PMSM Torque Estimator

Estimate electromechanical torque and power

Since R2020a

• 

Libraries:
Motor Control Blockset / Controls / Control Reference

Description

The PMSM Torque Estimator block generates electromechanical torque and power estimates to enable field-oriented control of a permanent magnet synchronous motor (PMSM). 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, 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, 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.

$T_e=\frac{3}{2}p\left\{{\psi }_m{I}_q+\left(L_d-L_q\right)I_d{I}_q\right\}$

or

$$T_e=\frac{3}{2}p({\psi }_d{i}_q-{\psi }_q{i}_d)$$

$P_{\text{e}}=T_e\cdot {\omega }_{\text{m}}$

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_m is the permanent magnet flux linkage (weber).

• ψ_d and ψ_qare the magnetic fluxes along the 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 PMSM, see Mathematical Model of PMSM.

Examples

Field-Weakening Control (with MTPA) of PMSM

Implements the field-oriented control (FOC) technique to control the torque and speed of a three-phase permanent magnet synchronous motor (PMSM). The FOC algorithm requires rotor position feedback, which is obtained by a quadrature encoder sensor. For details about FOC, see Field-Oriented Control (FOC).

• Open Model

Field-Weakening Control (with MTPA) of Nonlinear PMSM Using Lookup Table

Uses a lookup table (LUT) for a nonlinear permanent magnet synchronous motor (PMSM) and controller to run the motor using field-weakening control (with maximum torque per ampere (MTPA)). Use this example to replicate and run a finite element analysis (FEA) based nonlinear, high-fidelity PMSM in simulation. This example helps motor design engineers to simulate high-performance motors in real-world motor control applications. In addition, control system engineers can use this example to design control algorithms for a given set of motor parameter data to achieve high levels of accuracy in tracking and controlling speed and torque as well as to meet efficiency requirements, especially for high-performance motors.

• Open Model

PMSM Drive Characteristics and Constraint Curves

Uses Motor Control Blockset™ to show how to use the PMSM characteristic plotting and PMSM milestone speed identification functions to obtain a control trajectory.

• Open Live Script

PMSM Constraint Curves and Their Application

Uses Motor Control Blockset™ to explain the fundamentals of constraint curves, utilization of these curves to determine operating currents, and usage of the grid of these currents in simulation or deployment environments.

• Open Live Script

Ports

Input

I_d — D-axis current

scalar

Current along the d-axis of the rotating dq reference frame.

The unit of this port depends on the Input units parameter value. If you set this parameter to SI Units, the port accepts input signal in amperes.

Data Types: single | double | fixed point

I_q — Q-axis current

scalar

Current along the q-axis of the rotating dq reference frame.

The unit of this port depends on the Input units parameter value. If you set this parameter to SI Units, the port accepts input signal in amperes.

Data Types: single | double | fixed point

ω_m — Mechanical speed of rotor

scalar

Mechanical speed of the rotor.

The unit of this port depends on the Input units parameter value. If you set this parameter to SI Units, the port accepts input signal in rad/s.

Data Types: single | double | fixed point

L_d — D-axis inductance

scalar

D-axis winding inductance.

The unit of this port depends on the Input units parameter value. If you set this parameter to SI Units, the port accepts input signal in henries.

Dependencies

To enable this input port, set Motor parameter input method to Input port based Ld, Lq, and FluxPM.

Data Types: single | double | fixed point

L_q — Q-axis inductance

scalar

Q-axis winding inductance (in henries).

The unit of this port depends on the Input units parameter value. If you set this parameter to SI Units, the port accepts input signal in henries.

Dependencies

To enable this input port, set Motor parameter input method to Input port based Ld, Lq, and FluxPM.

Data Types: single | double | fixed point

Flux_PM — Permanent magnet flux linkage

scalar

Peak permanent magnet flux linkage.

The unit of this port depends on the Input units parameter value. If you set this parameter to SI Units, the port accepts input signal in weber.

Dependencies

To enable this input port, set Motor parameter input method to Input port based Ld, Lq, and FluxPM.

Data Types: single | double | fixed point

Output

T_e — Estimated torque

scalar

Mechanical torque output of the motor.

The unit of this port depends on the block input units defined by the Input units parameter. If you set this parameter to SI Units, the port outputs signal in Nm.

Data Types: single | double | fixed point

P_e — Estimated power

scalar

Power output of the motor.

The unit of this port depends on the block input units defined by the Input units parameter. If you set this parameter to SI Units, the port outputs signal in watts.

Data Types: single | double | fixed point

Parameters

Motor Parameters

Number of pole pairs — Number of pole pairs available in motor

4 (default) | scalar

Number of pole pairs available in the motor.

Motor parameter input method — Type of motor parameters

Linear model with lumped parameters (default) | Non-linear model with D,Q-flux linkage LUTs | Non-linear model with Ld, Lq, and FluxPM LUTs | Input port based Ld, Lq, and FluxPM

Motor parameters that the block uses to generate torque and power estimates.

• Linear model with lumped parameters — Generate estimates using lumped-circuit values for motor parameters L_d, L_q, and FluxPM.

• Non-linear model with D,Q-flux linkage LUTs — Generate estimates using d-axis flux linkage FluxD and q-axis flux linkage FluxQ lookup tables (LUTs).

• Non-linear model with Ld, Lq, and FluxPM LUTs — Generate estimates using L_d, L_q, and FluxPM LUTs, specified as block parameters.

• Input port based Ld, Lq, and FluxPM — Generate estimates using L_d, L_q, and FluxPM LUTs, specified as block inputs.

D-axis current breakpoint vector, id (A) — D-axis current lookup vector

[-40, -20, 0, 20] (default) | vector

D-axis current vector used in the following lookup tables, depending on the method used to specify the motor parameters.

• FluxD(i_d,i_q) and FluxQ(i_d,i_q) for the Non-linear model with D,Q-flux linkage LUTs method.

• L_d(i_d,i_q), L_q(i_d,i_q), and FluxPM(i_d,i_q) for the Non-linear model with Ld, Lq, and FluxPM LUTs method.

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs or Non-linear model with Ld, Lq, and FluxPM LUTs.

Q-axis current breakpoint vector, iq (A) — Q-axis current lookup vector

[-40, -20, 0, 20, 40] (default) | vector

Q-axis current vector used in the following lookup tables, depending on the method used to specify the motor parameters.

• FluxD(i_d,i_q) and FluxQ(i_d,i_q) for the Non-linear model with D,Q-flux linkage LUTs method.

• L_d(i_d,i_q), L_q(i_d,i_q), and FluxPM(i_d,i_q) for the Non-linear model with Ld, Lq, and FluxPM LUTs method.

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs or Non-linear model with Ld, Lq, and FluxPM LUTs.

Linear Model with Lumped Parameters

Stator d-axis inductance, Ld (H) — D-axis stator winding inductance

0.2e-3 (default) | scalar

Stator winding inductance (henry) along the direct-axis of the rotating dq reference frame.

Dependencies

To enable this parameter, set Motor parameter input method to Linear model with lumped parameters.

Stator q-axis inductance, Lq (H) — Q-axis stator winding inductance

0.2e-3 (default) | scalar

Stator winding inductance (henry) along the quadrature-axis of the rotating dq reference frame.

Dependencies

To enable this parameter, set Motor parameter input method to Linear model with lumped parameters.

Permanent magnet flux linkage, FluxPM (Wb) — Permanent magnet flux linkage

6.4e-3 (default) | scalar

Peak permanent magnet flux linkage (weber).

Dependencies

To enable this parameter, set Motor parameter input method to Linear model with lumped parameters.

Non-Linear Model with D,Q-Flux Linkage LUTs

D-axis flux linkage LUT, FluxD(id,iq) (Wb) — D-axis flux linkage lookup data

[-1.6,-1.6,-1.6,-1.6,-1.6;2.4,2.4,2.4,2.4,2.4;6.4,6.4,6.4,6.4,6.4;10.4,10.4,10.4,10.4,10.4]*1e-3 (default) | matrix

D-axis flux linkage FluxD(i_d,i_q) lookup table data (in weber).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

Q-axis flux linkage LUT, FluxQ(id,iq) (Wb) — Q-axis flux linkage lookup data

[-8,-4,0,4,8;-8,-4,0,4,8;-8,-4,0,4,8;-8,-4,0,4,8]*1e-3 (default) | matrix

Q-axis flux linkage FluxQ(i_d,i_q) lookup table data (in weber).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

Non-Linear Model with L_d, L_q, and FluxPM LUTs

Ld LUT, Ld(id,iq) (H) — D-axis inductance lookup data

0.2e-3 * ones(4, 5) (default) | matrix

D-axis inductance L_d(i_d,i_q) lookup table data (in henry).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with Ld, Lq, and FluxPM LUTs.

Lq LUT, Lq(id,iq) (H) — Q-axis inductance lookup table data

0.2e-3 * ones(4, 5) (default) | matrix

Q-axis inductance L_q(i_d,i_q) lookup table data (in henry).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with Ld, Lq, and FluxPM LUTs.

PM flux linkage LUT, FluxPM(id,iq) (Wb) — PM flux linkage lookup data

6.4e-3 * ones(4, 5) (default) | matrix

Permanent magnet flux linkage FluxPM(i_d,i_q) lookup table data (in weber).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with Ld, Lq, and FluxPM LUTs.

Input Units

Input units — Unit of input values

Per-Unit (PU) (default) | SI Units

Unit of the input values.

Base Voltage (V) — Nominal voltage limit

24/sqrt(3) (default) | scalar

Base voltage (in volts) for per-unit system.

Dependencies

To enable this parameter, set Input units to Per-Unit (PU).

Base Current (A) — Nominal current limit

19.3 (default) | scalar

Base current (in amperes) for per-unit system.

Dependencies

To enable this parameter, set Input units to Per-Unit (PU).

Base Speed (rpm) — Nominal speed limit

4107 (default) | scalar

Base speed (in rpm) for per-unit system.

Dependencies

To enable this parameter, set Input units to Per-Unit (PU).

Base torque (Nm) — Nominal torque limit

0.74112 (default) | scalar

Base torque (in Nm) for per-unit system. See Per-Unit System page for more details.

You cannot configure this parameter when you set Motor parameter input method to Linear model with lumped parameters or Non-linear model with Ld, Lq, and FluxPM LUTs. The block computes its value using the other parameters.

Dependencies

To display this parameter, set Input units to Per-Unit (PU).

Base power (W) — Nominal power limit

401.143 (default) | scalar

Base power (in W) for per-unit system. See Per-Unit System page for more details.

You cannot configure this parameter when you set Motor parameter input method to Linear model with lumped parameters or Non-linear model with Ld, Lq, and FluxPM LUTs. The block computes its value using the other parameters.

Dependencies

To display this parameter, set Input units to Per-Unit (PU).

Allow scaled-down motor parameters with CodeGen (higher precision with Fixed-Point data type) — Scale down internal parameters to match per-unit scale

on (default) | off

Option to scale down internal parameters to match per-unit scale when generating code.

• When you enable this option, the block scales down the internal constants and coefficients to match the per-unit scale. This allows for higher precision when you use the fixed-point data type. If you use this option with the single or double data type, some precision loss can occur depending on the number of bits allotted to the integer portion.

• When you disable this option, the block converts all the constants and coefficients used for internal calculations to SI units and then converts them back to the PU scale. This allows you to update the lookup table values in the generated code, typically, for applications such as controller tuning or end-of-line operations. You can also update the values manually for debugging or reusing previously generated code.

Dependencies

To enable this parameter, set Input units to Per-Unit (PU).

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