Indonesian J our nal of Electrical Engineering and Computer Science V ol. 41, No. 1, January 2026, pp. 90 ∼ 98 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v41.i1.pp90-98 ❒ 90 Comparati v e analysis of fractional-order sliding mode and pole placement contr ol f or r obotic manipulator Ahmed Bennaoui 1 , Salah Benzian 2 , Idr ees Nasser Alsolbi 3 , Aissa Ameur 1 1 Institute of Sciences, Uni v ersity Center Aou El Cherif Bouchoucha, Aou, Algeria 2 Department of Data Science, 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 19, 2025 Re vised No v 4, 2025 Accepted Dec 13, 2025 K eyw ords: Control ef fort Fractional-order sliding mode control Lagrangian mechanics Pole placement control Robotic manipulator Rob ustness T rajectory tracking ABSTRA CT Fractional-order sliding mode control (FOSMC) is benchmark ed ag ainst pole placement control (PPC) on a nonlinear tw o-link manipulator subjected to iden- tical trajectories and 10 N·m square disturbances. Quantitati v e head-to-head e vidence ag ainst industrial PPC is scarce, lea ving engineers uncertain when fractional designs justify their added comple xity . W e deri v e the plant via La- grange dynamics, implement both controllers in Python, and e v aluate tracking and torque ef fort using SciPy-based simulations. Under the adopted fractional deri v ati v e approximation, FOSMC attains RMSEs of 0.458 rad ( q 1 ) and 0.453 rad ( q 2 ) whereas PPC limits the errors to 0.365 rad and 0.337 rad. The frac- tional design, ho we v er , requires lo wer mean torques of 69.2/29.0 N·m compared to PPC’ s 86.1/41.4 N·m, e xposing a precision–ener gy trade-of f that no w f a v ours PPC on accurac y and FOSMC on actuation ef fort. The benchmark deli v ers de- plo yable e vidence that fractional sliding surf aces shift torque demand e v en when their tracking performance lags, and it moti v at es hardw are-in-the-loop v alida- tion to close the identied accurac y g ap. 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@lagh-uni v .dz 1. INTR ODUCTION Seminal assessments of manipulator dynamics underscore the enduring importance of rob ust robot control [1]. Robotic manipulators support precision manuf acturing, sur gery , and autonomous systems, yet their coupled nonlinear dynamics complicate linear feedback design [2], [3]. Classical controllers such as PID and pole placement control (PPC) are attracti v e for their simplicity , b ut their performance de grades in the presence of parameter v ariations, disturbances, and joint constraints, while high-g ain nonlinear alternati v es risk actuator stress and chattering [4]. Computed-torque and adapti v e baselines remain standard references for robot control tuning [3]. Re- cent surv e ys on sliding-mode and fractional-order design catalogue delay , estimation, and rob ustness challenges that underline the need for reproducible benchmarks [5]. Classical sliding-mode theory and its modern renements remain the backbone for rob ust robot con- trol design [6]-[8]. Broad robotics primers lik e wise codify the modeling assumptions and feedback architec- tures adopted here [9], [10]. On the fractional side, foundational te xts and frequenc y-domain approximations continue to moti v ate non-inte ger controllers for manipulators [11]-[15]. J ournal homepage: http://ijeecs.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 ❒ 91 Fractional-order control introduces non-inte ger calculus into the feedback path, enabling sm oother sliding dynamics without sacricing disturbance rejection [16]-[25]. Recent fractional sliding-mode designs report strong rob ustness g ains, yet surv e ys note that matched-condition benchmarks ag ainst industrial PPC are rarely documented, lea ving a practical guidance g ap for engineer s [5]. W ithout quantitati v e e vidence that isolates accurac y , torque ef fort, and settling beha viour under the same plant, practitioners cannot decide when fractional designs justify their added implementation comple xity . T o close this g ap, we deri v e a tw o-de gree-of-freedom (2-DOF) manipulator via Lagrange dynam ics, implement FOSMC and PPC in a single Python w orko w , and challenge both controllers with sinusoidal references plus a 10 N·m square disturbance between t = 2 s and t = 3 s. Performance is e v aluated using root mean square error (RMSE), mean torque, and transient sett ling metrics that align with industrial specications. The main contrib utions of this paper are summarized as follo ws: – A fully reproducible Python w orko w (supplementary le S1) that implements both controllers with matched dynamics, disturbance windo w , solv er tolerances, and post-processing; – A quantitati v e comparison between FOSMC and PPC under identical operating conditions using Python simulations, yielding the RMSE and mean-torque metrics cited throughout the manuscript; – A claried accurac y–torque trade-of f analysis that e xplains when PPC’ s precision outweighs FOSMC’ s ac- tuation sa vings for sur gical robotics, industrial automation, and collaborati v e systems. Recent FOSMC studies concentrate on fractional sliding-surf ace design, adapti v e observ ers, and x ed-time parameter tuning, yet the y seldom pro vide a reproducible, side-by-side benchmark ag ainst the pole- placement controllers still pre v alent in industrial deplo yments [17]-[20]. Rather than proposing another deri v a- ti v e of the fractional surf ace, this w ork positions itself as the missing empirical bridge between fractional and industrial controllers by i) rigorously matching plant model, disturbance windo w , reference trajectories, and numerical t olerances across FOSMC and PPC; ii) quantifying the accurac y–ener gy trade-of f with identi- cal RMSE, torque, and settling metrics; and iii) releasing an open Python w orko w (supplementary le S1) that future studies can e xtend to w ard h ybrid or learning-enhanced control schemes . This framing aligns the manuscript with current trends that emphasise deplo yable benchmarks and transparent rob ustness–ener gy re- porting, thereby clarifying the no v elty relati v e to te xtbook deri v ations. 2. PR OPOSED METHOD This section details the modeling foundation and controller formulations that constitute the proposed benchmarking w orko w . The 2-DOF manipulator’ s dynamics, deri v ed using Lagrangian mechanics, are e x- pressed as: M ( q ) ¨ q + C ( q , ˙ q ) ˙ q + G ( q ) = τ + d ( t ) (1) Where q = [ q 1 , q 2 ] T is the joint angle v ector , M ( q ) is the inertia matrix, C ( q , ˙ q ) is the Coriolis/centripetal matrix, G ( q ) is the gra vity v ector , τ is the control torque, and d ( t ) is the disturbance. The manipulator has links of length L 1 = L 2 = 1 m, mass M 1 = M 2 = 1 kg, and gra vit y g = 9 . 8 m/s 2 . Desired trajectories are q d 1 = sin(4 . 17 t ) , q d 2 = 1 . 2 sin(5 . 11 t ) , with a disturbance d ( t ) = [10 , 10] T N.m (t=2–3 s). This canon- ical representation follo ws established nonlinear manipulator modeling and L yapuno v-based stability analysis practices [21]. 2.1. Dynamic model The inertia matrix M , Coriolis/centripetal v ector C , and gra vity v ector G are dened as: m 11 = ( M 1 + M 2 ) L 2 1 + M 2 L 2 2 + 2 M 2 L 1 L 2 cos( q 2 ) , m 12 = m 21 = M 2 L 2 2 + M 2 L 1 L 2 cos( q 2 ) , m 22 = M 2 L 2 2 , c 1 = − M 2 L 1 L 2 sin( q 2 )(2 ˙ q 1 ˙ q 2 + ˙ q 2 2 ) , c 2 = M 2 L 1 L 2 sin( q 2 ) ˙ q 2 1 , g 1 = − ( M 1 + M 2 ) g L 1 sin( q 1 ) − M 2 g L 2 sin( q 1 + q 2 ) , g 2 = − M 2 g L 2 sin( q 1 + q 2 ) . Compar ative analysis of fr actional-or der sliding mode and pole placement contr ol (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
92 ❒ ISSN: 2502-4752 These s ine-based gra vity torques mirror the e xpressions embedded in supplementary le S1, k eeping the ana- lytical description and e x ecutable w orko w synchronized. 2.2. FOSMC design FOSMC uses a sliding surf ace: s i = ˙ e i + α D 1 . 5 e i + γ e β i , i = 1 , 2 (2) where e i = q i − q di , and the fractional deri v ati v e D 1 . 5 e i ≈ 5 e i [17], [19]. The control la w is: τ = M ( ¨ q d − f − FF − K s S + DD ) + C ˙ q + G (3) with f = M − 1 ( − C ˙ q − G ) , FF = [ α µD 0 . 5 e 1 , α µD 0 . 5 e 2 ] T , DD = [ − β γ ˙ e 1 e β − 1 1 , − β γ ˙ e 2 e β − 1 2 ] T , K s = 10 , α = 4 , γ = 9 , β = 3 , µ = 1 . 5 . 2.3. PPC design PPC uses computed torque control: τ = Mu ppc + C ˙ q + G (4) where u ppc = ¨ q d − K d ˙ e − K p e , with K p = diag (300 , 300) , K d = diag (20 , 20) [22], [25]. 3. METHOD The dynamics and controllers for the 2-DOF robotic manipulator were implemented in Python 3.8, and the complet e runnable script is no w hosted in Supplementary Listing S1 ( supplementary code.tex ). That document compiles the imports, TwoDOFRobot class, simulation dri v er , plotting routines, and animation pipeline that underpin the w orko w summarized here. Simulations were conducted using scipy.integrate. solve ivp (SciPy 1.7.3) with the RK45 solv er , a maximum time ste p of 0.01 s, and relati v e and abso- lute tolerances of 10 − 6 [23]. The simulation spanned 5 seconds with initial conditions [ q 1 , q 2 , ˙ q 1 , ˙ q 2 ] = [ − π , π , 0 , 0] rad, rad/s. A square w a v e disturbance of 10 N.m w as applied to both joints from t = 2 s to t = 3 s to e v aluate rob ustness [24]. Simulation data w as interpolated onto a 500-point uniform grid using scipy.interpolate.interp1d for consistent analysis. T able 1 consolidates the numerical and con- troller parameters together with their selection rationale, while the subsequent paragraphs detail the numerical v alidation w orko w . T able 1. Controller and numerical parameters with associated rationale P arameter V alue Role Justication α 4 FOSMC deri v ati v e g ain Maintains steep sliding slope without amplifying sensor noise. γ 9 FOSMC nonlinear g ain Pro vides 15% o v ershoot mar gin during the 10 N·m disturbance. β 3 Sliding polynomial order Supplies cubic stif fness that remo v es steady bias. µ 1.5 Fr actional feedforw ard scaling Matches attenuation predicted in [17]. K s 10 Sl iding surf ace g ain Guarantees < 1 s con v er gence per [20]. glfdif f g ain 5 Fractional placeholder Approximates Gr ¨ unw ald–Letnik o v beha viour while limiting chattering. K p diag(300,300) PPC proportional g ain Places poles at ω n ≈ 17 rad/s [25]. K d diag(20,20) PPC damping g ain Produces damping ratio ζ ≈ 0 . 8 . r tol , a tol 10 − 6 , 10 − 8 RK45 tolerances K eep numerical error < 10 − 4 rad vs tighter runs. ∆ t max 0.01 s Max solv er step Resolv es the 5 Hz reference without aliasing. Disturbance 10 N·m (2–3 s) Rob ustness stress test Replicates the payload sur ge in [24]. Initial state [ − π , π , 0 , 0] Start condition Excites both joints with opposing deections. Grid size 500 samples Post-processing Aligns RMSE/torque metrics on a shared time base. Numerical v alidation proceeded in three stages. First, the RK45 solv er w as re-run with r tol = 10 − 7 and a tol = 10 − 9 ; de viations from the nominal trajectories remained belo w 4 × 10 − 5 rad and 6 × 10 − 3 N·m, conrming tolerance suf cienc y . Second, disturbance-free simulations ( t < 2 s) were compared ag ainst a symbolic linearized model to v erify that the PPC g ains produced the tar geted ζ = 0 . 8 and ω n = 17 rad/s poles. Indonesian J Elec Eng & Comp Sci, V ol. 41, No. 1, January 2026: 90–98 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 ❒ 93 Third, the 500-point interpolated grid w as cross-check ed ag ainst the nati v e solv er timestamps, and the resulting RMSE changed by fe wer than 0.5%, v alidating the resampling pipeline. The initial condition v ector [ − π , π , 0 , 0] places the links at opposing e xtremes with zero v elocity so both controllers must o v ercome coupled inertia before the dist urbance. A 1 s w arm-up interv al allo ws the references to synchronize prior to the 10 N·m pulse between 2–3 s, which stresses rob ustness and chatter - ing mitig ation. All state, torque, and reference arrays are logged before interpolation, enabling reproducible recomputation of RMSE and mean torque as dened belo w . Performance w as a ssessed using RMSE for tracking accurac y and mean absolute torque for control ef fort, dened as: RMSE i = v u u t 1 N N X k =1 ( q i ( t k ) − q di ( t k )) 2 , i = 1 , 2 (5) Mean T orque i = 1 N N X k =1 | τ i ( t k ) | , i = 1 , 2 (6) where q i ( t k ) and q di ( t k ) are the a ctual and desired joint angles at time t k , τ i ( t k ) is the control torque, and N = 500 is the number of time steps [3]. Controller parameters were tuned empirically: FOSMC parameters ( α = 4 , γ = 9 , β = 3 , µ = 1 . 5 , K s = 10 ) were selected to balance rob ustness and chattering reduction [19], while PPC g ains ( K p = diag (300 , 300) , K d = diag (20 , 20) ) were chosen to ensure stable pole placement [25]. The simulation setup w as v alidated ag ainst established robotic control benchmarks [2], [4]. Ex ecuting python main.py from the project root replays the w orko w end-to-end: it runs both controllers with the 10 N·m disturbance injected between 2–3 s, interpolates the trajectories onto the 500-point grid, sa v es Figure 1 structure of a 2-DOF robot manipulator and Figures 2–5 plus the animation, and prints the RMSE and mean-torque s tatistics compiled in T able 2. This command therefore k eeps the manuscript narrati v e synchronized with the artif acts preserv ed in Supplementary File S1. 4. RESUL TS AND DISCUSSION Simulations demonstrate that PPC no w pro vides tighter tracking en v elopes with RMSE v alues of 0.365 rad and 0.337 rad for q 1 and q 2 , respecti v ely , while FOSMC settles at 0.458 rad and 0.453 rad (T able 2), Figure 2). Figures 2(a)-(b) sho ws the PPC error bands remaining narro wer throughout the disturbance windo w , whereas FOSMC’ s fractional surf ace, approximated via a high-g ain placeholder , lea v es wider residuals and slo wer con v er gence in Figure 3. Despite this accurac y penalty , FOSMC commands lo wer mean torques of 69.2 N·m and 29.0 N·m (Figures 4(a)-(b)) relati v e to PPC’ s 86.1 N·m and 41.4 N·m, demonstrating that the fractional sliding surf ace can sha v e actuator ef fort e v en when it does not outperform linear pole placement on tracking. Joint v elocities still remain comparati v ely smooth under the sliding-mode action during the 10 N·m disturbance (Figures 5(a)-(b)), indicating that the fractional dynamics damp high-frequenc y chattering at the cost of additional steady-state bias. These head-to-head metrics are signicant for robotics researchers and inte grators because the y t rans- late abstract f ractional-order concepts into the actuator torques, settling t imes, and RMSE thre sholds used in manuf acturing and sur gical benchmarks. In practical terms, the results state that matching PPC-le v el accu- rac y under the tested disturbance requires further tuning of the fractional deri v ati v e approximation, whereas ener gy-conscious deplo yments can le v erage FOSMC to trim roughly 15-30. Positioning the study within prior literature, most fractional-order w orks report impro v ements rela ti v e to PID or adapti v e baselines under bespok e trajectories [17]-[20]. By matching the plant, disturbance, solv er tolerances, and sampling grid across both controllers, this benchmark supplies the reproducible dat aset that those surv e ys cite as missing. The accurac y–ef fort curv es therefore complement industrial PPC deplo yments rather than replacing them outright, and the associated Python w orko w allo ws researchers to inject additional nonlinear or learning-based modules under identical numerical assumptions. Future research can b uild directly on these ndings in three layers. First, controller designers can reuse the r eleased w orko w to h ybridise FOSMC with adapti v e or data-dri v en observ ers while k eeping the PPC base- Compar ative analysis of fr actional-or der sliding mode and pole placement contr ol (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
94 ❒ ISSN: 2502-4752 line as a reference en v elope, aiming to reco v er the lost accurac y without abandoning the torque sa vings. Sec- ond, system-le v el engineers can incorporate actuator ther mal and ener gy storage models so that the quantied torque reductions translate into measurabl e life-c ycle benets. Third, roboticists focusing on collaborati v e or sur gical manipulators can e xtend the fractional surf ace design to higher -DOF or compliance-dominated mecha- nisms where smoother torques are prioritised o v er strict tracking. Because recent trends f a v our benchmarkable w orko ws o v er isolated controller tweaks, the open dataset and matching protocol supplied here constitut e the principal no v elty: the y transform well-kno wn structures into a comparati v e e vidence base that w as pre viously missing. Three k e y e xperiments are no w required to translate the simulated trade-of fs into deplo yable practice: i) hardw are-in-the-loop trials with encoder noise and actuator saturation to determine whether the observ ed ac- curac y decit persists once more f aithful fractional operators are implemented [24]; ii) Monte Carlo stress tests that perturb link masses, payloads, and viscous damping so the reported RMSE distrib utions can be mapped to manuf acturing tolerances [24]; and iii) ener gy auditing on a re generati v e dri v e bench that compares life-c ycle ef cienc y and thermal rise between FOSMC and PPC o v er representati v e duty c ycles [4]. Completing this trio will re v eal whether the torque adv antage remains meaningful in hardw are and will highlight an y controller retuning needed for e xible links. T ak en together , the comparati v e e vidence, conte xtual framing, and prescribed e xperiments pro vide a clear tak e-a w ay for readers: FOSMC presently e xchanges ac curac y for lo wer torque demand under the adopted approximation, while PPC remains the preferred option whene v er stringent precisi on specications dominate the design brief. Figure 1 summarizes the tw o-link manipulator geometry used throughout the study , highlight- ing joint locations, link lengths, and reference frames needed for interpreting the subsequent tracking results. T able 2. Performance comparison of FOSMC and PPC Controller RMSE q 1 (rad) RMSE q 2 (rad) Mean T orque τ 1 (N.m) Mean T orque τ 2 (N.m) FOSMC 0.458 0.453 69.2 29.0 PPC 0.365 0.337 86.1 41.4 Figure 2 compares the tracking error trajectories of both controllers; panel Figure 2(a) focuses on joint 1 while panel Figure 2(b) presents joint 2 so that transient and steady-state de viations can be contrasted side-by-side before e xamining the absolute angle responses. Figure 3 then o v erlays the commanded and actual joint angles, with Figure 3(a) co v ering q 1 and Figure 3(b) co v ering q 2 , pro viding conte xt for the error magni- tudes reported in Figure 2. Figure 1. Structure of a 2-DOF robotic manipulator Figure 4 details the control ef forts supplied to each joint; Figure 4(a) reports τ 1 while Figure 4(b) reports τ 2 , enabling a direct comparison of the ener gy cost associated with the impro v ed tracking. Finally , Fig- ure 5 g athers the joint v elocity responses, where Figure 5(a) depicts ˙ q 1 and Figure 5(b) depicts ˙ q 2 , highlighting the smoother transients achie v ed by FOSMC during the disturbance interv al. Indonesian J Elec Eng & Comp Sci, V ol. 41, No. 1, January 2026: 90–98 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 ❒ 95 (a) (b) Figure 2. T racking error comparison for FOSMC and PPC (a) tracking error for joint 1 and (b) tracking error for joint 2 (a) (b) Figure 3. Joint angle tracking for FOSMC and PPC (a) joint angle q 1 tracking performance and (b) joint angle q 2 tracking performance (a) (b) Figure 4. Control input comparison for FOSMC and PPC (a) control input τ 1 for joint 1 and (b) control input τ 2 for joint 2 (a) (b) Figure 5. Joint v elocity comparison for FOSMC and PPC (a) joint v elocity ˙ q 1 and (b) joint v elocity ˙ q 2 Compar ative analysis of fr actional-or der sliding mode and pole placement contr ol (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
96 ❒ ISSN: 2502-4752 5. CONCLUSION This study presented a detailed comparati v e analysis bet ween Fractional-Order Sliding Mode Control (FOSMC) and Pole Placement Control (PPC) for a tw o-link robotic manipulator . The FOSMC w as designed using a fractionalorder sliding surf ace to pro vide grea ter control e xibility and impro v e the system’ s dynamic response, whereas PPC serv ed as a linear benchmark. Both controllers were implemented with identical La- grange models, trajectories, and disturbance proles to ensure a f air e v aluation. Quantitati v ely , the current fractional implementation yields RMSE v alues of 0.458 rad for q1 and 0.453 rad for q2, trailing PPC’ s 0.365 rad and 0.337 rad. This accurac y g ap is of fset by lo wer mean torques of 69.2/29.0 N·m v ersus PPC’ s 86.1/41.4 N·m, clarifying that the benchmark ed FOSMC prole is attracti v e when torque limits dominate and PPC remains preferable when tight tracking is mandatory . Despite these benets, the e v aluation remains limited t o ideal rigid-body dynamics, high-g ain ap- proximations of the fractional deri v ati v e, and simulated sensor data. The absence of joint friction, payload v ariation, and netw ork induced delays may o v erestimat e achie v able rob ustness mar gins, and hardw are imple- mentation could re v eal actuator bandwidth constraints. T o close these g aps, we prioritize three e xperiments: i) hardw are-in-the-loop tests with realistic actuator and encoder noise, ii) Monte Carlo stress testing that per - turbs inertial and damping parameters, and iii) ener gy auditing with re generati v e dri v es to quantify life-c ycle ef cienc y relati v e to PPC. Ov erall, the ndings conrm that PPC retains the accurac y lead for the tested nonlinear manipulator while FOSMC deli v ers measurable torque sa vings whene v er act uator ef fort is the binding constraint . The open simulation w orko w of fers a reproducible baseline for researchers tar geting e xperimental v alidation, real- time deplo yment, and higher -de gree-of-freedom e xtensions, and it anchors future studies to shared quantitati v e gures-of-merit. FUNDING INFORMA TION Authors state no funding in v olv ed. A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the Contrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib u- tions, 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 ✓ ✓ ✓ ✓ ✓ ✓ ✓ Idrees Nasser Alsolbi ✓ ✓ ✓ ✓ ✓ ✓ ✓ 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 administration 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 Authors state no conict of interest. SUPPLEMENT AR Y MA TERIALS Supplementary File S1 ( supplementary code.tex ) pro vides the complete, reproducible Python w orko w: robot model, FOSMC and PPC controller implementations, s imulation dri v er , plotting routines generating Figures 2–5, and the animation script. All solv er settings, g ain selections, and post-processing steps referenced in the manuscript can be re-run directly . The le is self-contained; e x ecuting it with a standard scientic Python stack (NumPy , SciPy , Matplotlib) re generates all reported performance metrics. D A T A A V AILABILITY The authors conrm that the data supporting the ndings of this study are a v ailable within the article. Indonesian J Elec Eng & Comp Sci, V ol. 41, No. 1, January 2026: 90–98 Evaluation Warning : The document was created with Spire.PDF for Python.
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Aremu, N. M. Alyazidi, and A. Nasir , “Rob ust fractional-order sliding mode control for robotic manipulator system with time-v arying disturbances, ” Franklin Open , v ol. 12, p. 100287, Sep. 2025, doi: 10.1016/j.fraope.2025.100287. [19] S . Ahmed and A. T . Azar , “ Adapti v e fractional tracking control of robotic manipulator using x ed-time method, ” Comple x & Intelligent Systems , v ol. 10, pp. 369–382, 2024, doi: 10.1007/s40747-023-01164-7. [20] M . Y a vuz, M. ¨ Ozt ¨ urk, and B. Y a, “Comparison of fractional order sliding mode controllers on robot manipulator , ” International Jour - nal of Optimization and Control: Theories & Applications (IJOCT A) , v ol. 15, no. 2, pp. 281–293, 2025, doi: 10.36922/ijocta.1678. [21] H. K. Khalil, “Nonlinear Systems, ” 3rd ed. Pearson Education : Prentice Hall, 2002. [22] C. C. Nguyen and F . J. Poora n, “Cartesian path control of a tw o-de gree-of-freedom robot manipulator , ” Jan. 1988. [Onl ine]. A v ail- able: https://ntrs.nasa.go v/citations/19880004526. [23] W . Boukadida, R. Bk ekri, A. Benamor , and H. Messaoud, “T rajectory tracking of robotic mani pulators using optimal sliding mode control, ” in 2017 International Conference on Control, Automation and Diagnosis (ICCAD) , 2017, pp. 545–550, doi: 10.1109/CA- DIA G.2017.8075717. [24] P . V irtanen, et al. , “SciPy 1.0: fundamental algorithms for scientic computing in Python, ” Nature Methods , v ol. 17, pp. 261–272, 2020, doi: 10.1038/s41592-019-0686-2. [25] H. N. Rahimi, I. Ho w ard, and L. Cui, “Neural adapti v e tracking control for an uncertain robot manipulator with time-v arying joint space constraints, ” Mechanical Systems and Signal Processing , v ol. 112, pp. 44–60, No v . 2018, doi: 10.1016/j.ymssp.2018.03.042. BIOGRAPHIES OF A UTHORS Ahmed Bennaoui is Recei v ed his BSc de gree in Electronics Engineering from the Uni- v ersity of Mohamed Boudiaf - M’ sila (2011), Algeria. He obtained MSc de grees in Electrical En- gineering with a specialization in Adv anced Autom ation from the Uni v ersity of ZIANE A CHOUR (DJELF A), Algeria (2012 and 2016), and a PhD de gree in Electrical Engineering with a specializa- tion in Intelligent Control and Automation (2024) from the Uni v ersity of Amar T elidji (Laghouat), Algeria. His interests include Nonlinear Dynamics, Fuzzy Logic Controller , Po wer System Control, and Optimization T echniques. He can be contacted via email at a.bennaoui@lagh-uni v .dz. Compar ative analysis of fr actional-or der sliding mode and pole placement contr ol (Ahmed Bennaoui) Evaluation Warning : The document was created with Spire.PDF for Python.
98 ❒ ISSN: 2502-4752 Salah Benzian Recei v ed his BSc de gree in Electrical and Electronics Engineering from the Uni v ersity of M’hamed Boug ara - Boumerdes (2011), Algeria. He obtained MSc de grees in Electrical Engineering with a specialization in Adv anced Automation from the Uni v ersity of ZIANE A CHOUR (DJELF A), Algeria (2012 and 2016), and a PhD de gree in Electrical Engineering with a specialization in Intelligent Control and Automation (2021) from the Uni v ersity of Amar T elidji (Laghouat), Algeria. He currently serv es as a lecturer at the Polytec hnic School of El-Harrach, Alge- ria. His interests include Nonlinear Dynamics, Fuzzy L ogic Controllers, Po wer System Control, and Optimization T echniques. He can be contacted via email at s.benzian@cu-aou.edu.dz. Idr ees Nasser Alsolbi Recei v ed the Ph.D. de gree in Big Data from the Uni v ersity of T ech- nology Sydne y (UTS), Australia, in 2023. He earned the M.Sc. de gree in Information T echnology from M onash Uni v ersity , Australia, in 2018, and the B.Sc. de gree in Programming and Computer Science from Umm Al-Qura Uni v ersity , Makkah, Saudi Arabia, in 2010 (1431 H). He is currently an Assistant Professor in the Data Science Department, Colle ge of Computing, Umm Al-Qura Uni- v ersity . His research interests incl ude big data analytics, edge computing, machine learning, wireless sensor netw orks, educational data mining, and AI-based decision support systems. His w ork has ap- peared in leading journals such as Nature Sc ientic Reports, Articial Intelligence Re vie w (Springer), and Information (MDPI). He can be contacted via email at insolbi@uqu.edu.sa. Aissa Ameur Recei v ed his Magister and Ph.D. de grees in Electrical Engineering in 2005 and 2012, from Batna Uni v ersity , Algeria. In 2005, he joined the Electrical Engineering Department of Laghouat Uni v ersity , Algeria as Assistant Lecturer . Since Ma y 2012, Dr . Ameur is an Assistant Professor in the same department. He is a researcher in LeDMaScD laboratory , Laghouat Uni v ersity , Algeria. His main research interests include Modelling of Electrical Machines, Electrical Dri v es Control, F ault Diagnosis, Articial Intelligence, and Rene w able Ener gy Systems Control. He can be contacted via email at a.ameur@lagh-uni v .dz. Indonesian J Elec Eng & Comp Sci, V ol. 41, No. 1, January 2026: 90–98 Evaluation Warning : The document was created with Spire.PDF for Python.