Improved Tracking Accuracy of Par-4 Delta Parallel Robot Using Optimized FOPID Control with PSO Technique
DOI:
https://doi.org/10.18196/jrc.v6i4.26607Keywords:
Par-4 Delta Parallel Robot, Integer PID Controller, Fractional PID Controller, Tracking Accuracy, Particle Swarm OptimizationAbstract
The Par-4 Delta parallel robot is an excellent choice for most pick-and-place applications. The parallel robot has complex and high nonlinearities and the choice of control design is one key to improving the tracking performance and accuracy of parallel robots. This study proposes two structures of proportional-derivative-integral (PID) controller. The first scheme utilized Integer-order setting of controller's terms, while the second structure used integral and derivative terms with fractional orders and it is termed as fractional-order PID (FOPID) controller. The terms of FOPID controller are synthesized based on fractional calculus theorem. It has been shown that FOPID controller has high efficacy when applied to complex and nonlinear systems. However, the tuning of its terms is a critical issue in its design. As such, an algorithm-based particle swarm optimization (PSO) has been developed to tune the parameters of FOPID controller such as to achieve global minimum of tracking errors Par-4 Delta parallel robot. The effectiveness of optimized FOPID controller has been verified via numerical simulation and it is compared to integer PID (IPID) controller with the same PSO algorithm. The computer simulations have showed that better tracking errors have been obtained with FOPID controller compared to its counterpart. Using the root mean square of error (RMSE) as the metric of evaluation, the numerical results showed that PSO-FOPID achieved 60% and 62.9% improvement in terms of tracking accuracy along both the x-axis and the z-axis, respectively, as compared to IOPID applied controller techniques.
References
M. A. Laribi, L. Romdhane, and S. Zeghloul, “Advanced Synthesis of the DELTA Parallel Robot for a Specified Workspace,” in Parallel Manipulators, towards New Applications, 2008.
D. Zhang, “Global Stiffness Optimization of Parallel Robots Using Kinetostatic Performance Indices,” in Robot Manipulators Trends and Development, 2010.
J.-H. Ryu, Parallel Manipulators, New Developments. I-Tech Education and Publishing, 2012.
Z. Pei, Y. Zhang, and Z. Tang, “Model reference adaptive PID control of hydraulic parallel robot based on RBF neural network,” in 2007 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 1383–1387, 2007, doi: 10.1109/ROBIO.2007.4522366.
R. Garrido, A. Soria, and M. Trujano, “Visual PID control of a redundant parallel robot,” in 2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control, pp. 91–96, 2008, doi: 10.1109/ICEEE.2008.4723397.
M. A. Khosravi and H. D. Taghirad, “Robust PID control of fully-constrained cable driven parallel robots,” Mechatronics, vol. 24, no. 2, pp. 87–97, Mar. 2014, doi: 10.1016/j.mechatronics.2013.12.001.
X. Lu and M. Liu, “Optimal Design and Tuning of PID-Type Interval Type-2 Fuzzy Logic Controllers for Delta Parallel Robots,” Int. J. Adv. Robot. Syst., vol. 13, no. 3, May 2016, doi: 10.5772/63941.
L. Angel and J. Viola, “Fractional order PID for tracking control of a parallel robotic manipulator type delta,” ISA Trans., vol. 79, pp. 172–188, Aug. 2018, doi: 10.1016/j.isatra.2018.04.010.
A. J. Humaidi and A. I. Abdulkareem, “Design of Augmented Nonlinear PD Controller of Delta/Par4-Like Robot,” J. Control Sci. Eng., vol. 2019, pp. 1–11, Jul. 2019, doi: 10.1155/2019/7689673.
A. J. Humaidi, A. A. Oglah, S. J. Abbas, and I. K. Ibraheem, “Optimal Augmented Linear and Nonlinear PD Control Design for Parallel Robot Based on PSO Tuner,” Int. Rev. Model. Simulations, vol. 12, no. 5, p. 281, Oct. 2019, doi: 10.15866/iremos.v12i5.16298.
X. Zhang and Z. Ming, “Trajectory Planning and Optimization for a Par4 Parallel Robot Based on Energy Consumption,” Appl. Sci., vol. 9, no. 13, p. 2770, Jul. 2019, doi: 10.3390/app9132770.
J. Viola and L. Angel, “Delta Parallel Robotic Manipulator Tracking Control using Fractional Order Controllers,” IEEE Lat. Am. Trans., vol. 17, no. 3, pp. 393–400, Mar. 2019, doi: 10.1109/TLA.2019.8863309.
A. Al-Mayyahi, A. A. Aldair, and C. Chatwin, “Control of a 3-RRR Planar Parallel Robot Using Fractional Order PID Controller,” Int. J. Autom. Comput., vol. 17, no. 6, pp. 822–836, Dec. 2020, doi: 10.1007/s11633-020-1249-9.
S. Nguyen-Van, D. T. T. Thuy, N. N. T. Thanh, and N. N. Dinh, “Evolutionary Tuning of PID Controllers for a Spatial Cable-Driven Parallel Robot,” in Lecture Notes in Networks and Systems, pp. 411–424, 2021, doi: 10.1007/978-3-030-64719-3_46.
A. J. Humaidi, H. T. Najem, A. Q. Al-Dujaili, D. A. Pereira, I. K. Ibraheem, and A. T. Azar, “Social spider optimization algorithm for tuning parameters in PD-like Interval Type-2 Fuzzy Logic Controller applied to a parallel robot,” Meas. Control, vol. 54, no. 3–4, pp. 303–323, Mar. 2021, doi: 10.1177/0020294021997483.
Y.-J. Pak, Y.-S. Kong, and J.-S. Ri, “Robust PID optimal tuning of a Delta parallel robot based on a hybrid optimization algorithm of particle swarm optimization and differential evolution,” Robotica, vol. 41, no. 4, pp. 1159–1178, Apr. 2023, doi: 10.1017/S0263574722001606.
T. Yigit and H. Celik, “Dimension Synthesis and Optimized FOPID Control of the Delta Robot with Moth Swarm Algorithm,” Arab. J. Sci. Eng., vol. 48, no. 5, pp. 6889–6902, May 2023, doi: 10.1007/s13369-023-07601-6.
Y. Liu, Z. Luo, S. Qian, S. Wang, and Z. Wu, “Deep reinforcement learning and decoupling proportional-integral-derivative control of a humanoid cable-driven hybrid robot,” Int. J. Adv. Robot. Syst., vol. 21, no. 3, May 2024, doi: 10.1177/17298806241254336.
F. E. Serrano and M. Cardona, “Robust H-Infinity Control of Delta Parallel Robot with Disturbances,” in Lecture Notes in Networks and Systems, pp. 56–67, 2024, doi: 10.1007/978-3-031-54763-8_6.
D. Blanck-Kahan, G. Ortiz-Cervantes, V. Martínez-Gama, H. Cervantes-Culebro, J. E. Chong-Quero, and C. A. Cruz-Villar, “Neural-optimal tuning of a controller for a parallel robot,” Expert Syst. Appl., vol. 236, p. 121184, Feb. 2024, doi: 10.1016/j.eswa.2023.121184.
M. Aghaseyedabdollah, M. Abedi, and M. Pourgholi, “Interval type-2 fuzzy sliding mode control for a cable-driven parallel robot with elastic cables using metaheuristic optimization methods,” Math. Comput. Simul., vol. 218, pp. 435–461, Apr. 2024, doi: 10.1016/j.matcom.2023.11.036.
D. Zhu, Y. He, and F. Li, “Trajectory Tracking of Delta Parallel Robot via Adaptive Backstepping Fractional-Order Non-Singular Sliding Mode Control,” Mathematics, vol. 12, no. 14, p. 2236, Jul. 2024, doi: 10.3390/math12142236.
S. M. Mahdi, A. I. Abdulkareem, A. J. Humaidi, A. K. Al Mhdawi, and H. Al-Raweshidy, “Comprehensive Review of Control Techniques for Various Mechanisms of Parallel Robots,” IEEE Access, vol. 13, pp. 63381–63416, 2025, doi: 10.1109/ACCESS.2025.3557937.
A. J. Humaidi, M. R. Hameed, and A. H. Hameed, “Design of block-backstepping controller to ball and arc system based on zero dynamic theory,” J. Eng. Sci. Technol., vol. 13, no. 7, pp. 2084–2105, 2018.
A. J. Humaidi, M. E. Sadiq, A. I. Abdulkareem, I. K. Ibraheem, and A. T. Azar, “Adaptive backstepping sliding mode control design for vibration suppression of earth-quaked building supported by magneto-rheological damper,” J. Low Freq. Noise, Vib. Act. Control, vol. 41, no. 2, pp. 768–783, Jun. 2022, doi: 10.1177/14613484211064659.
H. Al-Khazraji, R. M. Naji, and M. K. Khashan, “Optimization of Sliding Mode and Back-Stepping Controllers for AMB Systems Using Gorilla Troops Algorithm,” J. Eur. des Systèmes Autom., vol. 57, no. 2, pp. 417–424, Apr. 2024, doi: 10.18280/jesa.570211.
Z. A. Waheed et al., “Control of Elbow Rehabilitation System Based on Optimal-Tuned Backstepping Sliding Mode Controller,” J. Eng. Sci. Technol., vol. 18, no. 1, pp. 584–603, 2023.
N. A. Alawad, A. J. Humaidi, and A. S. Alaraji, “Sliding Mode-Based Active Disturbance Rejection Control of Assistive Exoskeleton Device for Rehabilitation of Disabled Lower Limbs,” An. Acad. Bras. Cienc., vol. 95, no. 2, 2023, doi: 10.1590/0001-3765202320220680.
N. A. Alawad, A. J. Humaidi, and A. S. Alaraji, “Design of Active Disturbance Rejection Control for Rehabilitation-Assistant Device of Lower Limbs under Cross Coupling Effect,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 238, no. 15, pp. 7388–7398, Aug. 2024, doi: 10.1177/09544062241232230.
A. Q. Al-Dujaili, A. F. Hasan, A. J. Humaidi, and A. Al-Jodah, “Anti-disturbance control design of Exoskeleton Knee robotic system for rehabilitative care,” Heliyon, vol. 10, no. 9, p. 28911, May 2024, doi: 10.1016/j.heliyon.2024.e28911.
A. J. Humaidi and A. H. Hameed, “Robustness enhancement of MRAC using modification techniques for speed control of three phase induction motor,” J. Electr. Syst., vol. 13, no. 4, pp. 723–741, 2017.
Z. N. Mahmood, H. Al-Khazraji, and S. M. Mahdi, “Adaptive Control and Enhanced Algorithm for Efficient Drilling in Composite Materials,” J. Eur. des Systèmes Autom., vol. 56, no. 3, pp. 507–512, Jun. 2023, doi: 10.18280/jesa.560319.
A. J. Humaidi, A. H. Hameed, and M. R. Hameed, “Robust adaptive speed control for DC motor using novel weighted E-modified MRAC,” in 2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI), pp. 313–319, 2017, doi: 10.1109/ICPCSI.2017.8392302.
S. M. Mahdi and S. M. Raafat, “Robust Interactive PID Controller Design for Medical Robot System,” Int. J. Intell. Eng. Syst., vol. 15, no. 1, pp. 370–382, Feb. 2022, doi: 10.22266/IJIES2022.0228.34.
A. H. Hameed, S. A. Al-Samarraie, and A. J. Humaidi, “A novel control solution to nonlinear systems of unmatched perturbations with unknown bounds,” Meas. Control, vol. 58, no. 4, pp. 486–501, Apr. 2025, doi: 10.1177/00202940241269596.
A. Chemori, G. Sartori-natal, F. Pierrot, and R. Ada, “Control of Parallel Robots: Towards Very High Accelerations,” in h International Multi-Conference on Systems, Signals & Devices (SSD), pp. 1–8, 2013.
M. Mazare, M. Taghizadeh, and P. Ghaf-Ghanbari, “Fault-tolerant control based on adaptive super-twisting nonsingular integral-type terminal sliding mode for a delta parallel robot,” J. Brazilian Soc. Mech. Sci. Eng., vol. 42, no. 8, p. 443, Aug. 2020, doi: 10.1007/s40430-020-02510-3.
M. Zadehbagheri, A. Ma’arif, R. Ildarabadi, M. Ansarifard, and I. Suwarno, “Design of Multivariate PID Controller for Power Networks Using GEA and PSO,” J. Robot. Control, vol. 4, no. 1, pp. 108–117, Mar. 2023, doi: 10.18196/jrc.v4i1.15682.
A. Ma’arif, H. Nabila, Iswanto, and O. Wahyunggoro, “Application of Intelligent Search Algorithms in Proportional-Integral-Derivative Control of Direct-Current Motor System,” J. Phys. Conf. Ser., vol. 1373, no. 1, p. 12039, Nov. 2019, doi: 10.1088/1742-6596/1373/1/012039.
S. M. Mahdi, K. S. Khalid, and S. M. Mahdi, “PID controller tuning using ant colony method for servo hydraulic system,” J. Mech. Eng. Res. Dev., vol. 42, no. 4, pp. 148–152, Jun. 2019, doi: 10.26480/jmerd.04.2019.148.152.
Z. Bingul and O. Karahan, “Comparison of PID and FOPID controllers tuned by PSO and ABC algorithms for unstable and integrating systems with time delay,” Optim. Control Appl. Methods, vol. 39, no. 4, pp. 1431–1450, 2018, doi: 10.1002/oca.2419.
A. R. Nair and A. G. K. R, “Control Technique for Parallel Manipulator using PID,” Int. J. Eng. Res., vol. V5, no. 7, Jul. 2016, doi: 10.17577/IJERTV5IS070064.
X. Chen, L. Wu, and X. Yang, “Design of FOPID controller based on improved sparrow search algorithm,” 2022 IEEE 5th International Conference on Information Systems and Computer Aided Education, ICISCAE 2022, pp. 1–5, Aug. 12, 2022, doi: 10.1109/ICISCAE55891.2022.9927577.
F. Padula, R. Vilanova, and A. Visioli, “H∞ optimization-based fractional-order PID controllers design,” Int. J. Robust Nonlinear Control, vol. 24, no. 17, pp. 3009–3026, Nov. 2014, doi: 10.1002/rnc.3041.
S. Khodadoost, M. Saraee, S. Talatahari, and P. Sareh, “Optimal design of fractional-order proportional integral derivative controllers for structural vibration suppression,” Sci. Rep., vol. 14, no. 1, p. 17207, Jul. 2024, doi: 10.1038/s41598-024-68281-2.
F. A. G. S. Babu and S. B. T. Chiranjeevi, “Implementation of Fractional Order PID Controller for an AVR System Using GA and ACO Optimization Techniques,” IFAC-PapersOnLine, vol. 49, no. 1, pp. 456–461, 2016, doi: 10.1016/j.ifacol.2016.03.096.
A. M. Abed et al., “Trajectory tracking of differential drive mobile robots using fractional-order proportional-integral-derivative controller design tuned by an enhanced fruit fly optimization,” Meas. Control, vol. 55, no. 3–4, pp. 209–226, Mar. 2022, doi: 10.1177/00202940221092134.
H. I. Abdulameer and M. J. Mohamed, “Fractional Order Fuzzy Like PID Controller Design for Three Links Rigid Robot Manipulator,” Iraqi J. Comput. Commun. Control Syst. Eng., pp. 80–98, Dec. 2022, doi: 10.33103/uot.ijccce.22.4.7.
M. H. Setiawan, A. Ma’arif, M. F. Saifuddin, and W. A. Salah, “A Comparative Study of PID, FOPID, ISF, SMC, and FLC Controllers for DC Motor Speed Control with Particle Swarm Optimization,” Int. J. Robot. Control Syst., vol. 5, no. 1, pp. 640–660, Feb. 2025, doi: 10.31763/ijrcs.v5i1.1764.
A. M. Nassef and H. Rezk, “Optimal Tuning of FOPID-Like Fuzzy Controller for High-Performance Fractional-Order Systems,” Comput. Mater. Contin., vol. 70, no. 1, pp. 171–180, 2022, doi: 10.32604/cmc.2022.019347.
X. S. Yang, Optimization techniques and applications with examples. Wiley, 2018, doi: 10.1002/9781119490616.
S. Charkoutsis and M. Kara-Mohamed, “A Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems,” Results Control Optim., vol. 12, p. 100289, Sep. 2023, doi: 10.1016/j.rico.2023.100289.
S. Selvarajan, “A comprehensive study on modern optimization techniques for engineering applications,” Artif. Intell. Rev., vol. 57, no. 8, p. 194, Jul. 2024, doi: 10.1007/s10462-024-10829-9.
Z. Jakšić, S. Devi, O. Jakšić, and K. Guha, “A Comprehensive Review of Bio-Inspired Optimization Algorithms Including Applications in Microelectronics and Nanophotonics,” Biomimetics, vol. 8, no. 3, p. 278, Jun. 2023, doi: 10.3390/biomimetics8030278.
M. Z. bin M. Zain, J. Kanesan, J. H. Chuah, S. Dhanapal, and G. Kendall, “A multi-objective particle swarm optimization algorithm based on dynamic boundary search for constrained optimization,” Appl. Soft Comput. J., vol. 70, pp. 680–700, Sep. 2018, doi: 10.1016/j.asoc.2018.06.022.
A. G. Gad, “Particle Swarm Optimization Algorithm and Its Applications: A Systematic Review,” Arch. Comput. Methods Eng., vol. 29, no. 5, pp. 2531–2561, Aug. 2022, doi: 10.1007/s11831-021-09694-4.
Z. N. Mahmood, H. Al-Khazraji, and S. M. Mahdi, “PID-Based Enhanced Flower Pollination Algorithm Controller for Drilling Process in a Composite Material,” Ann. Chim. - Sci. des Matériaux, vol. 47, no. 2, pp. 91–96, Apr. 2023, doi: 10.18280/acsm.470205.
Z. Qin and D. Pan, “Improved Dual-Center Particle Swarm Optimization Algorithm,” Mathematics, vol. 12, no. 11, p. 1698, May 2024, doi: 10.3390/math12111698.
R. S. Raheem, M. Y. Hassan, and S. K. Kdahim, “Particle swarm optimization based interval type 2 fuzzy logic control for motor rotor position control of artificial heart pump,” Indones. J. Electr. Eng. Comput. Sci., vol. 25, no. 2, p. 814, Feb. 2022, doi: 10.11591/ijeecs.v25.i2.pp814-824.
E. S. Rahayu, A. Ma’arif, and A. Çakan, “Particle Swarm Optimization (PSO) Tuning of PID Control on DC Motor,” Int. J. Robot. Control Syst., vol. 2, no. 2, pp. 435–447, Jul. 2022, doi: 10.31763/ijrcs.v2i2.476.
E. Alfian, A. Ma’arif, P. Chotikunnan, and A. J. Abougarair, “Optimizing Light Intensity with PID Control,” Control Syst. Optim. Lett., vol. 1, no. 3, pp. 124–131, Sep. 2023, doi: 10.59247/csol.v1i3.38.
S. S. Ghintab and M. Y. Hassan, “PID-like IT2FLC-Based Autonomous Vehicle Control in Urban Areas,” Arab. J. Sci. Eng., May 2024, doi: 10.1007/s13369-024-09104-4.
D. M. Wonohadidjojo, G. Kothapalli, and M. Y. Hassan, “Position Control of Electro-hydraulic Actuator System Using Fuzzy Logic Controller Optimized by Particle Swarm Optimization,” Int. J. Autom. Comput., vol. 10, no. 3, pp. 181–193, Jun. 2013, doi: 10.1007/s11633-013-0711-3.
H. Al-Khazraji, K. Al-Badri, R. Al-Majeez, and A. J. Humaidi, “Synergetic Control Design Based Sparrow Search Optimization for Tracking Control of Driven-Pendulum System,” J. Robot. Control, vol. 5, no. 5, pp. 1549–1556, 2024, doi: 10.18196/jrc.v5i5.22893.
H. Al-Khazraji, W. Guo, and A. Humaidi, “Improved cuckoo search optimization for production inventory control systems,” Serbian J. Electr. Eng., vol. 21, no. 2, pp. 187–200, 2024, doi: 10.2298/SJEE2402187A.
M. Q. Kadhim, F. R. Yaseen, H. Al-Khazraji, and A. J. Humaidi, “Application of Terminal Synergetic Control Based Water Strider Optimizer for Magnetic Bearing Systems,” J. Robot. Control, vol. 5, no. 6, pp. 1973–1979, Oct. 2024, doi: 10.18196/jrc.v5i6.23867.
O. Toumia and F. Zouari, “Artificial intelligence and venture capital decision-making,” in Fostering Innovation in Venture Capital and Startup Ecosystems, pp. 16–38, 2024, doi: 10.4018/979-8-3693-1326-8.ch002.
G. Rigatos, M. Abbaszadeh, J. Pomares, P. Wira, and G. Cuccurullo, “Flatness-based control in successive loops for robotic manipulators and autonomous vehicles,” Int. J. Syst. Sci., vol. 55, no. 5, pp. 954–979, Oct. 2024, doi: 10.1080/00207721.2023.2301040.
G. Rigatos, P. Siano, P. Wira, M. Abbaszadeh, and F. Zouari, “Nonlinear H-infinity control for optimization of the functioning of mining products mills,” in IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society, pp. 2367–2372, 2018, doi: 10.1109/IECON.2018.8592736.
F. Zouari, K. Ben Saad, and M. Benrejeb, “Robust neural adaptive control for a class of uncertain nonlinear complex dynamical multivariable systems,” Int. Rev. Model. Simulations, vol. 5, no. 5, pp. 2075–2103, 2012.
F. Zouari, K. Ben Saad, and M. Benrejeb, “Robust Adaptive Control for a Class of Nonlinear Systems Using the Backstepping Method,” Int. J. Adv. Robot. Syst., vol. 10, no. 3, Mar. 2013, doi: 10.5772/54932.
G. S. Natal, A. Chemori, and F. Pierrot, “Dual-space adaptive control of redundantly actuated parallel manipulators for extremely fast operations with load changes,” in 2012 IEEE International Conference on Robotics and Automation, pp. 253–258, 2012, doi: 10.1109/ICRA.2012.6224597.
W. W. Shang, S. Cong, Z. X. Li, and S. L. Jiang, “Augmented Nonlinear PD Controller for a Redundantly Actuated Parallel Manipulator,” Adv. Robot., vol. 23, no. 12–13, pp. 1725–1742, Jan. 2009, doi: 10.1163/016918609X12496340080490.
N. A. Al-Awad, A. J. Humaidi, and A. S. Al-Araji, “Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system,” Acta Polytech., vol. 63, no. 3, Jul. 2023, doi: 10.14311/AP.2023.63.0158.
A. H. Hameed, S. A. Al-Samarraie, A. J. Humaidi, and N. Saeed, “Backstepping-Based Quasi-Sliding Mode Control and Observation for Electric Vehicle Systems: A Solution to Unmatched Load and Road Perturbations,” World Electr. Veh. J., vol. 15, no. 9, p. 419, Sep. 2024, doi: 10.3390/wevj15090419.
H. Al-Khazraji, K. Albadri, R. Almajeez, and A. J. Humaidi, “Synergetic Control-Based Sea Lion Optimization Approach for Position Tracking Control of Ball and Beam System,” Int. J. Robot. Control Syst., vol. 4, no. 4, pp. 1547–1560, Sep. 2024, doi: 10.31763/ijrcs.v4i4.1551.
S. M. Mahdi, K. S. Khalid, and S. M. Mahdi, “PID Controller Tuning Using Ant Colony Method for Servo Hydraulic System,” J. Mech. Eng. Res. Dev., vol. 42, no. 4, pp. 148–152, Jun. 2019, doi: 10.26480/jmerd.04.2019.148.152.
R. A. Kadhim, M. Q. Kadhim, H. Al-Khazraji, and A. J. Humaidi, “Bee Algorithm Based Control Design for Two-links Robot Arm Systems,” IIUM Eng. J., vol. 25, no. 2, pp. 367–380, Jul. 2024, doi: 10.31436/iiumej.v25i2.3188.
A. R. Ajel, A. J. Humaidi, I. K. Ibraheem, and A. T. Azar, “Robust Model Reference Adaptive Control for Tail-Sitter VTOL Aircraft,” Actuators, vol. 10, no. 7, p. 162, Jul. 2021, doi: 10.3390/act10070162.
M. Y. Hassan and S. S. Ezzaten, “PI-Like Interval Type-2 Fuzzy Logic Control Based Social Spider Optimization for distillation column,” in 2018 Third Scientific Conference of Electrical Engineering (SCEE), pp. 67–71, 2018, doi: 10.1109/SCEE.2018.8684171.
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