LUT based SynRM Control Reference

Generate lookup-table-based control reference currents for field-oriented control of SynRM and PMaSynRM

Since R2024a

Libraries:
Motor Control Blockset / Controls / Control Reference

Description

The LUT based SynRM Control Reference block generates the d-axis and q-axis reference currents for field-oriented control and field-weakening control of a synchronous reluctance motor (SynRM) and a permanent magnet-assisted synchronous reluctance motor (PMaSynRM). You can specify reference torque and feedback mechanical speed and the block outputs the corresponding reference current values. The block also supports the maximum torque per ampere (MTPA) and maximum torque per voltage (MTPV) operating regions.

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.

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).

Linear model with lumped parameters — Lumped parameters with L_d and L_q (for SynRM) or lumped parameters with L_d, L_q, and FluxPM (for PMaSynRM)
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 these curves.
Maximum torque per ampere (MTPA) curve (for SynRM)
$i_{d} + i_{q} = 0$
Maximum torque per ampere (MTPA) curve (for PMaSynRM)
$i_{d}^{2} + \frac{i_{d} ψ_{m}}{(L_{d} - L_{q})} = i_{q}^{2} .$
Constant torque trajectory (for SynRM)
$i_{q} = \frac{T}{1.5 P_{p} (L_{d} - L_{q}) i_{d}}$
Constant torque trajectory (for PMaSynRM)
$i_{q} = \frac{T}{1.5 P_{p} (ψ_{m} + (L_{d} - L_{q}) i_{d})} .$
Current limit curve
$i_{d}^{2} + i_{q}^{2} = i_{\max}^{2} .$
Voltage limit curve (for SynRM)
${(\frac{V_{D C}}{\sqrt{3}})}^{2} = {(i_{d} R_{s} - ω_{e} L_{q} i_{q})}^{2} + {(i_{q} R_{s} + ω_{e} L_{d} i_{d})}^{2} .$
Voltage limit curve (for PMaSynRM)
${(\frac{V_{D C}}{\sqrt{3}})}^{2} = {(i_{d} R_{s} - ω_{e} L_{q} i_{q})}^{2} + {(i_{q} R_{s} + ω_{e} L_{d} i_{d} + ω_{e} ψ_{m})}^{2} .$
- When the motor operates within the voltage constraints, the block solves for the intersection of the MTPA line and the constant torque trajectory.
- When the motor operates beyond the voltage constraints, the block solves for the intersection of the 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 the table values. The table values are clipped for ω and T values beyond the boundaries.
Non-linear model with Ld and Lq LUTs or 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
This method uses an approach similar to the lumped parameters 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) each time it computes i_d and i_q . The block iterates these computations until the i_d and i_q values converge.

Note
FluxPM(i_d,i_q) value is applicable only to a PMaSynRM. L_d(i_d,i_q) and L_q(i_d,i_q) values are applicable for both SynRM and PMaSynRM.
Non-linear model with D,Q-flux linkage LUTs — Nonlinear model with d-axis and q-axis flux linkage lookup tables.
This method uses an approach similar to the lumped parameters method, except that the block updates the values for ψ_d(i_d,i_q) and ψ_q(i_d,i_q) each time it computes i_d and i_q . The block iterates these computations until the i_d and i_q values converge.
Non-linear model with id and iq LUTs — Use this method 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 in Motor Control Blockset™.

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

In addition, you can 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 .

Based on the method you select in the Motor parameter input method parameter, you can use the lumped parameters or a nonlinear model to compute the reference currents as shown in this table.

Motor parameter input method	Vdc input method	Technique used to compute reference currents
`Linear model with lumped parameters`	`Specify via dialog`	The block uses the lumped parameters to compute the i_d and i_q LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter, using which it determines the reference currents.
	`Input port - use 3D LUT (voltage slice based)`	The block uses the lumped parameters to compute the 3-D i_d and i_q LUTs containing data for different voltages (or voltage slices specified in the DC bus voltage breakpoint vector, Vdc (V) parameter). It uses this data to determine the reference currents corresponding to the voltage specified at the input port V_dc .
	`Input port - use 2D LUT (scaled-w based)`	The block uses the lumped parameters to compute the 2-D i_d and i_q LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port V_dc ) by scaling the speed (ω).
`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 bus voltage, Vdc (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 V_dc .
	`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 bus voltage, Vdc (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port V_dc ) by scaling the speed (ω).
`Non-linear model with Ld and Lq LUTs`	`Specify via dialog`	The block computes the reference currents by using the given L_d and L_q LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter.
	`Input port - use 3D LUT (voltage slice based)`	The block uses the given 3-D L_d and L_q 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 V_dc .
	`Input port - use 2D LUT (scaled-w based)`	The block uses the given 2-D L_d and L_q LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port V_dc ) by scaling the speed (ω).
`Non-linear model with Ld, Lq, and FluxPM LUTs`	`Specify via dialog`	The block computes the reference currents by using the given L_d , L_q , and permanent magnet flux linkage LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter.
	`Input port - use 3D LUT (voltage slice based)`	The block uses the given 3-D L_d , L_q , and permanent magnet 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 V_dc .
	`Input port - use 2D LUT (scaled-w based)`	The block uses the given 2-D L_d , L_q , and permanent magnet flux linkage LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port V_dc ) by scaling the speed (ω).
`Non-linear model with id and iq LUTs`	`Specify via dialog`	The block determines the reference currents by using the given i_d , i_q LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter.
	`Input port - use 3D LUT (voltage slice based)`	The block uses the given 3-D i_d , i_q 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 V_dc .
	`Input port - use 2D LUT (scaled-w based)`	The block uses the given 2-D i_d , i_q LUTs for a fixed voltage specified in the DC bus voltage, Vdc (V) parameter. It uses these LUTs to compute the reference currents (corresponding to the voltage provided at the input port V_dc ) by scaling the speed (ω).

Examples

SynRM Constraint Curves and Their Application

Uses Motor Control Blockset™ to utilize the motor constraint curves to determine the operating currents and use lookup tables of these currents in simulation or deployment environments. The example uses the PMSM constraint curves described in the PMSM Drive Characteristics and Constraint Curves page.

Open Live Script

Field-Weakening Control (with MTPA) of Nonlinear Synchronous Reluctance Motors Using Lookup Table

Uses a lookup table (LUT) for a nonlinear synchronous reluctance motor 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 synchronous reluctance motor 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

Ports