LUT based PMSM Control Reference

Generate lookup-table-based control reference currents for field oriented control of permanent magnet synchronous motor

• Library:

• Motor Control Blockset / Controls / Control Reference

• 

Description

The LUT based PMSM Control Reference block generates the d-axis and q-axis reference currents for field-oriented control and field-weakening control of a permanent magnet synchronous motor (PMSM). The block accepts reference torque and feedback mechanical speed and outputs the corresponding reference current values.

The block uses i_d(T,ω) and i_q(T,ω) lookup tables (LUTs) to generate reference current values. Depending on the input method you use to specify the motor parameters, the block can either generate LUTs or use the data you provide.

You can specify the motor parameters using one of these methods.

• Lumped parameters with L_d, L_q, and FluxPM

  This method uses the lumped parameters to compute the i_d and i_q LUTs. The block obtains i_d and i_q for the given ω and T inputs by solving the equations associated with the following curves.

  Maximum torque per ampere (MTPA) line (IPMSM),

  $$i_d^2+\frac{i_d{\psi }_m}{(L_d-L_q)}=i_q^2.$$

  MTPA line (SPMSM), i_d = 0.

  Constant torque trajectory

  $$i_q=\frac{T}{1.5P_p({\psi }_m+(L_d-L_q)i_d)}.$$

  Current limit curve

  $$i_d^2+i_q^2=i_{\max }^2.$$

  Voltage limit curve

  $${\left(\frac{V_{DC}}{\sqrt{3}}\right)}^2={(i_d{R}_s-{\omega }_e{L}_q{i}_q)}^2+{(i_q{R}_s+{\omega }_e{L}_d{i}_d+{\omega }_e{\psi }_m)}^2.$$

  • When the motor is operating within the voltage constraints, the block solves for the intersection of MTPA line and constant torque trajectory.

  • When the motor is operating beyond the voltage constraints, the block solves for the intersection of voltage constraint curve and the constant torque trajectory.

  After computing the i_d and i_q tables from a grid of ω and T values, the block uses interpolation to find i_d^ref and i_q^ref for any ω and T inputs that lie within the range of table values. The table values are clipped for ω and T values beyond the boundaries.

• Nonlinear model with d-axis and q-axis stator winding inductances and permanent magnet flux linkage lookup tables

  This method uses an approach similar to the previous method, except that the block updates the values for L_d(i_d,i_q), L_q(i_d,i_q), and FluxPM(i_d,i_q) with every iteration it computes i_d and i_q. The block iterates these computations until the i_d and i_q values converge.

• Nonlinear model with d-axis and q-axis flux linkage lookup tables

  Use this option when you want to manually provide the i_d(T,ω) and i_q(T,ω) tables. Typically, you obtain these tables through simulations or dyno tests. You can also generate these tables using the mcbGenerateTables function provided with the Motor Control Blockset™ software.

For a detailed set of equations and assumptions that Motor Control Blockset uses for a PMSM, see Mathematical Model of PMSM.

Ports

Input

Tref — Reference torque value

scalar

Reference torque input value (in Nm) for which the block computes the reference current.

Data Types: single | double | fixed point

⍵m — Mechanical speed

scalar

Reference mechanical speed value (in rpm) for which the block computes the reference current.

Data Types: single | double | fixed point

Output

Idref — Reference d-axis current

scalar

Reference d-axis phase current (in Amperes).

Data Types: single | double | fixed point

Iqref — Reference q-axis current

scalar

Reference q-axis phase current (in Amperes).

Data Types: single | double | fixed point

Parameters

Motor topology — Type of PMSM

Interior PMSM (default) | Surface PMSM

Type of PMSM based on the placement of the permanent magnets.

Field Weakening control method — Type of field weakening control

CVCP (default) | CCCP | VCLMT | None

Type of field weakening control, specified as one of these:

• CVCP — Constant voltage constant power (CVCP) control method.

• CCCP — Constant current constant power (CCCP) control method.

• VCLMT — Voltage and current limited maximum torque (VCLMT) control method.

You can configure this parameter only in surface PMSMs with the motor parameters specified as linear lumped parameters. For all other configurations, the block uses the VCLMT control method.

Dependencies

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

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

4 (default) | scalar

Number of pole pairs available in the motor.

Stator resistance per phase (Ohm) — Resistance of stator phase winding (ohms)

0.36 (default) | scalar

Resistance of the stator phase winding (ohms).

Motor parameter input method — Type of motor parameters

Linear model with lumped parameters (default) | Non-linear model with Ld,Lq and FluxPM LUTs | Non-linear model with id and iq LUTs

Motor parameters that the block uses to generate the control reference currents.

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

• Non-linear model with Ld,Lq and FluxPM LUTs — Generate current reference using L_d, L_q, and FluxPM lookup tables.

• Non-linear model with id and iq LUTs — Generate current reference using i_d and i_q lookup tables.

Linear Model with Lumped Parameters

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

0.2e-3 (default) | scalar

Stator winding inductance (in henries) 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 (H) — Q-axis stator winding inductance

0.4e-3 (default) | scalar

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

Dependencies

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

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

6.4e-3 (default) | scalar

Peak permanent magnet flux linkage (in weber).

Dependencies

To enable this parameter, select the Linear model with lumped parameters option in the Motor parameter input method parameter.

Nonlinear Model with L_d, L_q, and FluxPM Lookup Tables

D-axis current vector (A) — D-axis current lookup vector

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

D-axis current vector used in the L_d, L_q, and FluxPM lookup tables.

Dependencies

To enable this parameter, select the Non-linear model with Ld, Lq and FluxPM LUTs option in the Motor parameter input method parameter.

Q-axis current vector (A) — Q-axis current lookup vector

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

Q-axis current vector used in the L_d, L_q, and FluxPM lookup tables.

Dependencies

To enable this parameter, select the Non-linear model with Ld, Lq and FluxPM LUTs option in the Motor parameter input method parameter.

Ld matrix (H) — D-axis inductance lookup data

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

D-axis inductance lookup table data.

Dependencies

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

Lq matrix (H) — Q-axis inductance lookup data

0.4e-3 * ones(4, 5) (default) | matrix

Q-axis inductance lookup table data.

Dependencies

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

PM flux linkage matrix (Wb) — Permanent magnet flux linkage lookup data

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

Permanent magnet flux linkage lookup table data.

Dependencies

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

Nonlinear Model with i_d and i_q Lookup Tables

Reference torque vector (Nm) — Torque reference lookup vector

[0 0.15 0.3] (default) | vector

Torque reference lookup vector used in i_d and i_q lookup tables (in Nm).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs.

Mechanical speed vector (rpm) — Rotor speed lookup vector

[0 1000 2000 6000] (default) | vector

Rotor speed lookup vector used in i_d and i_q lookup tables (in rpm).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs.

Reference id matrix (A) — Reference d-axis current lookup data

[0,0,0,-7.1;0,0,0,-7.1;0,0,0,-7.1] (default) | matrix

D-axis current reference lookup table data.

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs.

Reference iq matrix (A) — Reference q-axis current lookup data

[0,0,0,0;3.9091,3.9091,3.9091,0;7.1,7.1,7.1,0] (default) | matrix

Q-axis current reference lookup table data.

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs.

Motor Configuration

Viscous damping coefficient (Nm-s/rad) — Viscous damping coefficient

2.636875217824e-6 (default) | scalar

Viscous damping coefficient B_v of the motor in N·m/(rad/s).

DC bus voltage (V) — DC bus voltage (volts)

24 (default) | scalar

DC bus voltage (volts).

Current Limit (A) — Maximum phase current limit for motor (amperes)

7.1 (default) | scalar

Maximum phase current limit for the motor (amperes).

Input units — Unit of block input values

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

Unit of the block 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)

Torque corresponding to 1 per-unit. See Per-Unit System page for more details.

You cannot configure this parameter. Its value is internally computed using the other parameters.

Dependencies

To enable 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 Motor parameter input method to Non-linear model with id and iq LUTs and Input units to Per-Unit (PU).

Model Examples

PMSM Drive Characteristics and Constraint Curves

Use the PMSM characteristic plotting and PMSM milestone speed identification functions to obtain a control trajectory.

Open Live Script

Field-Weakening Control (with MTPA) of Non-Linear PMSM Using Look-Up Table

Uses a look-up table (LUT) for a non-linear PMSM and controller to run the motor using field-weakening control (with MTPA). Use this example to replicate and run a finite element analysis (FEA)-based non-linear high fidelity permanent magnet synchronous motor (PMSM) in simulation. This example helps motor design engineers to simulate high performance motors for 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 meet efficiency requirements especially for high-performance motors.

Open Example

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 R2022b