Inter national J our nal of P o wer Electr onics and Dri v e System (IJPEDS) V ol. 17, No. 3, September 2026, pp. 1822 ∼ 1830 ISSN: 2088-8694, DOI: 10.11591/ijpeds.v17.i3.pp1822-1830 ❒ 1822 Comparati v e simulation of fractional-order PD sliding mode and fuzzy logic contr ollers f or a second-order discr ete-time nonlinear system Ahmed Bennaoui 1 , Salah Benzian 1 , Hamza Sulimani 2 , Aissa Ameur 3 1 Institute of Sciences, Uni v ersity Center Aou El Cherif Bouchoucha, Aou, Algeria 2 Department of Computer and Netw ork Engineering, Colle ge of Computing, Umm Al-Qura Uni v ersity , Makkah, Saudi Arabia 3 F aculty of T echnology , Uni v ersity of Amar T elidji, Laghouat, Algeria Article Inf o Article history: Recei v ed Oct 20, 2025 Re vised May 15, 2026 Accepted Jul 8, 2026 K eyw ords: Fractional-order control Fuzzy logic control Nonlinear systems Po wer electronics and dri v e systems Sliding mode control ABSTRA CT T ight output re gulation in po wer con v erters and electric dri v e systems requires a control strate gy that simul taneously minimizes tracking error and maintains smooth actuation—tw o objecti v es that are intrinsically in tension for nonlinear , pa rameter -v arying plants. Despite the widespread deplo yment of fractional-order PD sliding mode control (FOPD-SMC) and Mamdani fuzzy logic control (FLC) in this domain, no prior study has placed them in a direct, metric-identical comparison on a common plant. The present w ork closes this g ap by implementing both controllers on the same second-order discrete-time nonlinear pla nt—representati v e of DC-DC con v erter output dynamics and motor -dri v e input-output beha vi or and e v aluating them under a composite reference that combines sinusoidally-modulated ramps with step transitions, scored by the inte gral of squared error (ISE) and int e gral of absolute error (IAE). FOPD-SMC achie v es ISE = 1 . 63 9 × 10 − 2 and IAE = 3 . 345 × 10 − 2 , outperforming FLC by 87.6% and 50.4%, respecti v ely; the adv antage originates from the non-inte ger memory embedded in the sliding surf ace via the Gr ¨ unw ald–Letnik o v operator and from the e xplicit decomposition of the control la w into nominal-tracking and rob ustness components. FLC, con v ersely , produces a chattering-free, continuously v arying control signal a structural consequence of smooth Gaussian membership functions and linguistic rule aggre g ation, at the cost of a mean absolute tracking error twice that of FOPD-SMC. These ndings establish a quantitati v e selection criterion: FOPD-SMC is recommended when tight v oltage or current re gulation is the primary objecti v e, while FLC is preferred where smooth torque deli v ery and reduced actuator stress outweigh mar ginal g ains in tracking accurac y . This is an open access article under the CC BY -SA license . Corresponding A uthor: Ahmed Bennaoui Institute of Sciences, Uni v ersity Center Aou El Cherif Bouchoucha Aou 03001, Algeria Email: a.bennaoui@cu-aou.edu.dz 1. INTR ODUCTION The proliferation of grid-connected in v erters, DC–DC switched-mode po wer supplies, and v ariable-speed electric dri v es has placed increasingly stringent demands on closed-loop re gulation: tight v oltage and current control in con v erter stages, precise speed tracking with f ast disturbance rejection in dri v e J ournal homepage: http://ijpeds.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 1823 systems, and, in both cases, a control signal that does not induce e xcessi v e switching stress or mechanical wear . Meeting these objecti v es simultaneously is non-tri vial, because po wer electronic plants are inherently nonlinear -switching phenomena, magnetic saturation, and duty-c ycle-dependent operating points generate beha viors that linear time-in v ariant models cannot reproduce—and because precision and smoothness are intrinsically competing requirements: a more aggressi v e la w reduces tracking error while typically e xciting higher -frequenc y actuation [1], [2]. Fix ed-g ain proport ional-inte gral-deri v ati v e (PID) re gulators, despite their industrial pre v alence, are especially sensiti v e to this tension: t h e ir parameters are tuned at a nominal operating point and de grade under nonlinear e xcursions or parameter drift [3], making adv anced model-e xible strate gies necessary for demanding con v erter and dri v e applications. T w o paradigms ha v e attracted sustained research attention in this conte xt. Sliding mode control (SMC) achie v es rob ust disturbance rejection by conning the system trajectory to a designer -chosen manifold; be yond that manifold, matched perturbations are structurally decoupled from the closed-loop output [1], [2]. Finite-time con v er gence e xtensions-T erminal SMC [4], nonsingular f ast TSMC [5], and global terminal SMC [6]-tighten this guarantee from asymptotic to nite-time. Incorporating fractional-order calculus [7] into the sliding surf ace has pro v ed a particularly producti v e direction: Pisano et al. [8] formulated a rigorous sliding-mode re gulator for fractional-order dynamics; Matignon [9] established the underlying stability theory; and Y in et al. [10], Xue et al. [11], and Monje et al. [12] demonstrated that replacing the classical inte ger -order deri v ati v e with a non-inte ger memory operator yields measura bly better tracking. This fractional-order PD sliding mode control (FOPD-SMC) approach has since bee n e xtended to po wer electronics, where W ang et al. [13] and Bennaoui et al. [14] reported impro v ed re gulation on boost and dual-acti v e-bridge con v erters. Fuzzy logic control (FLC), introduced by Zadeh [15] and Mamdani [16] and later systematized by Lee [17], Jang [18], Ross [19], P assino and Y urk o vich [20], and Feng [21], of fers a structurally dif ferent approach: by encoding e xpert kno wledge as linguistic if–then rules rather than an analytical plant m od e l, it inherently smooths the control action across the entire operating range. This adv antage has been conrmed across di v erse application domains, including h ybrid po wer systems [22], induction motor dri v es [23], po wer system stabilizers [24], and doubly-fed induction generator protection [25]. Building on these directions, T iw ary et al. [26] proposed a super -twisting sliding-mode re gulator for dual-acti v e-bridge con v erters, Abdelrahem et al. [27] applied a predicti v e sliding-mode scheme to wind-turbine generators, and Zhao and Guo [28] de v eloped PID design guidelines for nonlinear systems. Despite the breadth of this body of w ork, a critical question remains unanswered: when FOPD-SMC and FLC are tested on the same plant and dri v en by the same reference, ho w lar ge is the quantitati v e trade-of f between their tracking precision and their actuator smoothness ? Existing studies in v ariably e v aluate each paradigm in isolation on application-specic hardw are, so an y cross-paradigm inference is confounded by dif ferences in plant topology , operating conditions, and e v aluation criteria. Practitioners designing a v oltage re gulator or dri v e controller therefore lack a numerically grounded reference from which to read of f the accurac y cost of choosing FLC o v er FOPD-SMC, or the smoothness penalty of the re v erse selection. T o address this g ap, the present w ork mak es three contrib utions: i) Both controllers are implemented on the same second-order discrete-time nonlinear plant whose ARX structure emulates the input–output dynamics of DC–DC con v erter lters and electric motor dri v es; ii) Both are e v aluated under a composite reference combining sinusoidally-modulated ramps with step transitions—spanning the speed-ramp and load-step proles of real dri v e operation—and scored with identical ISE and IAE metric s; and iii) The measured precision-v ersus-smoothness trade-of f is translated into quantitati v e, e vidence-bas ed selection guidelines applicable to v oltage re gulators, DC–DC con v erters, and v ariable-speed dri v e systems. 2. METHOD 2.1. Resear ch design The study is a controlled simulation e xperiment that isolates each control la w by holding e v ery other v ariable x ed. The w orko w is: i) Dene a second-order discrete-time nonlinear plant representati v e of con v erter/dri v e dynamics; ii) Design FOPD-SMC and FLC with documented parameters and stability properties; iii) Dri v e both closed loops with an identical composite reference; and i v) Ev aluate tracking accurac y and control smoothness via ISE and IAE. All simulations were performed in Python 3.10 with NumPy and scikit-fuzzy . Compar ative simulation of fr actional-or der PD sliding mode and fuzzy lo gic contr oller s ... (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
1824 ❒ ISSN: 2088-8694 2.2. Plant model The controlled plant is a second-order discrete-time system described by (1). y [ i ] = 0 . 7 y [ i − 1] + 0 . 3 u [ i − 1] + 0 . 05 u [ i − 2] (1) This second-order autore gressi v e with eXogenous inputs (ARX) structure captures tw o k e y dynamic characteristics common to po wer electronic and dri v e system plants: i) The autore gressi v e coef cient 0 . 7 on y [ i − 1] represents the dominant ener gy-storage pole dynamics typical of a direct current (DC)–DC con v erter output lter (LC netw ork) or a motor winding with a signicant electrical time constant; and ii) The tw o input terms 0 . 3 u [ i − 1] + 0 . 05 u [ i − 2] model a delayed, distrib uted input-to-output response analogous to the combined ef fects of pulse width modulation (PWM) switching delays and electromagnetic inertia in electric dri v e systems [1], [11]. The presence of a second-order delayed-input term renders the control design non-tri vial, as an y controller must account for the additional phase lag introduced by u [ i − 2] . This benchmark structure follo ws t he approach of prior comparati v e controller e v aluation studies [10], [13] and pro vides a common, reproducible basis for assessing control la w performance independent of hardw are-specic con v erter topologies. The composite reference signal used in all closed-loop e xperiments consists of sinusoidally-modulated triangular ramps concatenated with a { 0 , 5 , 0 } square-w a v e se gment, emulating the speed-ramp proles and load-step disturbances encountered in real dri v e operation. 2.3. Fractional-order PD sliding mode contr oller The FOPD-SMC replaces the classical inte ger -order error deri v ati v e in the sliding surf ace with a Gr ¨ unw ald–Letnik o v (GL) operator of non-inte ger order α , injecting a weighted his tory of past error v alues into the surf ace computation and thereby enriching the controller’ s anticipatory capability [10], [11], [13]. The tracking error is (2). e [ i ] = y [ i ] − r [ i + 1] (2) The fractional-order sliding surf ace is as (3). s [ i ] = e [ i ] + λD α e [ i ] (3) Where λ = 2 . 0 and α = 0 . 5 . The GL recursion truncates the innite binomial series at M past samples, producing the causal nite-memory approximation used at each step i . D α e [ i ] ≈ 1 h α M j =0 ( − 1) j α j e [ i − j ] (4) The control la w includes equi v alent control: u eq [ i ] = − p q (5) where: p = (1 + λ ) a + λF i +1 , a = 0 . 7 y [ i ] + 0 . 05 u [ i − 1] − r [ i + 2] (6) q = (1 + λ )0 . 3 (7) F i +1 = min( M ,i +1) k =1 ( − 1) k α k e [ i + 1 − k ] , M = 20 (8) and switching control (9). u sw [ i ] = − k sw sign( s [ i ]) , k sw = 0 . 1 (9) The total control signal is (10). u [ i ] = u eq [ i ] + u sw [ i ] (10) Int J Po w Elec & Dri Syst, V ol. 17, No. 3, September 2026: 1822–1830 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 1825 Closed-loop stability is v eried through the quadratic L yapuno v candidate (11). V [ i ] = 1 2 s [ i ] 2 (11) The equi v alent term u eq is deri v ed to annihilate the plant dynamics and set s [ i + 1] = 0 on the nominal trajectory; the discontinuous term u sw then enforces ∆ V [ i ] < 0 for all s [ i ] ̸ = 0 , so the surf ace is globally attracti v e. The v alue k sw = 0 . 1 w as selected to bound the w orst-case residual perturbation while holding the discontinuous amplitude—and the resulting chattering—within acceptable limits [1], [2]. 2.4. Fuzzy logic contr oller The FLC adopts the Mamdani incremental architecture [16], [17]: the instantaneous tracking error e [ i ] = y [ i ] − r [ i + 1] and its one-step dif ference ∆ e [ i ] = e [ i ] − e [ i − 1] serv e as linguistic inputs, while ∆ u [ i ] is the inferred output increment. Each input is encoded by three Gaussian membership f u nc tions as sho w in Figures 1(a) and 1(b) and the output by v e triangular labels as sho ws in Figure 1(c). The nine-rule base as sho wn in T able 1 embeds the heuristic that lar ger errors or f aster error gro wth should trigger proportionally lar ger correcti v e increments. The crisp control signal is reconstructed as (12). u [ i ] = u [ i − 1] + Gain · ∆ u [ i ] , Gain = 1 . 8 . (12) Membership widths ( σ = 6 on [ − 10 , 10] for inputs; triangular partitions on [ − 15 , 15] for the output) distrib ute the linguistic co v erage e v enly across the e xpected operating range. Rule ring strengths are aggre g ated by min-max composition [16], [19], [20] and the crisp increment is reco v ered by centre-of-gra vity defuzzication. This inte grating structure-accumulated control rather than di rect output-is a standard strate gy in FLC-based dri v e and po wer -system compensation [22], [23], [25]. (a) (b) (c) Figure 1. Membership functions of the Mamdani FLC: (a) error , (b) error deri v ati v e, and (c) change in control signal Compar ative simulation of fr actional-or der PD sliding mode and fuzzy lo gic contr oller s ... (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
1826 ❒ ISSN: 2088-8694 T able 1. FLC rule base e \ ∆ e Ne g ati v e Zero Positi v e Ne g ati v e GP P Z Zero P Z N Positi v e Z N GN Notes: GP: great positi v e, P: positi v e, Z: zero N: ne g ati v e, GN: great ne g ati v e 2.5. Implementation and softwar e tools Both controllers were implemented in Python 3.10 using NumPy and scikit-fuzzy , in strictly separate closed loops sharing only the plant and reference. At each step i , the FOPD-SMC e v aluates the Gr ¨ unw ald–Letnik o v deri v ati v e (4) (memory depth M = 20 ), computes the sliding surf ace (3), and applies the total control la w (10). FLC fuzzies e [ i ] and ∆ e [ i ] , e v aluates the nine rules via Mamdani min–max inference, and applies the defuzzied increment through (12). ISE and IAE are computed from i = 2 onw ard to e xclude initialization transients. This study in v olv es only numerical simulation and requires no ethical appro v als. 3. RESUL TS AND DISCUSSION 3.1. Simulation conditions Both controllers were simulated on plant (1) for N = 600 samples ( T s = 1 , zero initial conditions) and dri v en by the same composite reference (sinusoidally-modulated ramp follo wed by a { 0 , 5 , 0 } square-w a v e se gment). T racking performance w as quantied by (13). ISE = 1 N − 2 N − 1 i =2 e [ i ] 2 , IAE = 1 N − 2 N − 1 i =2 | e [ i ] | (13) Where ISE assigns quadratic weight to transient e xcursions and IAE measures the mean absolute de viation o v er the full simulation horizon. 3.2. Pr esentation of r esults T able 2 reports quantitati v e performance under identical conditions. FOPD-SMC achie v es an ISE of 1 . 639 × 10 − 2 and an IAE of 3 . 345 × 10 − 2 , while FLC yields an ISE of 1 . 323 × 10 − 1 and an IAE of 6 . 742 × 10 − 2 . Figure 2 presents on same time axis, Figure 2(a) sho w reference and both outputs, Figure 2(b) sho w tracking errors, and Figure 2(c) sho w control signals. Figure 3 sho ws FOPD-SMC sliding surf ace s [ i ] . 3.3. Analysis and inter pr etation The measured reductions of 87.6% in ISE and 50.4% in IAE establish a consistent and reproducible tracking adv antage for FOPD-SMC o v er FLC. T ranslating the IAE v alues into per -sample terms: FOPD-SMC a v erages an absolute de viation of ≈ 0 . 033 per sample ag ainst ≈ 0 . 067 for FLC, so FLC’ s typical pointwise error is double that of its fractional-order counterpart across the entire 600-sample run. The ISE ratio of 8 . 07 signals that FLC generates pronounced transient o v ershoots at reference step transitions—spik es that the quadratic metric amplies disproportionately—as conrmed by the delayed output response visible in Figure 2(a), where FLC peak de viations reach 3–4 times the FOPD-SMC le v el during abrupt changes. T w o structural propert ies account for FOPD-SMC’ s superior performance. First, setting α = 0 . 5 in (3) gi v es s [ i ] access to a decaying-weight history of past errors: the GL operator assigns lar ger coef cients to recent samples and progressi v ely smal ler ones to older samples, so the surf ace responds to error trends that a purely instantaneous deri v ati v e w ould miss. Second, the control signal is constructed in tw o functionally separate part s— u eq handles the nominal plant trajectory while u sw pro vides a hard rob ustness mar gin ag ainst model residuals—so the tw o requirements ne v er compete. Figure 3 pro vides direct e vidence of this design: s [ i ] f alls sharply to zero within the rst fe w dozen samples and subsequently remains conned to a narro w corridor , conrming that the controller reaches and sustains sliding-mode operation throughout the full run. The precision g ain carries a visible cost i n Figure 2(b): the hard relay nonlinearity sign( · ) in u sw forces rapid amplitude transitions around the sliding manifold, e xciting unmodeled high-frequenc y plant dynamics and producing the characteristic oscillatory artif act that must be addressed in hardw are realizations through boundary-layer replacement or higher -order SMC schemes [1], [2]. FLC, by contrast, maps its inputs through smooth Gaussian functions and aggre g ates nine rules by min-max composition, so the control increment v aries Int J Po w Elec & Dri Syst, V ol. 17, No. 3, September 2026: 1822–1830 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 ❒ 1827 continuously with the error state; this structural smoothness eliminates rapid switching at the cost of the 3–4 × lar ger peak de viations observ ed in Figure 2(b) during abrupt reference changes. These observ ations mak e the precision-v ersus-smoothness trade-of f directly measurable on a common benchmark rather than inferred across heterogeneous application studies. T able 2. Performance comparison Controller ISE IAE FOPD-SMC 1 . 639 × 10 − 2 3 . 345 × 10 − 2 FLC 1 . 323 × 10 − 1 6 . 742 × 10 − 2 Figure 2. FOPD-SMC v ersus FLC on a common time axis: (a) reference and closed-loop outputs, (b) tracking errors, and (c) control signals Figure 3. FOPD-SMC sliding surf ace s [ i ] , conrming that the sliding mode is reached and maintained throughout the simulation horizon Compar ative simulation of fr actional-or der PD sliding mode and fuzzy lo gic contr oller s ... (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
1828 ❒ ISSN: 2088-8694 4. CONCLUSION This paper presented a controlled, cross-paradigm benchmarking of FOPD-SMC and Mamdani FLC on a common second-order discrete-time nonlinear plant under identical reference, initial conditions, and performance metrics. By remo ving the application-specic confounds present in prior studies—which typically e v aluate a single controller on one particular con v erter or dri v e topology—the e xperiment yields the rst directly comparable ISE/IAE measurements for these tw o control f amilies under a common e v aluation protocol. FOPD-SMC outperforms FLC with ISE = 1 . 639 × 10 − 2 and IAE = 3 . 345 × 10 − 2 , corresponding to reductions of 87.6% and 50.4%, respecti v ely , o v er FLC (ISE = 1 . 323 × 10 − 1 , IAE = 6 . 742 × 10 − 2 ). The performance adv antage stems from tw o cooperati ng mechanisms: the Gr ¨ unw ald–Letnik o v fractional-order deri v ati v e embedded in the sliding surf ace introduces an error -history memory that anticipates reference changes ea rlier than inte ger -order designs, while e xplicit decomposition of the control la w int o equi v alent and switching components ensures simultaneous nominal tracking and rob ustness to plant uncertainty . FLC, although 8.07 × less precise in ISE, inherently suppresses chattering through smooth rule-based inference, rendering it the preferred option in applications where actuator smoothness and reduced mechanical wear are paramount. The study is subject to t h r ee main limitations: only a single second-order plant structure is e v aluated; measurement noise, actuator saturation, and parametric uncertainty are not modeled; and the computational b urden of the Gr ¨ unw ald–Letnik o v recursion relati v e to FLC infer ence is not formally proled. Future w ork will e xtend the benchmark to e xperimental v alidation on a DC–DC con v erter and a motor -dri v e testbed, in v estig ate a h ybrid architecture in which FLC adapti v ely tunes the FOPD-SMC parameters ( λ , k sw ) in real time to combine high precision with chattering-free actuation, and assess performance on higher -order plants and multi-input multi-output dri v e congurations. A CKNO WLEDGEMENTS The authors e xtend their appreciation to Umm Al-Qura Uni v ersity , Saudi Arabia for funding this research w ork through grant number: 26UQ U4320283GSSR02. FUNDING INFORMA TION Funded by Umm Al-Qura Uni v ersity , Saudi Arabia, grant number: 26UQ U4320283GSSR02. A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the Contrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib utions, reduce authorship disputes, and f acilitate collaboration. Name of A uthor C M So V a F o I R D O E V i Su P Fu Ahmed Bennaoui ✓ ✓ ✓ ✓ ✓ ✓ Salah Benzian ✓ ✓ ✓ Hamza Sulimani ✓ ✓ ✓ ✓ Aissa Ameur ✓ ✓ ✓ C : C onceptualization I : I n v estig ation V i : V i sualization M : M ethodology R : R esources Su : Su pervision So : So ftw are D : D ata Curation P : P roject Administrati on V a : V a lidation O : Writing - O riginal Draft Fu : Fu nding Acquisition F o : F o rmal Analysis E : Writing - Re vie w & E diting CONFLICT OF INTEREST ST A TEMENT The authors declare no conict of interest. Int J Po w Elec & Dri Syst, V ol. 17, No. 3, September 2026: 1822–1830 Evaluation Warning : The document was created with Spire.PDF for Python.
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1830 ❒ ISSN: 2088-8694 BIOGRAPHIES OF A UTHORS Ahmed Bennaoui recei v ed hi s B.Sc. i n electronics engineering from the Uni v ersity of Mohamed Boudiaf (M’ sila, 2011), M .Sc. de grees in electrical engineering (adv anced automation) from the Uni v ersity of Ziane Achour (Djelf a, 2012 and 2016), and a Ph.D. in electrical engineering (intelligent control and automation, 2024) from the Uni v ersity of Amar T elidji (Laghouat), Algeria. He is currently with the Institute of Sciences, Uni v ersity Center Aou El Cherif Bouchoucha. His re search interests inc lude nonlinear dynamics, fuzzy logic control, po wer system control, and optimization techniques. In this study , he led the design and simulation of the FOPD-SMC and the analysis of control strate gies for nonlinear systems. He can be contacted at email: a.bennaoui@cu-aou.edu.dz. Salah Benzian recei v ed his B.Sc. from the Uni v ersity of M’hamed Boug ara, Boumerdes, Algeria, his M.Sc. from the Uni v ersity of Ziane Achour , Djelf a, Algeria, and his Ph.D. from the Uni v ersity of Amar T elidji, Laghouat, Algeria. He is currently with the Institute of Sciences, Uni v ersity Center Aou El Cherif Bouchoucha, Aou, Algeria. His research interests include fuzzy control, po wer systems, and optimization. In this study , he contrib uted to the controller design, the analysis of simulation results, and the preparation of the manuscript. He can be contacted at email: s.benzian@cu-aou.edu.dz. Hamza Sulimani is an assistant professor in the Department of Computer and Netw ork Engineering, Colle ge of Computing, Umm Al-Qura Uni v ersity , Makkah, Saudi Arabia. He recei v ed his B.S. de gree in electrical and computer Engineering from Umm Al-Qura Uni v ersity (2000), his M.S. de gree in electric al and computer engineering from King Abdulaziz Uni v ersity (2010), and his Ph.D. de gree in inf ormation technology from the Uni v ersity of T echnology Sydne y (UTS ), Australia (2024). His current research interests include computer netw ork architectures, c ybersecurity , fog computing for IoT protection, and machine learning applications in netw ork traf c analysis. He can be contacted at email: hhhsulimani@uqu.edu.sa. Aissa Ameur recei v ed his master’ s and Ph.D. de grees in electrical engineering from Batna Uni v ersity , Algeria, in 2005 and 2012, respecti v ely . Since 2005, he has been with the F aculty of T echnology , Uni v ersity of Amar T elidji (Laghouat), where he is an assistant professor and a researcher at the LeDMaScD laboratory . His research interests include modeling of electrical machines, e lectrical dri v e control, f ault di agnosis, articial intelligence, and rene w able ener gy systems. In this study , he de v eloped the FLC, conducted the result analysis, and contrib uted to the manuscript preparation. He can be contacted at email: a.ameur@lagh-uni v .dz. Int J Po w Elec & Dri Syst, V ol. 17, No. 3, September 2026: 1822–1830 Evaluation Warning : The document was created with Spire.PDF for Python.