**A. Appendix**

additional challenges and problems are introduced, such as the reduction of dynamic performance and the increase of harmonics. Nevertheless, the development of new processors technology (DSPs and FPGA) solves this problem due to

The authors would like to thank the managers and the members of the "Laboratoire d'électronique de puissance et commande (EPC) de l'Ecole Mohammadia d'Ingénieurs (EMI)" for their precious remarks and suggestions.

*A*, *B*, *C* control, input and output matrices of the induction motor model

*isα*, *is<sup>β</sup>* stator current components in *α β* reference frame *ϕr<sup>α</sup>*, *ϕr<sup>β</sup>* rotor flux components in *α β* reference frame *usα*, *us<sup>β</sup>* stator voltage components in *α β* reference frame

Recently, different works have been conducted to improve the effectiveness and the performance of the sensorless EKF for IM drive control. A bi-input EKF estimator, which deals with the estimation of the whole state of the machine together with stator and rotor resistances is presented. Another multi-model EKFs are proposed in order to improve EKF performance under different noise conditions. Then, a Kalman filter estimator has been designed for DTC controlled induction motor

the powerful calculations processing.

*Dynamic Data Assimilation - Beating the Uncertainties*

drives.

**Acknowledgements**

**Notations and symbols**

*Rs*, *Rr* stator and rotor resistances

*Tr* rotor time constant *Tem* electromagnetic torque

EKF extended Kalman filter ALO adaptive Luenberger observer

FPGA field-programmable gate array

DTC direct torque control AC alternating-current

IM induction motor PI proportional-integral *d*-*q* direct-quadrature MatLab matrix laboratory DSP digital signal processor

*TL* load torque *ω<sup>r</sup>* electrical speed Ω*<sup>r</sup>* mechanical speed *σ* Blondel's coefficient *p* pole pair number *J* inertia moment *f* friction coefficient

**Abbreviations**

**76**

*Ls*, *Lr*, *Lm* stator, rotor and mutual inductances


#### **Table A1.**

*The parameters of the used induction motor in simulation.*
