**Category: **eMotors** > **Controllers > Field
Oriented Controllers

The Field Oriented Controller (FOC) block attempts to maximize torque output by controlling the stator flux position in the direct (d) axis and current in the orthogonal quadrature (q) axis. The Field Oriented Controller (FOC) block includes many interconnected subsystems to accomplish this goal. Clarke’s and Park’s transformations are used to convert the 3-phase current measurement into DQ frame currents, which are applied to PI direct axis current control and PI quadrature axis current control, respectively. Each of these controllers is commanded by an outer loop PI speed controller that measures rotor shaft velocity, usually from a tachometer or encoder. DQ frame controls are converted back to 3-phase using the inverse Park’s transform and space vector pulse width modulation (SVPWM). SVPWM is typically used to lower harmonic content over typical PWM methods and increase DC link voltage. A current model estimates the rotor flux position from measured direct and quadrature currents, and known motor parameters. The flux (stator field) position estimate is used in the Park’s forward and inverse transformations.

**Current Model (Field Angle Estimator) Parameters**

**Number of Motor Poles:** Requires the number of motor
pole pairs.

**Sampling Rate (Hertz):** Sets the clock rate for all
the operations in the FOC. This rate must be set sufficiently large to provide
modulation depth for the SVPWM. A value of 10,000 Hz or greater are typically
set. Note that the simulation step size must at least meet this frequency.

**Inverter DC Bus Voltage**: Sets the voltage level of
the PWM pulses for each phase voltage. Units are in volts.

**Stator Self Inductance (per phase):** Requires the
3-phase AC induction motor stator per phase inductance in henries.

**Stator Leakage Inductance:** Requires the 3-phase AC
induction motor specified stator leakage inductance in henries.

**Rotor Leakage Inductance:** Requires the specified
3-phase AC induction motor rotor leakage inductance in henries.

**Rotor Resistance:** Requires the 3-phase AC induction
motor rotor winding resistance in ohms.

**PI Direct Axis Current Controller **

PI direct axis current control receives a direct axis current command from a field model and direct axis current measurement. The error between these quantities is then fed to an anti-windup PI compensator.

**Direct Axis Current Control Integral Gain:** Typically
sets the speed (bandwidth) and tracking error of the control loop. Units are
1/sec.

**Direct Axis Current Control Proportional Gain:**
Typically sets the damping of the control loop.

**Direct Axis Current Control Upper Sat Limit:** Sets
the upper output limit of the PI direct axis current controller. Hard limiting
is designed to prevent compensator integral wind-up. Units are in amps.

**Direct Axis Current Control Lower Sat Limit:** Sets
the lower output limit of the PI direct axis current controller. Hard limiting
is designed to prevent compensator integral wind-up. Units are in amps.

**PI Quadrature Axis Current Controller **

PI quadrature axis current control receives a quadrature axis current command from the speed controller and quadrature axis current measurement. The error between these quantities is then fed to an anti-windup PI compensator.

**Quadrature** **Axis Current Control Integral
Gain:** Typically sets the speed (bandwidth) and tracking error of the control
loop. Units are 1/sec.

**Quadrature** **Axis Current Control Proportional
Gain:** Typically sets the damping of the control loop.

**Quadrature** **Axis Current Control Upper Sat
Limit:** Sets the upper output limit of the PI quadrature axis current
controller. Hard limiting is designed to prevent compensator integral wind-up.
Units are in amps.

**Quadrature** **Axis Current Control Lower Sat
Limit:** Sets the lower output limit of the PI quadrature axis current
controller. Hard limiting is designed to prevent compensator integral wind-up.
Units are in amps.

**PI Speed Controller **

PI speed control receives a target speed command, and actual speed measurement. The error between these quantities is then fed to an anti-windup PI compensator.

**Speed Control Integral Gain:** Typically sets the
speed (bandwidth) and tracking error of the speed control loop. Units are
amp/rad.

**Speed Control Proportional Gain:** Typically sets the
damping of the speed.

**Speed Control Upper Sat Limit:** Sets the upper output
limit of the PI speed controller. Hard limiting is designed to prevent
compensator integral wind-up. Units are in amps.

**Speed Control Lower Sat Limit:** Sets the lower output
limit of the PI speed controller. Hard limiting is designed to prevent
compensator integral wind-up. Units are in amps.

**Diagram name: **FOC Controller

**Location: **Examples > eMotors > AC Induction

The following simulation example illustrates the application of the Field Orientated Controller (FOC) block in controlling speed of a 3-phase AC induction motor using a rotary encoder for feedback. Current is sensed using the motor model output currents. The command profile shows stable and accurate control of speed over a wide range of speeds.