Extended EMF Observer
Compute electrical position and mechanical speed of permanent magnet synchronous motor (PMSM)
Since R2023a
Libraries:
Motor Control Blockset /
Sensorless Estimators
Description
The Extended EMF Observer block computes electrical position, θe (or sin θe and cos θe) in addition to mechanical speed of PMSM from the measured voltage and current in the stationary αβ reference frame.
The block includes a linear extended EMF state observer that estimates the extended back-emf. It uses a low-pass filter to remove any noise in the estimated back-emf value. In addition, the block includes a speed feed-forward-based quadrature phase-locked loop (PLL) that acts as a speed observer. The speed observer uses the computed extended back-emf to determine the motor speed. The feed-forward PLL calculates speed with zero error even during constant angular acceleration. The block then computes the position output from the estimated motor electrical speed.
Equations
The following is the IPMSM state equation:
The following equations describe the reduced order PMSM state model:
Extended back-EMF,
The following equation describes the reduced dimensional state observer:
The following equations describe the extended EMF observer parameters:
To ensure convergence, if we select as well as select any negative value for α, then the extended EMF observer gain can be determined as:
where:
, , and .
, , and .
, , and .
, , and .
Note
A and C are observable pair.
"" and "" are the first-order and second-order differential operators respectively.
vα and vβ are the stator voltages along the α- and β-axes respectively.
iα and iβ are the stator currents along the α- and β-axes respectively.
eα and eβ are the extended back-EMF along the α- and β-axes respectively.
id and iq are the stator currents along the d- and q-axes respectively.
R is the stator resistance of PMSM.
Ld and Lq are the stator inductances of PMSM across d and q axes respectively.
KE is the EMF constant
ωre is the angular velocity at electrical angle.
θre is the rotor position at electrical angle.
are the estimated values.
ξ is the feedback gain.
Examples
Ports
Input
Output
Parameters
References
[1] Zhiqian Chen, M. Tomita, S. Doki and S. Okuma, "An extended electromotive force model for sensorless control of interior permanent-magnet synchronous motors," in IEEE Transactions on Industrial Electronics, vol. 50, no. 2, pp. 288-295, April 2003, doi: 10.1109/TIE.2003.809391.
[2] T. Ohnuma, S. Doki and S. Okuma, "Extended EMF observer for wide speed range sensorless control of salient-pole synchronous motor drives," The XIX International Conference on Electrical Machines - ICEM 2010, Rome, Italy, 2010, pp. 1-6, doi: 10.1109/ICELMACH.2010.5608087.
[3] G. Liu, H. Zhang and X. Song, "Position-Estimation Deviation-Suppression Technology of PMSM Combining Phase Self-Compensation SMO and Feed-Forward PLL," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 1, pp. 335-344, Feb. 2021, doi: 10.1109/JESTPE.2020.2967508.
Extended Capabilities
Version History
Introduced in R2023a