PMSM HDL

Three-phase permanent magnet synchronous motor with sinusoidal back electromotive force

Since R2022b

• 

Libraries:
Motor Control Blockset HDL Support / Electrical Systems / Motors

Description

The PMSM HDL block implements a three-phase permanent magnet synchronous motor (PMSM) with a sinusoidal back-electromotive force. The block uses three-phase input voltages to regulate the individual phase currents, thereby controlling the motor torque or speed.

The block generates code for fixed-step double- and single-precision targets using the Sample Time (s) parameter. It supports code generation for FPGA deployment and generates HDL-compatible code.

You can specify the PMSM parameters and operating mode using the Config input port. You can also use the PMSM Configuration block to generate the required configuration signal to specify at the Config input port.

Motor Construction

These diagrams show the interior and surface-mount PMSM construction with a single-pole pair on the motor.

The motor magnetic field due to the permanent magnets creates a sinusoidal rate of change of flux with the motor angle.

For the axes convention, the phase-a aligns with d-axis when the motor angle θ_r is zero.

Three-Phase Sinusoidal Model Electrical System

The block implements these equations expressed in the motor flux reference frame (dq frame). All quantities in the motor reference frame are referred to as the stator.

$$\begin{array}{l}{\omega }_e=P{\omega }_m\\ \frac{d}{dt}{i}_d=\frac{1}{L_d}{v}_d-\frac{R}{L_d}{i}_d+\frac{L_q}{L_d}P{\omega }_m{i}_q\end{array}$$

$$\frac{d}{dt}{i}_q=\frac{1}{L_q}{v}_q-\frac{R}{L_q}{i}_q-\frac{L_d}{L_q}P{\omega }_m{i}_d-\frac{{\lambda }_{pm}P{\omega }_m}{L_q}$$

$$T_e=1.5P[{\lambda }_{pm}{i}_q+(L_d-L_q)i_d{i}_q]$$

The L_q and L_d inductances represent the relation between the phase inductance and the motor position due to the saliency of the motor magnets. For a surface mount PMSM, $$L_d=L_q$$.

The equations use these variables.

Lq, Ld	q- and d-axis inductances (H)
R	Resistance of the stator windings (ohm)
iq, id	q- and d-axis currents (A)
vq, vd	q- and d-axis voltages (V)
ωm	Angular mechanical velocity of the motor (rad/s)
ωe	Angular electrical velocity of the motor (rad/s)
λpm	Permanent magnet flux linkage (Wb)
Ke	Back electromotive force (EMF) (Vpk_LL/krpm, where Vpk_LL is the peak voltage line-to-line measurement)
Kt	Torque constant (N·m/A) Kt = Rated torque of motor / Ia_peak_rated, where Ia_peak_rated is the peak amplitude of phase-a at rated current operation.
P	Number of pole pairs
Te	Electromagnetic torque (Nm)
Θe	Electrical angle (rad)

Mechanical System

The motor angular velocity is given by:

$$\begin{array}{c}\frac{d}{dt}{\omega }_m=\frac{1}{J}\left(T_e-T_f-F{\omega }_m-T_m\right)\\ \frac{d{\theta }_m}{dt}={\omega }_m\end{array}$$

The equations use these variables.

J	Combined inertia of motor and load (kgm^2)
F	Combined viscous friction of motor and load (N·m/(rad/s))
θm	Motor mechanical angular position (rad)
Tm	Motor shaft torque (Nm)
Te	Electromagnetic torque (Nm)
Tf	Motor shaft static friction torque (Nm)
ωm	Angular mechanical velocity of the motor (rad/s)

Power Accounting

For motor power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrMtr	Mechanical power	Pmot	$P_{mot}= -{\omega }_m{T}_e$
		PwrBus	Electrical power	Pbus	$P_{bus}= v_{an}{i}_a+ v_{bn}{i}_b+v_{cn}{i}_c$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrElecLoss	Resistive power loss	Pelec	$P_{elec}= -\frac{3}{2}(R_s{i}_{sd}^2+R_s{i}_{sq}^2)$
		PwrMechLoss	Mechanical power loss	Pmech	When Port Configuration is set to Torque: $P_{mech}= -\left({\omega }_m^{2}F+ \left|{\omega }_m\right|T_f\right)$ When Port Configuration is set to Speed: $P_{mech}= 0$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrMtrStored	Stored motor power	Pstr	$P_{str}= P_{bus}+ P_{mot}+ P_{elec} + P_{mech}$

The equations use these variables.

Rs	Stator resistance (ohm)
ia, ib, ic	Stator phase a, b, and c current (A)
isq, isd	Stator q- and d-axis currents (A)
van, vbn, vcn	Stator phase a, b, and c voltage (V)
ωm	Angular mechanical velocity of the motor (rad/s)
F	Combined motor and load viscous damping N·m/(rad/s)
Te	Electromagnetic torque (Nm)
Tf	Combined motor and load friction torque (Nm)

Amplitude Invariant dq Transformation

The block uses these equations to implement amplitude invariant dq transformation to ensure that the dq and three phase amplitudes are equal.

$\left[\begin{array}{c}{v}_{sd}\\ v_{sq}\end{array}\right]= \frac{2}{3} \left[\begin{array}{ccc}\text{cos}({\Theta }_{da})& \text{cos}({\Theta }_{da}-\frac{2\pi }{3})& \text{cos}({\Theta }_{da}+\frac{2\pi }{3})\\ -\text{sin}({\Theta }_{da})& -\text{sin}({\Theta }_{da}-\frac{2\pi }{3})& -\text{sin}({\Theta }_{da}+\frac{2\pi }{3})\end{array}\right]\left[\begin{array}{c}{v}_a\\ v_b\\ v_c\end{array}\right]$

$\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]= \left[\begin{array}{cc}\text{cos}({\Theta }_{da})& -\text{sin}({\Theta }_{da})\\ \begin{array}{c}\text{cos}({\Theta }_{da}-\frac{2\pi }{3})\\ \text{cos}({\Theta }_{da}+\frac{2\pi }{3})\end{array}& \begin{array}{c}-\text{sin}({\Theta }_{da}-\frac{2\pi }{3})\\ -\text{sin}({\Theta }_{da}+\frac{2\pi }{3})\end{array}\end{array}\right]\left[\begin{array}{c}{i}_{sd}\\ i_{sq}\end{array}\right]$

The equations use these variables.

Θda	dq stator electrical angle with respect to the rotor a-axis (rad)
vsq, vsd	Stator q- and d-axis voltages (V)
isq, isd	Stator q- and d-axis currents (A)
va, vb, vc	Stator voltage phases a, b, c (V)
ia, ib, ic	Stator currents phases a, b, c (A)

Examples

Field-Oriented Control (FOC) of PMSM Using Hardware-In-The-Loop (HIL) Simulation

Uses hardware-in-the-loop (HIL) simulation to implement the field-oriented control (FOC) algorithm to control the 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 more information on FOC, see Field-Oriented Control (FOC).

• Open Example

Ports

Input

Config — Block configuration signal

vector

Configuration signal for the PMSM HDL block containing the block configuration parameters. For more information about the constituent parameters, see the Config output of the PMSM Configuration block.

Data Types: single

PhaseVolt — Stator terminal voltages

1-by-3 array

Stator terminal voltages V_a, V_b, and V_c, in V.

Data Types: single

LdTrq/Spd — Load torque on motor or speed of motor shaft

scalar

Based on the mode of operation defined by the Port Configuration parameter available in the multiplexed Config input, the port supports one of these inputs:

• T_m — Load torque on the motor shaft, in N·m.

• ω_m — Angular velocity of the motor, in rad/s.

Data Types: single

Reset — Reset bus signal

scalar

Reset bus signal that the block uses to reset the internal integrators.

Data Types: Boolean

Output

Info — Bus signal

bus

The bus signal contains these block calculations.

Signal			Description	Variable	Units
IaStator			Stator phase current A	ia	A
IbStator			Stator phase current B	ib	A
IcStator			Stator phase current C	ic	A
IdSync			Direct axis current	id	A
IqSync			Quadrature axis current	iq	A
VdSync			Direct axis voltage	vd	V
VqSync			Quadrature axis voltage	vq	V
MtrSpd			Angular mechanical velocity of the motor	ωm	rad/s
MtrPos			Motor mechanical angular position	θm	rad
MtrTrq			Electromagnetic torque	Te	N·m
PwrInfo	PwrTrnsfrd	PwrMtr	Mechanical power	Pmot	W
		PwrBus	Electrical power	Pbus	W
	PwrNotTrnsfrd	PwrElecLoss	Resistive power loss	Pelec	W
		PwrMechLoss	Mechanical power loss	Pmech	W
	PwrStored	PwrMtrStored	Stored motor power	Pstr	W

PhaseCurr — Current for phase a, b, and c

1-by-3 array

Current for phase a, b, and c, i_a, i_b, and i_c, respectively, in A.

Torque — Motor torque

scalar

Motor torque, T_mtr, in N·m.

Speed — Motor speed

scalar

Angular speed of the motor, ω_mtr, in rad/s.

MtrElecAngle — Motor electrical angle

scalar

Electrical position of the motor, θ_e, in rad.

Data Types: single

Parameters

Sample time (s) — Sample time after which block executes again

1e-6 (default) | scalar

The fixed time interval (in seconds) between consecutive instances of block execution.

Extended Capabilities

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).

Version History

Introduced in R2022b