LUT based ACIM Control Reference

Generate lookup-table-based control reference currents for field-oriented control of induction motor

Since R2026a

• 

Libraries:
Motor Control Blockset / Controls / Control Reference

Description

The LUT-Based ACIM Control Reference block generates the stator d-axis and q-axis reference currents for field-oriented control and field-weakening control of an AC induction motor (ACIM). You can specify reference torque T and feedback mechanical speed ω and the block outputs the corresponding reference current values.

The block uses lookup tables (LUTs) to generate stator reference current values i_sd(T,ω) and i_sq(T,ω). 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 use the Motor parameter input method parameter to specify one of these options.

• Non-linear model with D,Q-flux linkage LUTs — The block uses a nonlinear model with d-axis and q-axis flux linkage lookup tables. This option computes the i_sd and i_sq LUTs. It obtains i_sd and i_sq for the given ω and T inputs by iteratively solving the equations of the associated constraint curves. To observe these constraint curves, use the options under the Plotting Options tab.

  The block updates the values for ψ_d(i_sd,i_sq) and ψ_q(i_sd,i_sq) each time it computes i_sd and i_sq. The block iterates these computations until the i_sd and i_sq values converge.

• Non-linear model with id and iq LUTs — Use this option when you want to manually provide the i_sd(T,ω) and i_sq(T,ω) tables. You can obtain these tables through custom algorithms or motor calibration tests on dyno.

You can also use the Vdc input method parameter to configure the block to accept a fixed reference DC voltage through the DC voltage to compute LUTs (V) parameter or a variable reference DC voltage through a separate input port V_dc.

Your choice of settings determines the technique that the block uses to compute reference currents.

Motor parameter input method	Vdc input method	Technique
Non-linear model with D,Q-flux linkage LUTs	Specify via dialog	The block computes the reference currents by using the d-axis and q-axis flux linkage LUTs for a fixed voltage specified in the DC voltage to compute LUTs (V) parameter.
	Input port - use 3D LUT (voltage slice based)	The block uses the 3-D d-axis and q-axis flux linkage LUTs containing data for different voltages (or voltage slices specified in the DC bus voltage breakpoint vector, Vdc (V) parameter). It uses these LUTs to compute the reference currents corresponding to the voltage provided at the input port Vdc.
	Input port - use 2D LUT (scaled-w based)	The block uses the 2-D d-axis and q-axis flux linkage LUTs for a fixed voltage specified in the DC voltage to compute LUTs (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port Vdc) by scaling the speed (ω).
Non-linear model with id and iq LUTs	Use Vdc for external calculations	The block uses the given 2-D id, iq LUTs to compute the reference currents by scaling the speed (ω).
	Input port - use 3D LUT (voltage slice based)	The block uses the given 3-D id, iq LUTs containing data for different voltages (or voltage slices specified in the DC bus voltage breakpoint vector, Vdc (V) parameter). It uses these LUTs to determine the reference currents corresponding to the voltage provided at the input port Vdc.
	Input port - use 2D LUT (scaled-w based)	The block uses the given 2-D id, iq LUTs for a fixed voltage specified in the DC voltage to compute LUTs (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port Vdc) by scaling the speed (ω).

For a detailed set of equations and assumptions that Motor Control Blockset™ uses for an ACIM, see Mathematical Model of Induction Motor.

Examples

Estimate Induction Motor Parameters Using Parameter Estimation Blocks

Uses the parameter estimation blocks provided by Motor Control Blockset™ to estimate these parameters of an AC induction motor (ACIM):

• Open Model

Ports

Input

T^ref — 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 rad/sec) for which the block computes the reference current.

Data Types: single | double | fixed point

V_dc — DC bus voltage

scalar

Variable DC bus voltage (in volts).

Dependencies

To enable this port, set Vdc input method to Input port - use 3D LUT (voltage slice based) or Input port - use 2D LUT (scaled-w based).

Data Types: single | double | fixed point

Output

I_sd^ref — Reference stator d-axis current

scalar

Reference stator d-axis phase current (in amperes).

Data Types: single | double | fixed point

I_sq^ref — Reference stator q-axis current

scalar

Reference stator q-axis phase current (in amperes).

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.

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

0.36 (default) | scalar

Resistance of the stator phase winding (in ohms).

Motor parameter input method — Type of motor parameters

Non-linear model with D,Q-flux linkage LUTs (default) | Non-linear model with id and iq LUTs

Motor parameters that the block uses to generate the control reference currents. Set the parameter to one of these values:

• Non-linear model with D,Q-flux linkage LUTs — Determine reference currents from the reference tables generated using d-axis and q-axis flux linkage lookup tables.

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

Vdc input method — Input method for Vdc

Specify via dialog | Use Vdc for external calculations | Input port - use 3D LUT (voltage slice based) | Input port - use 2D LUT (scaled-w based)

Use one of these options to specify the Vdc input:

• Specify via dialog — Specify the fixed reference voltage Vdc using the DC voltage to compute LUTs (V) parameter. This setting is default if Motor parameter input method is set to Non-linear model with D,Q-flux linkage LUTs.

• Use Vdc for external calculations — Specify the fixed reference voltage Vdc using the input port V_dc. This setting is default if Motor parameter input method is set to Non-linear model with id and iq LUTs.

• Input port - use 3D LUT (voltage slice based) — Specify the variable reference voltage Vdc using the input port Vdc. When you select this option, the block computes the reference current data for the given voltage by using a 3-D lookup table (LUT) based on voltage slicing.

• Input port - use 2D LUT (scaled-w based) — Specify the variable reference voltage Vdc using the input port Vdc. When you select this option, the block computes the reference current data for the given voltage by using a 2-D LUT based on motor speed (ω) scaling.

DC voltage to compute LUTs (V) — DC bus voltage (volts)

24 (default) | scalar

DC bus voltage (in volts).

Dependencies

To enable this parameter, set Vdc input method to Specify via dialog or Input port - use 2D LUT (scaled-w based).

DC bus voltage breakpoint vector, VdcVec (V) — DC bus voltage lookup vector (volts)

[18,30] (default) | vector

DC bus voltage lookup vector used in i_d and i_q lookup tables (in volts).

Dependencies

To enable this parameter, set Vdc input method to Input port - use 3D LUT (voltage slice based).

Choose the speed input type — Speed input type

Use rotor speed (ωm) (mechanical speed (rad/s)) (default) | Use stator synchronous speed (ωmsync = ωm + slipm) (mechanical speed (rad/s))

Specify the speed input type.

• Use rotor speed (ωₘ) (mechanical speed (rad/s)) — Use the rotor speed as reference speed.

• Use stator synchronous speed (ωmsync = ωm + slipm) (mechanical speed (rad/s)) — Use the stator synchronous speed as reference speed.

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

[0 10 20 30] (default) | vector

d-axis current vector (in amperes) in the ψ_d and ψ_d lookup tables.

Dependencies

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

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

[0 10 20 30 40] (default) | vector

q-axis current vector (in amperes) in the ψ_d and ψ_d lookup tables.

Dependencies

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

Slip-based LUT, Slip(id,iq) (electrical speed (rad/s)) — Reference slip lookup data

[0,0,0,0,0;0,0,0,0,0;0,0,0,0,0;0,0,0,0,0] (default) | vector

Slip lookup table data (in rad/sec). If you set Choose the speed input type to Use stator synchronous speed (ωmsync = ωm + slipm) (mechanical speed (rad/s)), the block computes the stator synchronous speed from the mechanical speed and slip.

Dependencies

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

Use measured (instead of computed) torque — Use measured value of torque

off (default) | on

Select this parameter to provide measured (instead of computed) torque lookup data to the block.

Dependencies

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

Measured torque LUT, T(id,iq) (Nm) — Measured lookup data

[-3.4560,-1.7280,0, 1.7280, 3.4560;-2.4960,-1.2480,0, 1.2480, 2.4960;-1.5360,-0.7680,0, 0.7680, 1.5360;-0.5760,-0.2880,0, 0.2880, 0.5760] (default) | vector

Measured torque lookup table data (in Nm).

Dependencies

To enable this parameter:

• Set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

• Select the Use measured (instead of computed) torque parameter.

Enable percentages for torque breakpoint vector — Enable percentage values for torque breakpoint vector

off (default) | on

Select this parameter to specify the percentage torque breakpoint vector values and the torque envelope values for the speed breakpoint vector (in the following parameters):

• Reference percentage torque breakpoint vector, Trefpct (%)

• Torque envelope for speed breakpoint vector, wrpm (rpm)

Enable custom breakpoint vectors for torque and speed — Use custom breakpoints for torque and speed

off (default) | on

Select this parameter to use custom lookup vectors for motor torque and speed quantities.

Dependencies

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

Reference torque breakpoint vector, Tref (Nm) — Torque reference lookup vector

[0,0.15,0.3] (default) | vector

Torque reference lookup vector used in the i_d and i_q lookup tables (in Nm). The vector can have any number of elements.

Dependencies

To enable this parameter, clear the Enable percentages for torque breakpoint vector parameter and either:

• Set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

• Select the Enable custom breakpoint vectors for torque and speed parameter.

or

• Set Motor parameter input method to Non-linear model with id and iq LUTs.

Mechanical speed breakpoint vector, wrpm (rpm) — Rotor speed lookup vector

[0,1000,2000,6000] (default) | vector

Rotor speed lookup vector used in the i_d and i_q lookup tables (in rpm). The vector can have any number of elements.

Dependencies

To enable this parameter, either:

• Set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

• Select the Enable custom breakpoint vectors for torque and speed parameter.

or

• Set Motor parameter input method to Non-linear model with id and iq LUTs.

Reference percentage torque breakpoint vector, Trefpct (%) — Torque reference lookup vector (in percentage)

[0,50,100] (default) | vector

Torque reference lookup vector used in the i_d and i_q lookup tables (in percentage). The vector can have any number of elements.

Dependencies

To enable this parameter, select the Enable percentages for torque breakpoint vector parameter, and either:

• Set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

• Select the Enable custom breakpoint vectors for torque and speed parameter.

or

• Set Motor parameter input method to Non-linear model with id and iq LUTs.

Torque envelope for speed breakpoint vector, T (Nm) — Torque envelope values for speed breakpoint vector

[0.3 0.3 0.15 0.05] (default) | vector

Torque envelope values used to compute the percentage values of the torque reference lookup vector (specified in the Reference percentage torque breakpoint vector, Trefpct (%) parameter).

Dependencies

To enable this parameter, select the Enable percentages for torque breakpoint vector parameter and either:

• Set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

• Select the Enable custom breakpoint vectors for torque and speed parameter.

or

• Set Motor parameter input method to Non-linear model with id and iq LUTs.

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

7.1 (default) | scalar

Maximum phase current limit for the motor (in amperes).

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

2.636875217824e-6 (default) | scalar

Viscous damping coefficient B_v of the motor in Nm/(rad/s).

Nonlinear Model with D,Q-Flux Linkage LUTs

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

[0,0,0,0,0;0.009,0.009,0.009,0.009,0.0090;0.018,0.018,0.018,0.018,0.0180;0.027,0.027,0.027,0.027,0.0270] (default) | vector

d-axis flux linkage 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) — Reference q-axis flux linkage lookup data

[0,0.0015,0.003,0.0045,0.0060;0,0.0015,0.003,0.0045,0.0060;0,0.0015,0.003,0.0045,0.0060;0,0.0015,0.003,0.0045,0.0060] (default) | vector

q-axis flux linkage 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.

Nonlinear Model with i_d and i_q LUTs

Reference id LUT, id(Tref,wrpm) (A) — Reference d-axis current lookup data

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

d-axis current reference 2-D lookup table data (in amperes).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs and Vdc input method to Use Vdc for external calculations or Input port - use 2D LUT (scaled-w based).

Reference id LUT, id(Tref,wrpm,Vdc) (A) — Reference d-axis current lookup data

cat(3,[0,0,0,0;3.8539,3.8539,3.8539,0;6.9513,6.9513,6.9513,0],[0,0,0,0;3.8539,3.8539,3.8539,3.7611;6.9513,6.9513,6.9513,5.4848]) (default) | matrix

d-axis current reference 3-D lookup table data (in amperes).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs and Vdc input method to Input port - use 3D LUT (voltage slice based).

Reference iq LUT, iq(Tref,wrpm) (A) — Reference q-axis current lookup data

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

q-axis current reference 2-D lookup table data (in amperes).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs and Vdc input method to Use Vdc for external calculations or Input port - use 2D LUT (scaled-w based).

Reference iq LUT, iq(Tref,wrpm,Vdc) (A) — Reference q-axis current lookup data

cat(3,[0,0,0,7.1;0.4579,0.4579,0.4579,7.1;1.4457,1.4457,1.4457,7.1],[0,0,0,0;0.4579,0.4579,0.4579,1.2581;1.4457,1.4457,1.4457,4.5085]) (default) | matrix

q-axis current reference 3-D lookup table data (in amperes).

Dependencies

To enable this parameter, set Motor parameter input method to Non-linear model with id and iq LUTs and Vdc input method to Input port - use 3D LUT (voltage slice based).

Input Units

Input units — Unit of measure of block input values

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

Unit of measure of the block input values.

Base voltage (V) — Nominal voltage limit

24/sqrt(3) (default) | scalar

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

Dependencies

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

Base torque (Nm) — Nominal torque limit

0.93271 (default)

Torque (in Nm) corresponding to one per-unit. See Per-Unit System page for more details.

You cannot configure this parameter. The block computes this value internally 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

Parameter to scale down internal parameters to match the 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 option 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 it uses for internal calculations to SI units and then converts them back to the per-unit scale. This option 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).

Plotting Options

The block enables this tab only when you set Motor parameter input method to Non-linear model with D,Q-flux linkage LUTs.

Enable saving the computed LUTs — Enable block to save computed LUTs

off (default) | on

Enable the block to save the lookup table data that the block computes when you click the Compute (and plot) id and iq LUTs button.

Use default options for plotting — Use default options to plot constraint curves

on (default) | off

Enable the block to use default plotting options when you click the Plot constraint curves button to plot the constraint curves of motor.

Motor speed (RPM) — Motor speed for plotting constraint curves

3000 (default) | scalar

Motor speed (in rpm) that the block should use when you click the Plot constraint curves button to plot the constraint curves of motor.

Dependencies

To enable this parameter, clear the Use default options for plotting parameter.

Motor torque (Nm) — Motor torque for plotting constraint curves

0.1 (default) | scalar

Motor torque (in Nm) that the block should use when you click the Plot constraint curves button to plot the constraint curves of motor.

Dependencies

To enable this parameter, clear the Use default options for plotting parameter.

Enable plotting the drive characteristics — Enable block to plot drive characteristics

off (default) | on

Enable the block to plot the drive characteristics when you click the Plot constraint curves button to plot the constraint curves of motor.

Dependencies

To enable this parameter, clear the Use default options for plotting parameter.

Include the drive characteristics for an increased motor current — Enable block to plot drive characteristics for increased motor current

off (default) | on

Enable the block to include drive characteristics for an increased motor current. To generate these drive characteristics in the plot, click the Plot constraint curves button.

Note

You can plot the characteristics for an increased motor current only when the current is higher than the rated current of the motor.

Dependencies

To enable this parameter, clear the Use default options for plotting parameter and select the Enable plotting the drive characteristics parameter.

Compute (and plot) id and iq LUTs — Compute and plot id and iq lookup data

button

When you click this button, the block computes and plots the lookup table data for id and iq currents.

Plot constraint curves — Plot constraint curves of motor

button

When you click this button, the block plots the constraint curves of the motor.

Compute and show — Compute and show characteristic torque and speed

button

When you click this button, the block computes and shows the following torque and speed characteristics:

• Rated torque — Rated torque of motor (in Nm).

• Rated speed — Rated speed of motor (in rpm).

• Maximum speed — Maximum speed of motor (in rpm).

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 R2026a