Lq Estimator

Estimate stator inductance (L_q) of permanent magnet synchronous motor (PMSM)

Since R2023a

• 

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

Description

The Lq Estimator block computes the q-axis stator inductance L_q of a PMSM using the phase currents, stator resistance, and the test configuration elements.

The block estimates L_q using either impedance measurement or phase difference measurement. You can use the Estimation technique parameter to select one of these estimation methods.

• Impedance measurement (recommended) — The block aligns the rotor to zero electrical position by injecting a constant current I_d along the d-axis. It then injects a high frequency current along the q-axis and uses a PI current controller to regulate the current. The block uses the applied voltages and measured currents to estimate the impedance, and the estimated impedance and stator resistance to estimate L_q.

• Phase difference measurement (for backward compatibility) — The block locks the rotor along the d-axis by injecting a constant voltage V_d. Locking the motor ensures that the rotor remains stationary (aligned with d-axis) during frequency injection. To estimate q-axis stator inductance, the block injects a high-frequency voltage signal along the q-axis and then performs a frequency sweep process by gradually reducing the injected signal frequency using the step size defined by the Step for frequency sweep (Hz) parameter. During frequency sweep, the block monitors the magnitude of the motor phase current. When the injected signal frequency reaches the value of the Minimum frequency (Hz) parameter, the block starts the estimation process by injecting a signal with rising frequency having a step size of Frequency step size for estimation (Hz) with number of steps defined by the Number of frequencies for estimation parameter. To set these parameter values for sweep and estimation, see PMSM Parameter Estimation Configurator.

  This image shows the frequency sweep and the incremental steps of rising frequency.

  

  The L_q estimation process uses the measured frequency sweep time duration as well as the step size of the changing frequency to estimate L_q.

Examples

New

Simulate PMSM Parameter Estimations

Use parameter estimation blocks to simulate PMSM resistance, inductance, and back EMF estimations.

• Since R2026a
• Open Live Script

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

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

StartStop — Control signal for L_q estimation

logical

Signal that either starts or stops L_q estimation:

• 1 (rising edge of a pulse) — This signal initiates the L_q estimation.

• 0 (falling edge of a pulse) — This signal immediately stops the L_q estimation process. If you interrupt the estimation process abruptly before completion, the block does not compute or output the L_q value.

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

Lq — Estimated q-axis stator inductance

scalar

Estimated q-axis stator inductance (in henries).

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
InjFreq			Frequency of signal injected most recently	Hz
status		0	Lq estimation did not start yet.	-
		1	Lq estimation is in progress.	-
		2	Lq estimation completed successfully.	-
		8200	If Estimation technique is set to Impedance measurement, Lq estimation failed because the feedback current is low compared to the reference current Id. Check that all phase contacts with the inverter are in good condition, that the current sensing ADC is configured correctly, and that inverter gain and offsets are correct. Read the phase A current feedback while the test is in progress. If the current is increasing slowly, change the PI controller gains using the Proportional gain and Integral gain parameters in the PMSM Parameter Estimation Configurator block. If there is no phase A current feedback, the inverter is in a faulty state or current measurement failed. If Estimation technique is set to Phase difference measurement, Lq estimation failed because the current feedback from the motor did not increase proportionally to the rise in the injected voltage. Check the motor connections and ensure the ADC correctly measures Ia and Ib.	-
		8201	If Estimation technique is set to Impedance measurement, the feedback current exceeded the reference Id current. Reduce current PI controller gains by adjusting the Proportional gain and Integral gain parameters in the PMSM parameter estimation configurator block. If Estimation technique is set to Phase difference measurement, estimated Lq is negative because the phase difference is greater than 90°. Check the phase difference in the log output, and adjust the injected frequency range as needed. Make sure the Current measurement delay parameter is accurately configured in the PMSM Parameter Estimation Configurator block, and try increasing the PWM frequency.	-
		8202	Lq estimation failed due to low peak amplitude of high-frequency feedback current before the applied voltage reached 50% PU. Reduce the operating frequency by adjusting the Select frequency (Hz) parameter in the PMSM Parameter Estimation Configurator block, but check that the rotor remains stationary at the new frequency.
		8203	Lq estimation failed because the estimated impedance is lower than the stator resistance. Check the input stator resistance.
Iq			Q-axis current	A
Vq			Q-axis voltage	V
PhaseDiff_rad			Phase difference between the injected voltage and current response	radians

Data Types: single

Parameters

Estimation technique — q-axis inductance estimation technique

Impedance measurement (recommended) (default) | Phase difference measurement (for backward compatibility)

Since R2026a

Technique that the block uses for q-axis inductance estimation, specified as:

• Impedance measurement (recommended) — Estimate L_d using impedance measurement.

• Phase difference measurement (for backward compatibility) — Estimate L_q using phase difference measurement.

Block sample time — Sample time for impedance measurement

50e-6 (default) | scalar

Since R2026a

Sample time (in seconds) for parameter estimation using impedance measurements.

Dependencies

To enable this parameter, set Estimation technique to Impedance measurement (recommended).

Maximum current limit (A) — Maximum allowed current during test

15 (default) | scalar

Maximum allowed current (in amperes) during testing.

Step size during injected voltage ramp up (per-unit) — Step size during injected voltage ramp up

0.0001 (default) | scalar

Step size (in per-units) during ramp up of injected voltage.

Number of sinusoidal voltage injections per frequency sweep step — Number of sinusoidal voltage injections per frequency during frequency sweep

5 (default) | scalar

Number of sinusoidal voltage injections per frequency for each frequency sweep step.

Number of sinusoidal voltage injections per frequency during Lq estimation — Number of sinusoidal voltage injections per frequency during Lq estimation

5 (default) | scalar

Number of sinusoidal voltage injections per frequency for each Lq estimation step.

Extended Capabilities

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

Version History

Introduced in R2023a

R2026a: New block parameters added for configuring estimation technique

The block can now perform inductance estimation using the impedance-based technique. Configure the estimation technique with the following new block parameters:

• Estimation technique

• Block sample time