# Flux Observer

Compute electrical position, magnetic flux, and electrical torque of rotor

• Library:
• Motor Control Blockset / Sensorless Estimators

• ## Description

The Flux Observer block computes the electrical position, magnetic flux, and electrical torque of a PMSM by using the per unit voltage and current values along the α- and β-axes in the stationary αβ reference frame.

### Equations

These equations describe the computation of the electrical position, magnetic flux, and electrical torque by the block.

`${T}_{\text{e}}=\frac{3}{2}P\left({\psi }_{\alpha }{I}_{\beta }-{\psi }_{\beta }{I}_{\alpha }\right)$`

where:

• ${V}_{\alpha }$ and ${V}_{\beta }$ are the α-axis and β-axis voltages.

• ${I}_{\alpha }$ and ${I}_{\beta }$ are the α-axis and β-axis current.

• $R$ is the stator resistance of the motor.

• $L$ is the stator inductance of the motor.

• $P$ is the number of motor pole pairs.

• $\psi$ is the rotor magnetic flux.

• ${\psi }_{\alpha }$ and ${\psi }_{\beta }$ are the rotor magnetic fluxes along the α- and β-axes.

• ${T}_{e}$ is the electrical torque of the rotor.

• ${\theta }_{e}$ is the electrical position of the rotor.

## Ports

### Input

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Voltage component along the α-axis in the stationary αβ reference frame.

Data Types: `single` | `double` | `fixed point`

Voltage component along the β-axis in the stationary αβ reference frame.

Data Types: `single` | `double` | `fixed point`

Current along the α-axis in the stationary αβ reference frame.

Data Types: `single` | `double` | `fixed point`

Current along the β-axis in the stationary αβ reference frame.

Data Types: `single` | `double` | `fixed point`

The pulse (true value) that resets the block algorithm.

Data Types: `single` | `double` | `fixed point`

### Output

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The electrical position of the rotor as estimated by the block.

#### Dependencies

To enable this port, set Block output to `Position`.

Data Types: `single` | `double` | `fixed point`

The magnetic flux of the rotor as estimated by the block.

#### Dependencies

To enable this port, set Block output to `Flux`.

Data Types: `single` | `double` | `fixed point`

The electrical torque of the rotor as estimated by the block.

#### Dependencies

To enable this port, set Block output to `Torque`.

Data Types: `single` | `double` | `fixed point`

## Parameters

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### Motor parameters

Select the unit of the α and β-axes voltage and current input values.

Select one or more quantities that the block should compute and display in the block output.

Note

You must select at least one value. The block displays an error message if you click or without selecting any value.

Number of pole pairs available in the motor.

#### Dependencies

To enable this parameter, set Block output to `Torque`.

Stator phase winding resistance of the motor in ohms.

Stator winding inductance of the motor along d-axis in Henry.

The fixed time interval in seconds between two consecutive instances of block execution.

### Datatypes

Unit of the electrical position output.

#### Dependencies

To enable this parameter, set Block output to `Position`.

Data type of the electrical position output.

#### Dependencies

To enable this parameter, set Block output to `Position`.

Unit of the magnetic flux output.

#### Dependencies

To enable this parameter, set Block output to `Flux`.

Data type of the magnetic flux output.

#### Dependencies

To enable this parameter, set Block output to `Flux`.

Unit of the electrical torque output.

#### Dependencies

To enable this parameter, set Block output to `Torque`.

Data type of the electrical torque output.

#### Dependencies

To enable this parameter, set Block output to `Torque`.

 O. Sandre-Hernandez, J. J. Rangel-Magdaleno and R. Morales-Caporal, "Simulink-HDL cosimulation of direct torque control of a PM synchronous machine based FPGA," 2014 11th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Campeche, 2014, pp. 1-6. (doi: 10.1109/ICEEE.2014.6978298)

 Y. Inoue, S. Morimoto and M. Sanada, "Control method suitable for direct torque control based motor drive system satisfying voltage and current limitations," The 2010 International Power Electronics Conference - ECCE ASIA -, Sapporo, 2010, pp. 3000-3006. (doi: 10.1109/IPEC.2010.5543698)

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