PMSM Mechanical Parameter Estimator

Estimate back EMF constant, rotor inertia, and viscous damping of permanent magnet synchronous motor (PMSM)

Since R2023a

• 

Libraries:
Motor Control Blockset / Parameter Estimation / PMSM Parameter Estimation

Description

The PMSM Mechanical Parameter Estimator block uses the phase currents and voltages, DC voltage across the motor, motor position and speed, stator resistance, d-axis inductance, as well as the other test configuration elements to compute the following mechanical parameters of a PMSM:

• Back EMF constant (K_e)

• Rotor inertia (J)

• Viscous damping (B)

The block runs the motor using closed-loop field-oriented control (FOC) with a limited speed during which it runs the tests to estimate the back-EMF constant (K_e) and viscous damping (B). After a pre-configured duration, the block concludes these tests to compute K_e and B, and then, triggers coast-down by shutting down all six inverter switches. The coast-down results in gradual decline in motor speed which eventually reaches zero. The block measures and uses the time to reach zero-speed to calculate rotor inertia (J).

Examples

Estimate PMSM Parameters Using Parameter Estimation Blocks

Uses the parameter estimation blocks provided by Motor Control Blockset™ to estimate these parameters of a permanent magnet synchronous motor (PMSM) with a quadrature encoder sensor:

• Open Model

Estimate PMSM Parameters Using Parameter Estimation Blocks on Real-Time Systems

Uses the parameter estimation blocks provided by Motor Control Blockset™ to estimate these parameters of a permanent magnet synchronous motor (PMSM):

• Open Model

Ports

Input

Iabc — Three-phase current response

vector

The three-phase current response (in amperes) of the motor measured by the current sensors.

Note

Providing phase-c current input is optional. The block functionality is not impacted if you do not provide the phase-c current input.

Data Types: single

Vdc — DC link voltage

scalar

DC bus voltage (in volts) that you provide to the inverter.

Data Types: single

Theta — Rotor position

scalar

Current position (in per-unit) of the rotor. For more details about the per-unit system, see Per-Unit System.

Data Types: single

Speed — Rotor speed

scalar

Current motor speed (in RPM).

Data Types: single

Rs — Estimated stator resistance

scalar

Estimated stator resistance (in ohms) of the PMSM. You can either connect this input port to the Rs output of the PMSM Rs Estimator block or provide the resistance value manually using a Constant block.

Data Types: single

Ld — Estimated d-axis stator inductance

scalar

Estimated d-axis stator inductance (in henries) of the PMSM. You can either connect this input port to the Ld output of the Ld Estimator block or provide the d-axis inductance value manually using a Constant block.

Data Types: single

StartFOC — Begin closed loop FOC

logical

Signal that starts running the motor in closed-loop FOC mode:

• 1 (rising edge of a pulse) — This signal initiates mechanical parameter estimation by running the motor in closed-loop using FOC.

• 0 (falling edge of a pulse) — This signal starts running the motor using open-loop control.

Data Types: single

StartStop — Control signal for mechanical parameter estimation

logical

Signal that either starts or stops block execution:

• 1 (rising edge of a pulse) — This signal initiates block execution.

• 0 (falling edge of a pulse) — This signal immediately stops block execution and any tests that the block is running. If you interrupt the estimation process abruptly before completion, the block does not compute or output the mechanical parameter values.

Data Types: Boolean

Config — Bus signal input

bus

This table summarizes the expected configuration elements in the bus signal input.

Category	Configuration element			Units
Elements for motor and inverter hardware	Number of pole pairs			-
	Rated speed of motor			RPM
	Rated current of motor			A
	Maximum measurable inverter current			A
	Board resistance			ohms
	Current sense gain			A/ADC Count
	Voltage sense gain			V/ADC Count
	Parameter estimation sample time			seconds
Elements for estimating motor inductances (Ld and Lq)	Maximum frequency			Hz
	Minimum frequency			Hz
	Step for frequency sweep			Hz
	Frequency step size for estimation			Hz
	Number of frequencies for estimation			-
Elements for estimating back EMF constant (Ke), motor inertia (J), and friction constant (B)	Back EMF estimation time			seconds
	Back EMF estimation maximum speed limit			RPM
	Specify current controller gains (off/on)			-
	Proportional gain			-
	Integral gain			-
	Iq reference current as a ratio of rated motor current			PU current
	Lower speed limit for inertia estimation			RPM

You can connect this input port to the Config output port of the PMSM Parameter Estimation Configurator block.

Data Types: single

Output

Vabc — a, b, and c-axis stator reference voltage components

vector

Stator reference voltage components along the a, b, and c axes of the abc reference frame. Each voltage component has a range between -1 and 1.

Data Types: single

Ke — Estimated back EMF constant

scalar

Estimated back EMF constant of the PMSM (in V/m/s).

Data Types: single

J — Estimated rotor inertia

scalar

Estimated inertia of the PMSM (in kg.m²).

Data Types: single

B — Estimated viscous damping

scalar

Estimated viscous damping of the PMSM (in N.s/m).

Data Types: single

InverterEn — Inverter control signal

logical

Signal that switches on or switches off the inverter:

• 1 (logical high) — For the duration when this signal is high, all six switches of the inverter are switched on.

• 0 (logical low) — For the duration when this signal is low, all six switches of the inverter are switched off.

Data Types: single

Log — Debug signals

bus

Debug signals that the block provides for examination. The bus includes these debug signals.

Debug signal			Description	Units
status		0	Mechanical parameter estimation did not start yet.	-
		1	Mechanical parameter estimation is in progress.	-
		2	Mechanical parameter estimation completed successfully.	-
		8300	Back EMF estimation failed because the motor failed to reach 90% of Back EMF estimation maximum speed limit (RPM) within the period of Back EMF estimation time (s)+10 seconds. For more details about the Back EMF estimation maximum speed limit (RPM) and Back EMF estimation time (s) parameters, see PMSM Parameter Estimation Configurator.	-
CoastDownTime			Measured coast-down duration	seconds
Vdq			Voltages across d and q axes	volts
Idq			Currents across d and q axes	amperes
VIAlphaBeta			Voltages and currents across α and β axes	volts, amperes

Data Types: single

Parameters

Slowdown factor for current PI controller gains [1,20] — Slowdown factor for current PI controllers when estimating back-EMF

5 (default) | scalar

Slowdown factor (specified as an integer between 1 and 20) for the current PI controllers during back-EMF estimation. A smaller value results in more aggressive controllers.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023a

R2025a: New block parameter added

The Block Parameters dialog box now includes advanced options for configuring the parameter estimation process.