# SynRM Torque Estimator

**Libraries:**

Motor Control Blockset /
Controls /
Control Reference

## Description

The SynRM Torque Estimator block generates electromechanical torque and power estimates to enable field-oriented control of a synchronous reluctance motor (SynRM) and permanent magnet-assisted synchronous reluctance motor (PMaSynRM). The block outputs mathematically computed electromechanical torque for the given motor parameters. To measure the torque value accurately, consider using a physical sensor.

The block accepts feedback values of *d-* and *q*-axis
currents and mechanical speed as inputs.

The block generates these estimates from motor parameters specified using one of these methods.

`Linear model with lumped parameters`

— Lumped parameters with*d*-axis and*q*-axis stator winding inductances and permanent magnet flux linkage.`Non-linear model with D,Q-flux linkage LUTs`

— Nonlinear model with*d*-axis and*q*-axis flux linkage lookup tables.`Non-linear model with Ld and Lq LUTs`

— Nonlinear model with*d*-axis and*q*-axis stator winding inductance lookup tables.`Non-linear model with Ld, Lq, and FluxPM LUTs`

— Nonlinear model with*d*-axis and*q*-axis stator winding inductances and permanent magnet flux linkage lookup tables.`Input port based Ld and Lq`

—*d*-axis and*q*-axis stator winding inductance values provided using separate input ports.`Input port based Ld, Lq, and FluxPM`

—*d*-axis and*q*-axis stator winding inductances and permanent magnet flux linkage values provided using separate input ports.

### Equations

If you select `Per-Unit (PU)`

in the **Input
units** parameter, the block scales down the internal parameters to match
the per-unit scale by default. You can also configure the block to convert the inputs to
SI units before performing any computation and convert them back to per unit values
after calculating the output by using the **Allow scaled-down motor parameters
with CodeGen (higher precision with Fixed-Point data type)**
parameter.

These equations describe the computation of electromechanical torque and power estimates by the block.

**Note**

The following equations for SynRM and PMaSynRM follow a
*d*-*q* axis notation that is identical to
that of a permanent magnet synchronous motor (PMSM).

For SynRM:

$${T}_{e}=\frac{3}{2}p\left({L}_{d}-{L}_{q}\right){I}_{d}{I}_{q}$$

For PMSynRM:

${T}_{e}=\frac{3}{2}p\left\{{\psi}_{m}{I}_{q}+\left({L}_{d}-{L}_{q}\right){I}_{d}{I}_{q}\right\}$

or

For both SynRM and PMaSynRM:

$${T}_{e}=\frac{3}{2}p({\psi}_{d}{i}_{q}-{\psi}_{q}{i}_{d})$$

${P}_{\text{e}}={T}_{e}\cdot {\omega}_{\text{m}}$

where:

${L}_{\text{d}}$ and ${L}_{\text{q}}$ are the

*d*-axis and*q*-axis stator winding inductances (henry).${I}_{\text{d}}$ and ${I}_{\text{q}}$ are the

*d*-axis and*q*-axis current (amperes).*ψ*is the permanent magnet flux linkage (weber)._{m}*ψ*and_{d}*ψ*are the magnetic fluxes along the_{q}*d-*and*q*-axes (weber).$$p$$ is the number of pole pairs available in the motor.

$${\omega}_{m}$$ is the mechanical speed of the rotor (rad/s).

For a detailed set of equations and assumptions that Motor Control Blockset™ uses for a synchronous reluctance machine, see Synchronous Reluctance Machine (Simscape Electrical).

## Examples

## Ports

### Input

### Output

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2024a**