-to-torque conversion. This leads to torque reduction until the motor reaches steady state, where load torque matches motor torque. This equilibrium point depends on the motor’s instantaneous load, with key characteristics:

• The induction mechanism requires a speed difference between motor speed and stator flux speed. Induction motors rotate near but below synchronous frequency.
• This slip must exist, even when using FOC control algorithms.
• The induction motor’s rotor is not externally excited, meaning it requires no slip rings or brushes, resulting in robust, low-cost and maintenance-free operation – similar to sensorless BLDC controllers.
• Torque generation is determined by the angle formed between rotor and stator flux.

Notes:
(1) Ω = rotor speed
(2) Slip S: The parameter connecting rotor and stator, representing the difference between synchronous frequency and actual motor speed

(3) Defines rotating magnetic field speed versus rotating rotor speed

3. FOC Technology

1) Introduction

Traditional voltage/frequency control offers poor performance. To achieve better control performance, mathematical transformation is required to decouple torque generation and magnetic field functions. This decoupled torque and flux control is commonly called rotor flux linkage control or FOC.

First consider DC motors: Their excitation and torque generation can be independently adjusted. The key is that the windings are managed to ensure the flux generated by the rotor is perpendicular to the stator field. Flux and torque can be controlled separately, with rotor current determining torque magnitude.

Induction motors are completely different. In all cases, only the stator current can be controlled. In asynchronous motors, the source of power and magnetic field is the stator phase voltage, where flux and torque are interdependent (coupled). FOC aims to separately control the torque and flux components, mimicking DC motor control – similar to how BLDC motor controllers operate.

3) Why Use FOC?

Asynchronous motors have limitations under V/Hz control that FOC can resolve by decoupling the influence between torque and flux. With decoupled flux control, the torque-producing component of stator flux can be treated as independent torque control. This decoupled control allows the magnetic field to be maintained at an appropriate level during low speeds while controlling torque to regulate speed. Decoupling requires introducing certain mathematical transformations.

4) Technical Background

FOC involves controlling stator current represented as a vector. The control is based on mapping: transforming a three-phase time and speed dependent system into a two-axis time-invariant system, making the structure resemble DC machine control. FOC requires two constant input references: the torque component (aligned with q-axis) and flux component (aligned with d-axis).

FOC is based on projections, with a control structure that manages instantaneous electrical quantities. This enables precise mathematical model control during all operating conditions (steady-state and transient) with independent bandwidth limitations. FOC solves traditional solution problems:

Easily achieves constant references (torque and flux components of stator current)

Facilitates direct torque control because in the (d,q) reference frame, torque expression becomes:

By maintaining the amplitude of rotor flux (ΦR) at a fixed value, torque (m) and torque component (isq) have a linear relationship. Controlling the torque component of stator current vector enables torque control.

5) Space Vector Definition and Projection

Three-phase voltage, current and flux in AC motors can be analyzed using complex space vectors.