# Enhanced State and Unknown Input Estimation for Synchronous Reluctance Motor Using Takagi-Sugeno Fuzzy Proportional Multi-Integral Observer

Wail Hamdi, Ramzi Saadi, Mohamed Yacine Hammoudi, Rabiaa Houili, Mohamed Benbouzid, Yassine Himeur, Sami Miniaoui, Shadi Atalla, Wathiq Mansoor

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Wail Hamdi, Ramzi Saadi, Mohamed Yacine Hammoudi, Rabiaa Houili, Mohamed Benbouzid, et al. Enhanced State and Unknown Input Estimation for Synchronous Reluctance Motor Using Takagi-Sugeno Fuzzy Proportional Multi-Integral Observer. IEEE Access, 2024, 12, pp.42908 - 42920. 10.1109/access.2024.3378583. [hal-05340417](https://hal-univ-brest.fr/hal-05340417v1)

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Distributed under a Creative Commons Attribution 4.0 International License
Received 5 February 2024, accepted 9 March 2024, date of publication 18 March 2024, date of current version 26 March 2024.

Digital Object Identifier 10.1109/ACCESS.2024.3378583

RESEARCH ARTICLE

# Enhanced State and Unknown Input Estimation for Synchronous Reluctance Motor Using Takagi-Sugeno Fuzzy Proportional Multi-Integral Observer

WAIL HAMDI<sup>1</sup>, RAMZI SAADI<sup>1</sup>, MOHAMED YACINE HAMMOUDI<sup>1</sup>, RABIAA HOUILI<sup>1</sup>, MOHAMED BENBOUZID<sup>2,3</sup>, (Fellow, IEEE), YASSINE HIMEUR<sup>4</sup>, (Senior Member, IEEE), SAMI MINIAOUI<sup>4</sup>, (Member, IEEE), SHADI ATALLA<sup>4</sup>, (Member, IEEE), AND WATHIQ MANSOOR<sup>4</sup>, (Senior Member, IEEE)

Corresponding author: Yassine Himeur (yhimeur@ud.ac.ae)

**ABSTRACT** This study introduces a novel approach to enhance state and unknown input estimation for the synchronous reluctance motor, utilizing the Takagi-Sugeno fuzzy representation. A proportional multi-integral observer structure is introduced, capable of capturing a wider range of unknown input dynamics compared to the previous proportional integral observer utilized in prior research. Stability conditions, obtained using the quadratic Lyapunov function, are formulated as linear matrix inequalities to guarantee the asymptotic convergence of the estimation error. To evaluate the effectiveness of the proposed observer, different cases were considered, including scenarios with slow and fast variations of the unknown input. Through hardware-in-the-loop validation, the results clearly demonstrate the superiority of the proposed method over the earlier approach. This advancement signifies a significant improvement in the estimation accuracy and reliability of the Synchronous Reluctance Motor.

**INDEX TERMS** Hardware in the loop validation, synchronous reluctance motor, proportional multi-integral observer, Takagi-Sugeno fuzzy systems, unknown input observer.

## I. INTRODUCTION

The landscape of electric motor technology has experienced tremendous advances in recent years. Among the novel developments, the synchronous reluctance motor (SynRM) has emerged as a standout option, due to its considerable economic and technical benefits. The key advantage of SynRM is its non-reliance on rare-earth permanent magnets, which are not only expensive and scarce but also have significant geopolitical and environmental implications [1], [2]. Recently, the growing interest in SynRM among researchers has led to the emergence of new studies on these

The associate editor coordinating the review of this manuscript and approving it for publication was Xiaojie Su<sup>1</sup>.

machines. A number of these investigations, such as [3] and [4], specifically delve into the areas of fault detection and advanced control strategies.

A significant aspect that ensures the optimal performance of SynRM is its control strategy. The most prominent among these strategies are the Field Oriented Control (FOC) and Direct Torque Control (DTC). The FOC offers advantages like low torque ripple, constant switching frequency and decoupling of the flux and torque components, making it widely popular for SynRM applications [5]. Despite its benefits, FOC has severe limits, prompting researchers to alternative control methods. These limitations include high computational burden, limited dynamics due to the lack of direct torque control, and a lack of robustness due to

<footnote n="1">¹Laboratory of Energy Systems Modeling (LMSE), Department of Electrical Engineering, University of Biskra, Biskra 07000, Algeria</footnote>

<footnote n="2">²Institut de Recherche Dupuy de Lôme (UMR CNRS 6027 IRDL), University of Brest, 29238 Brest, France</footnote>

<footnote n="3">³Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China</footnote>

<footnote n="4">⁴College of Engineering and Information Technology, University of Dubai, Dubai, United Arab Emirates</footnote>
its reliance on motor parameters [6]. On the other hand, DTC boasts of a simpler control structure, faster dynamic response, and robustness against parameter variations. Recent advancements have witnessed the integration of sensorless control techniques, primarily based on model reference adaptive systems [7], [8] and sliding mode observers [9], [10], to further enhance the efficiency and reliability of the SynRM control. With the advent of modern computational tools and wide band-gap semiconductor devices, it is also possible to implement more sophisticated control algorithms that can adapt to real-time changes and improve overall motor performance. As the quest for greener and more efficient technologies continues, control strategies for SynRM are expected to evolve further, incorporating advanced predictive techniques to achieve even higher efficiencies and performance levels [11], [12].

Unknown input estimation serves a critical role not only in fault detection and diagnosis but also in control systems. Accurate estimation enables control techniques such as feedforward, robust, and predictive control to function optimally. Simultaneously, it is crucial for fault detection and diagnosis, enhancing system reliability and safety by aiding in the identification and correction of technical problems. Its application is versatile, as shown by Jing Na et al. in [13], where it is used in vehicle engine torque estimation. In [14], the authors innovatively apply an unknown input decoupled filter design in linear time-varying systems, especially where common assumptions aren't met. The application of unknown input estimation is further extended to road roughness estimation in [15]. Moreover, a sophisticated application is presented by Qianyue Luo et al. in [16] where model predictive control based on an unknown input observer is utilized to address the control problem of heterogeneous vehicle platoons. Additionally, in [17], an unknown input observer is used specifically for fault diagnosis of an intelligent hydraulic pump. Each of these references emphasizes the variety of applications and the importance of accurate unknown inputs estimation in maintaining efficient system operation, particularly in systems like the SynRM.

Furthermore, the Takagi-Sugeno (TS) fuzzy representation stands as a robust and potent tool for the analysis of nonlinear systems. Employing a weighted sum of multiple linear models, this representation skillfully captures complex dynamics, effectively bypassing the daunting mathematical intricacies that often accompany the analysis of nonlinear systems. With their intuitive, adaptable nature, and the ease they afford in implementation, TS fuzzy representations emerge as an attractive choice for a wide range of complex engineering applications, including but not limited to, the study of SynRM dynamics [18], [19], and [20].

The role of the TS observer, specifically in the estimation of states and unknown inputs, has been well-documented in the literature. It utilizes the information derived from the system's outputs to estimate the unknown inputs, providing a highly beneficial solution for systems where direct measurement of certain inputs is impossible or impractical.

Dong Zhao et al. [21] introduce a novel approach for state and unknown input estimation specifically designed for TS fuzzy models. While, Damiano Rotondo et al. [22] propose a robust unknown input observer capable of state and fault estimation in discrete-time TS systems. Designing unknown input observers for TS uncertain systems has been explored and implemented on Turbo-Reactor in [23], [24], where the authors utilized a combination of a proportional integral observer and the sliding mode method. Additionally, in [25] the authors present a sensor fault diagnosis method, leveraging an $H^\infty$ sliding mode and unknown input observer within TS systems, a technique notable for its ability to handle uncertain premise variables. Nasreddine Bouguila et al. [26] presented an unknown input observer that employs a decoupling approach. This method offers precise estimation capabilities without requiring prior knowledge about the form of the unknown input. Another implementation of the decoupling approach along with the proportional integral observer have been utilized in order to design an active fault tolerant control for TS systems affected by sensors faults in [27]. This innovation significantly broadens its applications, particularly in fault detection. These studies underline the potential of TS observers in improving the accuracy and reliability of state and unknown input estimation.

The primary contribution in this article involves an innovative approach to improving the estimation of unknown inputs applied to the SynRM. The proposed method involves the use of a proportional multi integral observer (PMIO) for the estimation of unknown inputs. This PMIO operates under the assumption that the $q^{th}$ derivative of the unknown input is null. In contrast, the method proposed by Boukhlof et al in [28] employs a PIO on SynRM, which operates under the narrower assumption that only the first derivative of the unknown input is null. In practical cases, this assumption may not consistently hold, resulting in a less precise representation of the unknown input dynamics. Conversely, the PMIO, with its broader assumption, frequently proves to be more realistic, leading to improved accuracy in representing the dynamics of the unknown input. This method, therefore, allows for more precise estimation of unknown inputs, particularly in the case of variable inputs. The validity of our proposition is confirmed through a hardware-in-the-loop (HIL) test, where we compare the performance of the PMIO with that of the PIO. This comparative analysis, which forms a crucial part of our research, provides robust empirical evidence supporting our proposed improvements.

The HIL approach serves as a powerful tool that connects between simulation and real-world systems, allowing a safe and efficient way to test components while they interact with simulated environments [29]. By leveraging HIL, this study gains enhanced testing reliability and efficiency, making it possible to conduct comprehensive examinations of system components under various simulated conditions. Notably, it was utilized for the construction of a cost-efficient, intelligent neural predictive control for
hybrid electric vehicles [30]. In a separate study, HIL was implemented for optimizing linear controllers via genetic algorithms, specifically for a brushless DC motor in electric scooters under fluctuating operational conditions [31]. The HIL validation can be implemented using two dSPACE card boards. In this setup, one board acts as the hardware controller, while the second emulates the target system. This methodology has gained traction and has been employed in numerous studies [32], [33], [34]. Among these applications, Liu et al. uniquely explored the SynRM drive systems using a Hermite neural network-based second-order sliding-mode control [34]. Their work stands out as the first to apply the two dSPACE configuration explicitly for the SynRM. Subsequent research, the application of an unknown input observer for this motor based on PIO, continued to harness the potential of the HIL implementation [28].

The main contributions of this paper to the improvement of unknown input estimation for the SynRM are summarized as follows:

* Enhancement of unknown input estimation performance through the application of a PMIO, demonstrating improved efficiency compared to the traditional PIO utilized in previous research.

* Executed a successful application of the HIL technique for the validation of an unknown input observer specifically designed for SynRM, enhancing the practical applicability and reliability of such observers.

The remainder of this paper is structured as follows: Section II introduces the mathematical model of the SynRM. The PMIO structure, along with the stability conditions of the estimation error dynamics, are detailed in Section III. Section IV demonstrates the application of the PMIO to the SynRM in order to compute the observer gains. A comparison of the PIO and PMIO through simulation results is presented in Section V. Section VI then delves into the real-time implementation of the proposed method using a hardware-in-the-loop test. Finally, the conclusion and prospects for improvement are suggested in Section VII.

## II. MATHEMATICAL MODELING OF SYNCHRONOUS RELUCTANCE MOTOR

### A. NON-LINEAR DYNAMICAL MODEL OF SYNCHRONOUS RELUCTANCE MOTOR

The dynamical model of the synchronous reluctance motor is typically described in the rotational d-q reference frame. This frame is a transformation from the three-phase stator currents or voltages into two orthogonal axes, denoted as ‘d’ (direct) and ‘q’ (quadrature). The d-q transformation facilitates the analysis of electrical machines by representing three-phase dynamics in a simplified two-phase format.

Given in the d-q frame, the equations of the SynRM capture the relationship between voltages, currents, flux linkages, and the electromagnetic torque. These equations, along with other motor parameters like resistance, inductance, and the number of pole pairs, help form a comprehensive model of the motor dynamics.

Here are the specific equations as described in [35]:

$$ egin{cases} V_{sd} = R_s i_{sd} + L_d \frac{di_{sd}}{dt} - \omega L_q i_{sq} \\ V_{sq} = R_s i_{sq} + L_q \frac{di_{sq}}{dt} + \omega L_d i_{sd} \\ \frac{d\omega}{dt} = \frac{3}{2} \frac{p^2}{J_m} (L_d - L_q) i_{sd} i_{sq} - \frac{f}{J_m} \omega - \frac{p}{J_m} T_L(t) \end{cases} \quad (1) $$

where: $V_{sd}$ and $V_{sq}$ are the direct and the quadrature stator voltages respectively. $i_{sd}$ and $i_{sq}$ are the direct and the quadrature stator currents. $\omega$ is the rotor electrical angular speed. $T_L(t)$ is the resistant torque which is the unknown input affecting the state dynamics. The rest of the parameters are defined in Table 1.

This model is crucial for the design and efficacy of observers in SynRMs. Observers rely on the model’s accuracy and detail to continuously monitor and estimate the motor’s internal states. The non-linearity in the model accounts for various real-world factors, ensuring that the mathematical representation closely mimics the actual behavior of the motor.

By defining $x(t) = [i_{sd} \ i_{sq} \ \omega]$, $u(t) = [u_{sd} \ u_{sq}]$ the state space representation of the SynRM is presented as follows:

$$ \begin{cases} \dot{x}(t) = A(x)x(t) + Bu(t) + ET_L(t) \\ y(t) = Cx(t) \end{cases} \quad (2) $$

where:

$$ A(x(t)) = \begin{bmatrix} \frac{-R_s}{L_d} & \frac{L_q}{L_d}\omega & 0 \\ \frac{-L_d}{L_q}\omega & \frac{-R_s}{L_q} & 0 \\ \alpha i_{sq} & 0 & -\frac{f}{J_m} \end{bmatrix}, \quad B = \begin{bmatrix} \frac{1}{L_d} & 0 \\ 0 & \frac{1}{L_q} \\ 0 & 0 \end{bmatrix} \\ E = \begin{bmatrix} 0 \\ 0 \\ -\frac{p}{J_m} \end{bmatrix}, \quad C = \begin{bmatrix} 0 & 0 & 1 \end{bmatrix}, \quad \alpha = \frac{3p^2}{2Jm}(L_d - L_q) $$

The parameters of the motor are presented in Table 1.

<table><caption>TABLE 1. Synchronous reluctance motor parameters [36].</caption><thead><tr><th>Parameters</th><th>Values</th></tr></thead><tbody><tr><td>Rated power</td><td>P<sub>r</sub> = 2.2[KW]</td></tr><tr><td>Rated voltage</td><td>V<sub>r</sub> = 220/380[V]</td></tr><tr><td>Rated speed</td><td>Ω<sub>r</sub> = 1500[rpm]</td></tr><tr><td>Stator resistance</td><td>R<sub>s</sub> = 1.71 [Ω]</td></tr><tr><td>Inductance of direct axis</td><td>L<sub>d</sub> = 0.15 [H]</td></tr><tr><td>Inductance of quadratic axis</td><td>L<sub>q</sub> = 0.04 [H]</td></tr><tr><td>Moment of inertia</td><td>J<sub>m</sub> = 0.0137 [Kg.m<sup>2</sup>]</td></tr><tr><td>Number of pair of poles</td><td>p = 2</td></tr><tr><td>Friction coefficient</td><td>f = 0.00036 [Nm/rad/s]</td></tr></tbody></table>
## B. TAKAGI-SUGENO FUZZY REPRESENTATION OF SYNCHRONOUS RELUCTANCE MOTOR

The TS fuzzy multi-model serves as an effective representation of the intricate, nonlinear dynamics of the SynRM. The selected observer is based on this model, benefiting from the TS model's combination of local linear models. By incorporating the sector nonlinearity approach [37], nonlinearity analysis is simplified, making it an efficient method for SynRM state and unknown input observation.

The TS multi-model is given as follows:

$$ \left\{ \begin{array}{l} \dot{x}(t) = \sum_{i=1}^{r} \mu_i(x(t))(A_i x(t) + B_i u(t) + E_i d(t)) \\ y(t) = C x(t) \end{array} \right. \qquad (3) $$

Consider $x(t) \in R^n$ as the state vector, while $u(t) \in R^{n_u}$ is recognized as the known input vector and $d(t) \in R^{n_d}$ is the unknown input vector. Additionally, $y \in R^{n_y}$ acts as the output vector. The known matrices are represented by $A_i \in R^{n_{xi}}$, $B_i \in R^{n_{xi}}$, $E_i \in R^{n_{id}}$. Lastly, $\mu_i(x(t))$ is identified as the weighting functions that verifies the convex sum property described as follows:

$$ \left\{ \begin{array}{l} \sum_{i=1}^{r} \mu_i (x(t)) = 1 \\ 0 \le \mu_i (x(t)) \le 1, \quad \forall i = 1, \dots, r \end{array} \right. \qquad (4) $$

By defining the premise variable $\xi_1 = i_{sq}$ and $\xi_2 = \omega$ as the nonlinear terms in the dynamical model of the SynRM in (2), the weighting functions can be described as follows:

$$ \mu_i(x(t)) = \prod_{j=1}^{2} M_{ij}(\xi_j) \qquad (5) $$

where the membership functions of the fuzzy rules are:

**Rule1:** $M_{11} = W_1(\xi_1)$, $M_{12} = W_1(\xi_2)$

**Rule2:** $M_{21} = W_1(\xi_1)$, $M_{22} = W_2(\xi_2)$

**Rule3:** $M_{31} = W_2(\xi_1)$, $M_{32} = W_1(\xi_2)$

**Rule4:** $M_{41} = W_2(\xi_1)$, $M_{42} = W_2(\xi_2)$

And using the sector nonlinearity approach the following functions are obtained:

$$ W_1(\xi_1) = \frac{\xi_1 - \xi_{1min}}{\xi_{1max} - \xi_{1min}}, \quad W_2(\xi_1) = \frac{\xi_{1max} - \xi_1}{\xi_{1max} - \xi_{1min}} $$

$$ W_1(\xi_2) = \frac{\xi_2 - \xi_{2min}}{\xi_{2max} - \xi_{2min}}, \quad W_2(\xi_2) = \frac{\xi_{2max} - \xi_2}{\xi_{2max} - \xi_{2min}} $$

Hence, the sub-matrices $A_i$, $B_i$ and $E_i$ of the multi-model (3) are given as follows:

$$ A_1 = \begin{bmatrix} \frac{-R_s}{L_d} & \frac{L_q}{L_d} \omega_{max} & 0 \\ -\frac{L_q}{L_d} \omega_{max} & \frac{-R_s}{L_q} & 0 \\ \alpha i_{sqmax} & 0 & -\frac{f}{Jm} \end{bmatrix} $$

$$ A_2 = \begin{bmatrix} \frac{-R_s}{L_d} & \frac{L_q}{L_d} \omega_{min} & 0 \\ -\frac{L_q}{L_d} \omega_{min} & \frac{-R_s}{L_q} & 0 \\ \alpha i_{sqmax} & 0 & -\frac{f}{Jm} \end{bmatrix} $$

$$ A_3 = \begin{bmatrix} \frac{-R_s}{L_d} & \frac{L_q}{L_d} \omega_{max} & 0 \\ -\frac{L_q}{L_d} \omega_{max} & \frac{-R_s}{L_q} & 0 \\ \alpha i_{sqmin} & 0 & -\frac{f}{Jm} \end{bmatrix} $$

$$ A_4 = \begin{bmatrix} \frac{-R_s}{L_d} & \frac{L_q}{L_d} \omega_{min} & 0 \\ -\frac{L_q}{L_d} \omega_{min} & \frac{-R_s}{L_q} & 0 \\ \alpha i_{sqmin} & 0 & -\frac{f}{Jm} \end{bmatrix} $$

$$ B_i = \begin{bmatrix} \frac{1}{L_d} & 0 \\ 0 & \frac{1}{L_q} \\ 0 & 0 \end{bmatrix}, \quad E_i = \begin{bmatrix} 0 \\ 0 \\ -\frac{p}{Jm} \end{bmatrix}, \quad \forall i = 1 \dots 4 $$

After substituting the parameters of the system in the sub-matrices, the following results are obtained:

$$ A_1 = \begin{bmatrix} -11.4 & 186.67 & 0 \\ -2625 & -42.75 & 0 \\ 2890.51 & 0 & -0.0263 \end{bmatrix} $$

$$ A_2 = \begin{bmatrix} -11.4 & -186.67 & 0 \\ 2625 & -42.75 & 0 \\ 2890.51 & 0 & -0.0263 \end{bmatrix} $$

$$ A_3 = \begin{bmatrix} -11.4 & 186.67 & 0 \\ -2625 & -42.75 & 0 \\ -2890.51 & 0 & -0.0263 \end{bmatrix} $$

$$ A_4 = \begin{bmatrix} -11.4 & -186.67 & 0 \\ 2625 & -42.75 & 0 \\ -2890.51 & 0 & -0.0263 \end{bmatrix} $$

$$ B_i = \begin{bmatrix} 6.67 & 0 \\ 0 & 25 \\ 0 & 0 \end{bmatrix}, \quad E_i = \begin{bmatrix} 0 \\ 0 \\ -145.9854 \end{bmatrix}, \quad \forall i = 1 \dots 4 $$

## III. PROPORTIONAL MULTI-INTEGRAL OBSERVER DESIGN

The implementation of the PMI observer is achieved by the following assumption:

$$ A_1 : d^{(q)}(t) = 0 \qquad (6) $$

The successive derivatives of $d(t)$ will be defined in the following state form:

$$ \begin{bmatrix} \dot{d}(t) \\ \dot{d}_1(t) \\ \vdots \\ \dot{d}_{q-1}(t) \end{bmatrix} = \begin{bmatrix} d_1(t) \\ d_2(t) \\ \vdots \\ d_q(t) \end{bmatrix} \qquad (7) $$
This assumption allows the rewrite of the system (eq 3) as
follows:

$$
\left\{
\begin{aligned}
\dot{x}_a(t) &= \sum_{i=1}^{r} \mu_i(x(t))(\tilde{A}_i x_a(t) + \tilde{B}_i u(t)) \\
y(t) &= \tilde{C} x_a(t)
\end{aligned}
\right.
\qquad (8)
$$

where:

$$
\begin{gather*}
x_a(t) = \begin{bmatrix} x(t) \\ d(t) \\ d_1(t) \\ d_2(t) \\ \vdots \\ d_{q-1}(t) \end{bmatrix}, \quad \tilde{A}_i = \begin{bmatrix} A_i & E_i & 0 & \cdots & 0 & 0 \\ 0 & 0 & I_{n_d} & \cdots & 0 & 0 \\ 0 & 0 & 0 & \cdots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & 0 & 0 & I_{n_d} \\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix} \\
\tilde{B}_i = \begin{bmatrix} B_i \\ 0 \\ \vdots \\ 0 \end{bmatrix}, \quad \tilde{C} = \begin{bmatrix} C & 0 & 0 & \cdots & 0 & 0 \end{bmatrix}
\end{gather*}
$$

The structure of the PMI observer of the system (eq 8) is
given as follows:

$$
\left\{
\begin{aligned}
\dot{\hat{x}} &= \sum_{i=1}^{r} \mu_i(\hat{x}(t)) (A_i \hat{x}(t) + B_i u(t) + E_i d(t)) \\
&\quad + L_p(y(t) - \hat{y}(t)) \\
\hat{y}(t) &= C x(t) \\
\dot{\hat{d}} &= L_{I0}(y(t) - \hat{y}(t)) + \hat{d}_1(t) \\
\hat{d}_1(t) &= L_{I1}(y(t) - \hat{y}(t)) + \hat{d}_2(t) \\
\vdots \\
\dot{\hat{d}}_{q-1}(t) &= L_{Iq-1}(y(t) - \hat{y}(t))
\end{aligned}
\right.
\tag{9}
$$

And under the augmented form as:

$$
\left\{
\begin{aligned}
\dot{\hat{x}}_a(t) &= \sum_{i=1}^{r} \mu_i(\hat{x}(t))(\tilde{A}_i \hat{x}_a(t) + \tilde{B}_i u(t) + \tilde{L}(y(t) - \hat{y}(t))) \\
\hat{y}(t) &= \tilde{C} \hat{x}_a(t)
\end{aligned}
\right.
\qquad (10)
$$

where:

$$
\tilde{L} = \begin{bmatrix} L_P \\ L_I \end{bmatrix}, \quad L_I = \begin{bmatrix} L_{I0} \\ L_{I1} \\ \vdots \\ \vdots \\ L_{Iq-1} \end{bmatrix}
$$

Lemma 1 [38]: Let $f(x) : \mathbb{R}^n \Rightarrow \mathbb{R}^n$ be a vector function with $f_i(x) : \mathbb{R}^n \Rightarrow \mathbb{R}$ its $i^{th}$ component. By assuming that $f(x)$ is differentiable, then there are constant vectors $z_1, \dots, z_n \in (a, b)$, $zi \neq a$, $zi \neq b$ for $i = 1, \dots, n$ such that:

$$
f(a) - f(b) = \sum_{i=1}^{n} \sum_{j=1}^{n} e_n(i) e_n(j)^T \frac{\partial f_i(z_j)}{\partial x_j} (a-b) \quad (11)
$$

where $E_n$ is the canonical basis of the vectorial space $\mathbb{R}^n$ for all $n \ge 1$:

$$
E_n = \{e_n(i) | e_n(i) = (0, \dots, 0, \underbrace{1}_{i}, 0, \dots, 0)^T, i = 1, \dots, n\} \quad (12)
$$

Applying the TS representation, the following form is
obtained:

$$
f(a) - f(b) = \sum_{i=1}^{S \le 2n^2} h_i(z(t)) H_i \cdot (a-b) \quad (13)
$$

The subsequent theorem delivers adequate conditions
outlined as LMI to guarantee the asymptotic convergence of
the error dynamic:

*Theorem 1:* if there exist matrices such that $P = P^T \in \mathbb{R}^{n_{x_a} \times n_{x_a}} > 0$ and $M \in \mathbb{R}^{n_{x_a} \times n_y}$, the estimation error will tend towards zero asymptotically at a decay rate of $\alpha$. This condition is ensured if the accompanying LMI holds $\forall i = 1, \dots, S$:

$$
\tilde{A}_i^T P + P \tilde{A}_i - M \tilde{C} - \tilde{C}^T M^T < -2\alpha P \quad (14)
$$

The observer gain is given by:

$$
\tilde{L} = P^{-1} M \qquad (15)
$$

proof: The trajectory of the estimation error, denoted as $e_a(t) = x_a(t) - \hat{x}_a(t)$, is defined as follows:

$$
\dot{e}_a(t) = \tilde{\Phi}(x_a(t)) - \tilde{\Phi}(\hat{x}_a(t)) - \tilde{L}\tilde{C}e(t) \quad (16)
$$

where:

$$
\tilde{\Phi}(x_a(t)) = \sum_{i=1}^{r} \mu_i(x(t))(\tilde{A}_i x_a(t) + \tilde{B}_i u(t)) \quad (17)
$$

With the application of the mean value theorem mentioned in
Lemma 1, the trajectory of error turns into:

$$
\dot{e}_a(t) = \sum_{i=1}^{S} h_i(z(t)) (\tilde{A}_i - \tilde{L}\tilde{C}) e(t) \quad (18)
$$

The quadratic Lyapunov function is used to analyze the
stability of the error dynamics, denoted as:

$$
V(t) = e_a(t)^T P e_a(t) \quad (19)
$$

The derivative of function $V(t)$ concerning $t$ is:

$$
\dot{V}(t) = \sum_{i=1}^{S} h_i(z(t)) e_a^T ((\tilde{A}_i - \tilde{L}\tilde{C})^T P + P(\tilde{A}_i - \tilde{L}\tilde{C})) e_a \quad (20)
$$

The stability of the estimation error dynamics is obtained
by ensuring the negativity of (20), and to further improve the
performance of the estimation, this negativity is giving by
using the following decay rate:

$$
\dot{V}(t) \leq -2\alpha V(t) \quad (21)
$$
By substituting (19) and (20) in (21) the following inequality is obtained:

$$ \sum_{i=1}^{S} \mu_i(z(t)) e_a^T (\tilde{\mathcal{A}}_i^T - \tilde{C}^T \tilde{L}^T P + P \tilde{\mathcal{A}}_i - P \tilde{L} \tilde{C} + 2\alpha P) e_a < 0 \quad (22) $$

The inequality (22) is not linear with respect to the variables $P$ and $\tilde{L}$. By using the following change of variable on this inequality, then the Theorem 1 is established in the form of an LMI:

$$ M = P\tilde{L} \quad (23) $$

## IV. OBSERVER DESIGN FOR SYNCHRONOUS RELUCTANCE MOTOR

Figure 1 illustrates the overall schematic diagram of the implementation of the observer with the SynRM.

<figure><img src="image_2.png" /><figcaption>FIGURE 1. Overall schematic diagram of the observer.</figcaption></figure>

This section presents the procedure of gain-calculating of the PMI observer on SynRM. In order to validate Theorem 1.

### A. IDENTIFYING THE TERMS $\tilde{\mathcal{A}}_i$

Since that $\forall i = 1...r$ the matrices $\tilde{B}_i$ are identical, then the value of $\tilde{\Phi}(x_a)$ in (17) can be reduced to:

$$ \tilde{\Phi}(x_a) = \sum_{i=1}^{r} \mu_i(x(t)) [\tilde{\mathcal{A}}_i x_a(t)] = \tilde{\mathcal{A}}(x_a) x_a \quad (24) $$

where:

$$ \tilde{\mathcal{A}}(x_a) = \begin{bmatrix} \mathcal{A}(x) & E & 0 & \dots & 0 & 0 \\ 0 & 0 & I_{nd} & \dots & 0 & 0 \\ 0 & 0 & 0 & \dots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \dots & 0 & I_{nd} \\ 0 & 0 & 0 & \dots & 0 & 0 \end{bmatrix} $$

According to Lemma 1, the MVT is applied as follows:

$$ \frac{\partial \tilde{\Phi}(z)}{\partial x_a} = \begin{bmatrix} \frac{\partial \mathcal{A}(x)x}{\partial x} & E & 0 & \dots & 0 & 0 \\ 0 & 0 & I_{nd} & \dots & 0 & 0 \\ 0 & 0 & 0 & \dots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \dots & 0 & I_{nd} \\ 0 & 0 & 0 & \dots & 0 & 0 \end{bmatrix} $$

where:

$$ \frac{\partial \mathcal{A}(x)x}{\partial x} = \begin{bmatrix} -\frac{R_s}{L_d} & \frac{L_q}{L_d} \omega & \frac{L_q}{L_d} i_{sq} \\ -\frac{L_d}{L_q} \omega & -\frac{R_s}{L_q} & -\frac{L_d}{L_q} i_{sd} \\ \alpha i_{sq} & \alpha i_{sd} & -\frac{f}{Jm} \end{bmatrix} $$

Through the use of the TS representation on $\frac{\partial \tilde{\Phi}(z)}{\partial x_a}$, the terms $\tilde{\mathcal{A}}_i$ can be obtained as follows:

$$ \tilde{\mathcal{A}}_i = \begin{bmatrix} \mathcal{A}_i & E & 0 & \dots & 0 & 0 \\ 0 & 0 & I_{nd} & \dots & 0 & 0 \\ 0 & 0 & 0 & \dots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \dots & 0 & I_{nd} \\ 0 & 0 & 0 & \dots & 0 & 0 \end{bmatrix} $$

where:

$$ \begin{align*} A_1 &= \begin{bmatrix} 0 & 186.67 & 16 \\ -2625 & 0 & -225 \\ 2890.51 & 2890.51 & 0 \end{bmatrix} \\ A_2 &= \begin{bmatrix} 0 & -186.67 & 16 \\ 2625 & 0 & -225 \\ 2890.51 & 2890.51 & 0 \end{bmatrix} \\ A_3 &= \begin{bmatrix} 0 & 186.67 & -16 \\ -2625 & 0 & -225 \\ -2890.51 & 2890.51 & 0 \end{bmatrix} \\ A_4 &= \begin{bmatrix} 0 & -186.67 & -16 \\ 2625 & 0 & -225 \\ -2890.51 & 2890.51 & 0 \end{bmatrix} \\ A_5 &= \begin{bmatrix} 0 & 186.67 & 16 \\ -2625 & 0 & 225 \\ 2890.51 & -2890.51 & 0 \end{bmatrix} \\ A_6 &= \begin{bmatrix} 0 & -186.67 & 16 \\ 2625 & 0 & 225 \\ 2890.51 & -2890.51 & 0 \end{bmatrix} \\ A_7 &= \begin{bmatrix} 0 & 186.67 & -16 \\ -2625 & 0 & 225 \\ -2890.51 & -2890.51 & 0 \end{bmatrix} \\ A_8 &= \begin{bmatrix} 0 & -186.67 & -16 \\ 2625 & 0 & 225 \\ -2890.51 & -2890.51 & 0 \end{bmatrix} \end{align*} $$
<figure><img src="image_3.png" /><figcaption>FIGURE 2. Schematic diagram of indirect field-oriented control with simultaneous state and unknown input observer.</figcaption></figure>

## B. SYNTAX CODE IN MATLAB

In order to solve the LMI constraints defined in Theorem 1, the Yalmip toolbox is employed. Yalmip is a renowned modeling language in MATLAB, specially tailored for optimization problems. It provides an intuitive framework for formulating and solving optimization problems, ranging from linear and polynomial to semidefinite programming tasks. Its integration with several solvers allows for a broad spectrum of optimization problems to be tackled efficiently. In the context of our problem, utilizing Yalmip facilitates the accurate definition and solution of the constraints, particularly beneficial for complex systems where manual computation might be prone to errors. Here, the constraints are defined as follows:

» P = sdpvar(6,6);
» M = sdpvar(6,1,'full');
» F=[P >= Tolerance];
» for i=1:r
» F=[F,A{i}'P+PA{i}-MC-C'M'+2alphaP<= -Tolerance ];
» end

where the observation matrix $C \in \mathbb{R}^{1 \times 3}$ is given by: $C = [0 \ 0 \ 1]$

## C. SOLVING THE CONVEX OPTIMIZATION PROBLEM

By considering the output as the rotor's electrical angular speed, denoted as $y(t) = \omega(t)$, and a decay rate of $\alpha = 6.5$, Theorem 1 is applied to derive the following gains for the PMIO where its order is $q = 3$ (P3IO):

$$L_p = \begin{bmatrix} 8.5621 \times 10^{-12} \\ -5.8990 \times 10^{-12} \\ 1.3533 \times 10^4 \end{bmatrix}, \quad L_I = \begin{bmatrix} -4.7362 \times 10^3 \\ -6.1513 \times 10^4 \\ -2.6645 \times 10^5 \end{bmatrix}$$

## V. SIMULATION RESULTS

In this analysis, a comparison is drawn between the PMIO and PIO methods. The objective is to highlight the effectiveness of the proposed approach compared to the one introduced by Boukhlouf et al. in their previous work [28], where the PIO was implemented. To begin with, the Indirect

Field-Oriented Control strategy is incorporated alongside the unknown input observer, which serves to regulate the SynRM. Figure 2 illustrates the control scheme structure utilized in the experiment. Since the primary focus of this paper is on enhancing the state estimation performance, the control gains for the current and speed regulator were determined using the classical pole placement method. The gains of the speed regulator of the “IP” type are $K_{P\Omega} = 2.5933$ and $K_{I\Omega} = 32.4337$, while those of the current regulator of type “PI” are $K_{Pi} = 154.3210$ and $K_{Ii} = 1759.26$.

The observer gains obtained from PIO proposed by Boukhlouf et al. in [28] are given as follows:

$$L_1 = \begin{bmatrix} 8.2961 \times 10^{-11} \\ -3.0162 \times 10^{-12} \\ 1.2254 \times 10^4 \\ -1.4678 \times 10^3 \end{bmatrix}, \quad L_2 = \begin{bmatrix} 8.2961 \times 10^{-11} \\ 3.0162 \times 10^{-12} \\ 1.2254 \times 10^4 \\ -1.4678 \times 10^3 \end{bmatrix} \\ L_3 = \begin{bmatrix} -8.2961 \times 10^{-11} \\ 3.0162 \times 10^{-12} \\ 1.2254 \times 10^4 \\ -1.4678 \times 10^3 \end{bmatrix}, \quad L_4 = \begin{bmatrix} -8.2961 \times 10^{-11} \\ -3.0162 \times 10^{-12} \\ 1.2254 \times 10^4 \\ -1.4678 \times 10^3 \end{bmatrix}$$

While those of the proposed method are given in the previous section.

The experiment was structured around the speed profile depicted in Figure 3, maintaining a consistent magnetic flux reference at 0.8(Wb). To rigorously assess the observer's resilience and the stability of the estimation error dynamics, specific initial conditions were chosen, represented by $x_0(t) = [-1 \ 2 \ 50]$ and $\hat{x}_0(t) = [0 \ 0 \ 0]$. This not only set a baseline for the experiment but also enabled a thorough evaluation of the observer's performance. A comprehensive analysis of the state estimation outcomes can be discerned from Figures 3 to 6 pertaining to the P3IO methodology. For a comparative perspective, Figure 7 delineates the estimation processes of the unknown input for the PIO approach. Meanwhile, a more detailed representation of the P3IO's unknown input estimation is captured in Figure 8.
Together, these figures offer an encompassing view and relative efficiencies of PIO and P3IO under the set conditions.

<figure><img src="image_4.png" /><figcaption>FIGURE 3. Rotor angular speed curve.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Direct axis stator current.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 5. Quadrature axis stator current.</figcaption></figure>

Examining Figures 3 to 5, which respectively depict speed, direct current, and quadratic current, it's clear that the observer provides an efficient state estimation despite differing initial conditions between the observer and the motor. Figure 6, illustrating the state estimation error, further

<figure><img src="image_7.png" /><figcaption>FIGURE 6. State estimation error.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 7. Unknown input of PIO.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>FIGURE 8. Unknown input of P3IO.</figcaption></figure>

supports this finding. The error is seen to converge to zero, a strong indicator of the observer's effectiveness in accurate state estimation, demonstrating its proficiency irrespective of the initial disparities.

The simulation results provide insightful comparisons between the two observers. These results clearly illustrate the superior performance of PMIO in estimating unknown inputs, particularly those with rapid variations. Figure 8 Unlike the PIO, which assumes unknown inputs to be constant and thus
<figure><img src="image_10.png" /><figcaption>FIGURE 9. Unknown input error comparison.</figcaption></figure>

<table><caption>TABLE 2. Unknown input estimation performance.</caption><thead><tr><th>Observer performance</th><th>Integral Square Error</th><th>Integral Absolute Error</th><th>Mean squared error</th></tr></thead><tbody><tr><td>PIO</td><td>2.1914</td><td>1.2916</td><td>0.8547</td></tr><tr><td>P3IO</td><td>1.8412</td><td>0.5970</td><td>0.7834</td></tr></tbody></table>

falters in its estimation accuracy for variable ones Figure 7. This improvement is further clarified by the results presented in Figure 9 and Table 2.

## VI. HARDWARE-IN-THE-LOOP VALIDATION

To assess the performance of the observer for SynRM, a comprehensive experimental approach was undertaken leveraging the hardware-in-the-loop (HIL) methodology. This method ensures the observer is assessed under conditions simulating real-world scenarios. The entire setup for this experiment was carefully assembled at the MSE Laboratory as showcased in Figure 10. Figure 11 illustrates the HIL test structure, highlighting the significance of the two dSPACE 1104 cards which operate at a sampling time of $T_s = 0.0001(s)$. The primary role of the first card is to emulate both the observer and the control circuit, guaranteeing that the observer's response and adjustments are analyzed in real-time. On the other hand, the second card's role was specialized for the SynRM emulation. Its responsibility was to replicate the behavior and characteristics of the SynRM under various conditions.

A comprehensive test is being conducted to evaluate the observer's ability in estimating states when subjected to a scenario of no load torque, implying the absence of the unknown input, in real-world applications. To ensure an unbiased and rigorous assessment, the speed profile and flux reference are kept consistent with those used in simulation tests. This intentional alignment not only provides a cohesive framework for comparison but also streamlines the analysis of results from both simulated and actual operational conditions. The primary goal of this evaluation is to ascertain the observer's practicality, resilience, and efficiency, offering crucial insights into its suitability for real-time applications.

<figure><img src="image_11.png" /><figcaption>FIGURE 10. Test bench for hardware-in-the-Loop validation.</figcaption></figure>

<table><caption>TABLE 3. State estimation performance.</caption><thead><tr><th>Observer performance</th><th>Integral Square Error</th><th>Integral Absolute Error</th><th>Mean squared error</th></tr></thead><tbody><tr><td>e<sub>isd</sub>(A)</td><td>0.0023</td><td>0.0458</td><td>0.0005</td></tr><tr><td>e<sub>isd</sub>(A)</td><td>0.0640</td><td>0.2676</td><td>0.0128</td></tr><tr><td>e<sub>ω</sub>(rad/s)</td><td>0.0675</td><td>0.2878</td><td>0.0135</td></tr></tbody></table>

The results depicted in Figures 12 through 15, along with those from Table 3, demonstrate the observer's successful estimation of SynRM states despite the disturbances in information transmission between the two platforms. Notably, the estimation error was minimal and within acceptable limits, underscoring the robustness and reliability of the observer under challenging real-time application conditions.

## A. COMPARATIVE RESULTS

### 1) CASE 1 (SLOW UNKNOWN INPUT VARIATION)

A comparative analysis was performed under conditions where the variation in the unknown input was slow. Figure 16 illustrates the actual unknown input and its corresponding estimations, while table 4 illustrates different performance criterion of the estimation error.

Under this circumstance, the disparity between both observers was found to be minimal, and both of them displayed competent performance, suggesting that they are both capable of handling unknown input with slower dynamics. The PIO, even though primarily tailored for estimating unknown inputs with null derivatives, seems to demonstrate flexibility in accommodating those with slow variations. The behavior of PIO implies a certain level of resilience when encountering slowly varying unknown inputs, essentially considering them almost like inputs with negligible derivatives. Table 4 provides quantitative insights into this behavior, where the differences in errors, although slight, are still observable.

The Integral Square Error (ISE), Integral Absolute Error (IAE), and Mean Squared Error (MSE) provide different perspectives on the performance. The PIO's slightly higher
<figure><img src="image_12.png" /><figcaption>FIGURE 11. Structure of hardware-in-the-loop validation.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 12. Rotor angular speed curve.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>FIGURE 13. Direct axis stator current.</figcaption></figure>

error values, compared to P3IO, imply that although it can handle slow variations, it is not as precise as the latter.

## 2) CASE 2 (FAST UNKNOWN INPUT VARIATION)

This case is specifically designed for scenarios where the unknown input variation is rapid. Figure 17 comprehensively

<figure><img src="image_15.png" /><figcaption>FIGURE 14. Quadrature axis stator current.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>FIGURE 15. State estimation error.</figcaption></figure>

displays both the actual unknown input and its corresponding estimates. The PIO's difficulty in accurately estimating rapidly changing unknown inputs becomes evident from the results. Its performance degradation is attributed to its inherent design limitations, which do not accommodate high variations. In contrast, the PMIO, with its design inherently built to handle such variations, showed a significant
<figure><img src="image_17.png" /><figcaption>FIGURE 16. Unknown input estimation (case 1).</figcaption></figure>

<table><caption>TABLE 4. Unknown input estimation performance (case 1).</caption><thead><tr><th>Observer performance</th><th>Integral Square Error</th><th>Integral Absolute Error</th><th>Mean squared error</th></tr></thead><tbody><tr><td>PIO</td><td>0.0431</td><td>0.4116</td><td>0.0054</td></tr><tr><td>P3IO</td><td>0.0186</td><td>0.2553</td><td>0.0023</td></tr></tbody></table>

<figure><img src="image_18.png" /><figcaption>FIGURE 17. Unknown input estimation (case 2).</figcaption></figure>

<table><caption>TABLE 5. Unknown input estimation performance (case 2).</caption><thead><tr><th>Observer performance</th><th>Integral Square Error</th><th>Integral Absolute Error</th><th>Mean squared error</th></tr></thead><tbody><tr><td>PIO</td><td>1.0349</td><td>2.3026</td><td>0.1078</td></tr><tr><td>P3IO</td><td>0.0873</td><td>0.6382</td><td>0.0095</td></tr></tbody></table>

advantage in terms of adaptability and performance. Under these conditions, the performance disparity between the two observers became considerably more noticeable.

The results presented in Table 5 further highlight this distinction. A detailed analysis of the PIO's estimation error performances under these conditions indicates that fast-varying unknown inputs amplify the estimation error, leading to pronounced deviations from the anticipated outcomes. In contrast, the PMIO demonstrates a notable resilience against such changes, consistently maintaining low errors.

## VII. CONCLUSION

This research paper underscores a significant contribution towards enhancing the estimation of unknown inputs applied to synchronous reluctance motors. This improvement has been diligently validated through both simulation models and hardware-in-the-loop experimentation. A new approach was introduced in the form of the PMIO, which exhibits marked improvements over the previously proposed PIO. The proficiency of the unknown input estimation was tested in two scenarios, namely slow and fast variations. While the performance of PMIO demonstrated its superiority in both instances, the key contribution was notably evident in the case of fast input variations.

Despite the successful implementation of the observer for estimating the unknown input, it has certain limitations that need to be addressed. The current model overlooks the effects of magnetic saturation, which introduces pronounced nonlinear characteristics in stator flux and inductances. Additionally, the model does not account for parameter variations. This oversight reduces the observer's accuracy in estimating both the system's states and the unknown inputs. This is because the observer's effectiveness hinges on the accuracy of the system's mathematical model; inaccuracies in modeling phenomena like saturation or parameter variations lead to a misrepresentation of the system's behavior. Moreover, while the proposed method enhances accuracy in estimating unknown inputs compared to the PIO, the PMIO is also constrained by its reliance on prior knowledge about the form of these inputs.

For future work, two primary areas should be addressed. The first involves enhancing the dynamical model of the SynRM by incorporating the impact of saturation and parameter variations. This enhancement will significantly improve the reliability and applicability of the HIL tests, as it will greatly refine the system's accuracy. The second objective is to advance the estimation of unknown inputs using more robust methodologies. In contrast to the PMIO, the decoupling approach seeks to obviate the need for prior knowledge about the form of unknown inputs, accommodating a wider range of signals. This approach aims to eliminate the impact of these inputs from the estimation error dynamics, thus nullifying their influence regardless of their form.

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<figure><img src="image_19.png" /></figure>

**WAIL HAMDI** was born in Biskra, Algeria, in 1997. He received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Biskra, Algeria, in 2018 and 2020, respectively, where he is currently pursuing the Ph.D. degree in electrical engineering. He is also a part of the LMSE Laboratory, University of Biskra. His research interests include control systems and the observer design for fuzzy nonlinear systems.
<figure><img src="image_20.png" /></figure>

**RAMZI SAADI** was born in Biskra, Algeria, in June 1987. He received the B.Sc., master's, and Ph.D. degrees in electrical engineering from the University of Biskra, in 2008, 2010, and 2015, respectively. Since 2015, he is currently an Associate Professor with the University of Biskra, where he is also a member of the MSE Laboratory. His research interests include renewable energies, fuel cells, energy management, electric vehicles, and dc/dc converters.

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**MOHAMED YACINE HAMMOUDI** was born in Biskra, Algeria, in October 1980. He received the Engineering, Magister Diploma, and Ph.D. degrees in electrical engineering from the University of Biskra, in 2003, 2006, and 2015, respectively. Since 2009, he has been an Assistant Professor with the University of Biskra, where he is also a member of the MSE Laboratory. His research interests include advanced control in power electronics systems and ac machines.

**RABIAA HOUILI** was born in Khenchela, Algeria, in March 1996. She received the B.Sc. and M.Sc. degrees in electrotechniques from the University of Mohamed Khider Biskra, Algeria, in 2018 and 2020, respectively. She is currently pursuing the Ph.D. degree with the University of Biskra, Algeria. Her research interest includes developing the power electronics systems used in hybrid-electric automobile applications.

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**MOHAMED BENBOUZID** (Fellow, IEEE) received the Ph.D. degree in electrical and computer engineering from the National Polytechnic Institute of Grenoble, Grenoble, France, in 1994, and the Habilitation à Diriger des Recherches degree from the University of Amiens, Amiens, France, in 2000. After receiving the Ph.D. degree, he joined the University of Amiens, where he was an Associate Professor of electrical and computer engineering. Since September 2004, he has been

with the University of Brest, Brest, France, where he is currently a Full Professor of electrical engineering. He is also a Distinguished Professor and a 1000 Talent Expert with Shanghai Maritime University, Shanghai, China. His main research interests and experience include control of electric machines, variable-speed drives for traction, propulsion, and renewable energy applications, and fault diagnosis of electric machines. He is a fellow of IET. He is the Editor-in-Chief of the *International Journal on Energy Conversion and the Applied Sciences* (MDPI) Section on Electrical, Electronics and Communications Engineering. He is a Subject Editor for the *IET Renewable Power Generation*.

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**YASSINE HIMEUR** (Senior Member, IEEE) received the M.Sc. and Ph.D. degrees in electrical engineering, in 2011 and 2015, respectively, and the Ph.D. and Habilitation (by Research) degrees, in July 2017, which granted him the official authorization to supervise research. His academic journey led him to join the University of Dubai after serving as a Postdoctoral Research Fellow with Qatar University, from 2019 to 2022. From 2013 to 2019, he was a Senior Researcher

with the Algerian Center for Development of Advanced Technologies

(CDTA), where he also served as the Head of the TELECOM Division, from 2018 to 2019. He is currently an Assistant Professor of engineering and information technology with the University of Dubai. Throughout his career, he has been actively involved in conducting research and development projects and has played a significant role in proposing and co-leading several research proposals under the NPRP grant (QNRF, Qatar). With more than 100 research publications in high-impact venues, he has made valuable contributions to the field. His current research interests include big data and the IoTs, AI/ML/DL, healthcare technologies, digital twins, metaverse, recommender systems, smart grids, building energy management, smart buildings, NLP, generative AI, and cybersecurity. He was honored to receive the Best Paper Award from the 11th IEEE SIGMAP in Austria, in 2014.

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**SAMI MINIAOUI** (Member, IEEE) received the Ph.D. degree in information systems from the University of Lausanne, Switzerland. He is currently an Associate Professor with the College of Engineering and Information Technology, University of Dubai. He has more than 15 years of teaching experience in several countries, such as France, Switzerland, and United Arab Emirates. He has published several research articles on the use of emergent technologies in re-engineering

business processes, such as RFID, wireless sensor networks, and NFC. He also focuses on artificial intelligence and its techniques, such as machine learning and deep learning, as well as technology adoption and diffusion. His main research interest includes smart city applications.

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**SHADI ATALLA** (Member, IEEE) is currently an Associate Professor and the Director of the Computing and Information Systems Program, University of Dubai. With more than 15 years of experience in teaching and research, he is a prominent data science evangelist and certified big data trainer, highly regarded in the industry. He has published several articles in international scientific journals and has contributed significantly to the field of data science. His research interests include

developing data science algorithms, curriculum development, and artificial intelligence. He serves as the Chair of the Computer Society of IEEE UAE, showcasing his leadership qualities and dedication to advancing the field.

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**WATHIQ MANSOOR** (Senior Member, IEEE) received the Ph.D. degree in computer engineering from Aston University, U.K. His Ph.D. study was on the design and implementation of multiprocessor systems and communications protocols for computer vision applications. He is currently a Professor with the University of Dubai. He has an excellent academic leadership experience in well-known universities worldwide. He has published

many research articles in the area of intelligent systems, image processing, deep learning, security, ubiquitous computing, web services, and neural networks. His current research interests include intelligent systems and security using neural networks with deep learning models for various applications. He has organized many international and national conferences and workshops. He has supervised many Ph.D. and bachelor's projects in the field of computer engineering and innovation in business, in addition to co-supervising many postgraduate students through research collaboration with international research groups.

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