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 or an induction motor 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 how the block computes the electrical position, magnetic flux, and electrical torque for a PMSM.

$${\psi }_{\alpha }= {{\displaystyle \int }}^{\text{}}(V_{\alpha }-I_{\alpha }R)\text{dt}- \left(L_s\cdot I_{\alpha }\right)$$

${\psi }_{\beta }= {{\displaystyle \int }}^{\text{}}(V_{\beta }-I_{\beta }R)\text{dt}- \left(L_s\cdot I_{\beta }\right)$

$$\psi = \sqrt{{\psi }_{\alpha }^2+{\psi }_{\beta }^2}$$

$T_{\text{e}}=\frac{3}{2}P({\psi }_{\alpha }{I}_{\beta }-{\psi }_{\beta }{I}_{\alpha })$

${\theta }_{\text{e}}= {\tan }^{-1}\frac{{\psi }_{\beta }}{{\psi }_{\alpha }}$

These equations describe how the block computes the rotor electrical position, rotor magnetic flux, and electrical torque for an induction motor.

$${\psi }_{\alpha }=\frac{L_r}{L_m} \left({{\displaystyle \int }}^{\text{}}(V_{\alpha }-I_{\alpha }R)\text{dt}- \sigma L_s{I}_{\alpha }\right)$$

$${\psi }_{\beta }=\frac{L_r}{L_m} \left({{\displaystyle \int }}^{\text{}}(V_{\beta }-I_{\beta }R)\text{dt}- \sigma L_s{I}_{\beta }\right)$$

$$\sigma =1-\frac{L_m^2}{L_r\cdot L_s}$$

$$\psi = \sqrt{{\psi }_{\alpha }^2+{\psi }_{\beta }^2}$$

$T_{\text{e}}=\frac{3}{2}\cdot P\cdot \frac{L_m}{L_r}({\psi }_{\alpha }{I}_{\beta }-{\psi }_{\beta }{I}_{\alpha })$

${\theta }_{\text{e}}= {\tan }^{-1}\frac{{\psi }_{\beta }}{{\psi }_{\alpha }}$

where:

• $V_{\alpha }$ and $V_{\beta }$ are the α-axis and β-axis voltages (Volts).

• $I_{\alpha }$ and $I_{\beta }$ are the α-axis and β-axis current (Amperes).

• $$R$$ is the stator resistance of the motor (Ohms).

• $$L_s$$ is the stator inductance of the motor (Henry).

• $$L_r$$ is the rotor inductance of the motor (Henry).

• $$L_m$$ is the magnetizing inductance of the motor (Henry).

• $\sigma$ is the total leakage factor of the induction motor.

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

• $$\psi$$ is the rotor magnetic flux (Weber).

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

• $$T_e$$ is the electrical torque of the rotor (Nm).

• ${\theta }_e$ is the electrical position of the rotor (Radians).

Ports

Input

Vα — α-axis voltage

scalar

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

Data Types: single | double | fixed point

Vβ — β-axis voltage

scalar

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

Data Types: single | double | fixed point

Iα — α-axis current

scalar

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

Data Types: single | double | fixed point

Iβ — β-axis current

scalar

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

Data Types: single | double | fixed point

Rst — Reset block

scalar

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

Data Types: single | double | fixed point

Output

θe — Electrical position of motor

scalar

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

Ψ — Rotor flux of motor

scalar

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

Te — Electrical torque of motor

scalar

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

Motor parameters

Motor selection — Type of motor

PMSM (default) | ACIM

Select the type of motor that the block supports.

Input units — Unit of voltage and current inputs

SI unit (default) | Per-unit

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

Block output — Select outputs that block should compute

Position (default) | Flux | Torque

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 Ok or Apply without selecting any value.

Pole pairs — Number of pole pairs available in motor

4 (default) | scalar

Number of pole pairs available in the motor.

Dependencies

To enable this parameter, set Block output to Torque.

Stator resistance (ohm) — Stator winding resistance

0.36 (default) | scalar

Stator phase winding resistance of the motor in ohms.

Stator d-axis inductance (H) — Stator winding inductance along d-axis

0.2e-3 (default) | scalar

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

Dependencies

To enable this parameter, set Motor selection to PMSM.

Stator leakage inductance (H) — Leakage inductance of stator winding

0.0068 (default) | scalar

Leakage inductance of the induction motor stator winding in Henry.

Dependencies

To enable this parameter, set Motor selection to ACIM.

Rotor leakage inductance (H) — Leakage inductance of rotor winding

0.0068 (default) | scalar

Leakage inductance of the induction motor rotor winding in Henry.

Dependencies

To enable this parameter, set Motor selection to ACIM.

Magnetizing inductance (H) — Magnetizing inductance of induction motor

0.0300 (default) | scalar

Magnetizing inductance of the induction motor in Henry.

Dependencies

To enable this parameter, set Motor selection to ACIM.

Cutoff frequency (Hz) — Cutoff frequency of internal high-pass filter

3.1863 (default) | scalar

Cutoff frequency of the internal high-pass filter (that filters noise) in Hertz.

The Flux Observer block uses an internal first order IIR high-pass filter. You should set the Cutoff frequency (Hz) for this filter to a value that is lower than the lowest frequency corresponding to the minimum speed of the motor. For example, you can enter a value that is one-tenth of the lowest electrical frequency of the stator voltages and the currents. However, you can adjust this value to determine a more accurate cutoff frequency that generates the desired block output.

Discrete step size (s) — Sample time after which block executes again

50e-6 (default) | scalar

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

Datatypes

Position unit — Unit of electrical position output

Radians (default) | Degrees | Per-unit

Unit of the electrical position output.

Dependencies

To enable this parameter, set Block output to Position.

Position datatype — Data type of electrical position output

single (default) | double | fixed point

Data type of the electrical position output.

Dependencies

To enable this parameter, set Block output to Position.

Flux unit — Unit of magnetic flux output

Weber (default) | Per-unit

Unit of the magnetic flux output.

Dependencies

To enable this parameter, set Block output to Flux.

Flux datatype — Data type of magnetic flux output

single (default) | double | fixed point

Data type of the magnetic flux output.

Dependencies

To enable this parameter, set Block output to Flux.

Torque unit — Unit of electrical torque output

Nm (default) | Per-unit

Unit of the electrical torque output.

Dependencies

To enable this parameter, set Block output to Torque.

Torque datatype — Data type of electrical torque output

single (default) | double | fixed point

Data type of the electrical torque output.

Dependencies

To enable this parameter, set Block output to Torque.

Model Examples

Sensorless Field-Oriented Control of PMSM

Implements the field-oriented control (FOC) technique to control the speed of a three-phase permanent magnet synchronous motor (PMSM). For details about FOC, see Field-Oriented Control (FOC).

Open Example

Sensorless Field-Oriented Control of Induction Motor

Uses sensorless position estimation to implement the field-oriented control (FOC) technique to control the speed of a three-phase AC induction motor (ACIM). For details about FOC, see Field-Oriented Control (FOC).

Open Example

References

[1] 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)

[2] 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)

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2020a