Extreme Learning Machine-Based Repetitive Proportional Derivative Controller for Robust Tracking and Disturbance Rejection in Rotational Systems
DOI:
https://doi.org/10.18196/jrc.v6i2.25896Keywords:
Plug-in Repetitive Control, Extreme Learning Machine, Rotational Systems, Periodic Signal Tracking, Multi-Periodic Disturbance Compensation, Aperiodic Disturbance CompensationAbstract
Tracking periodic signals and rejecting periodic disturbances are common applications of repetitive control (RC). However, traditional RC methods struggle to compensate for aperiodic disturbances and adapt to system uncertainties, limiting their real-world effectiveness. Existing hybrid approaches often require extensive parameter tuning or suffer from high computational costs, creating a research gap in achieving both adaptability and efficiency. This paper proposes an improved control strategy called extreme learning machine repetitive proportional derivative control (ELMRPDC), which integrates repetitive proportional derivative control (RPDC) with an extreme learning machine (ELM). RPDC ensures accurate tracking of periodic signals, while ELM estimates and compensates for disturbances, enhancing overall performance. Unlike conventional neural network-based controllers, ELM enables rapid adaptation with minimal computational overhead, making it more suitable for real-time applications on resource-constrained systems. The proposed method is analyzed for stability using the Lyapunov approach, ensuring convergence of tracking errors. Extensive simulations are conducted on both rotational and linear dynamic systems under various disturbance conditions, including periodic, time-varying, multi-periodic, and aperiodic disturbances, such as vibration-induced disruptions in machinery. The study also evaluates the impact of hidden layer neuron variations in ELM on disturbance rejection. The best performance is observed for multi-period sinusoidal disturbances, achieving an RMSE of 1.8630 degrees at 1500 neurons, reducing error by 67.47% compared to conventional RPDC. These results highlight ELMRPDC’s advantages in computational efficiency, real-time feasibility, and robustness against complex disturbances. The approach holds significant promise for precise reference tracking and disturbance rejection across diverse industrial applications.
References
T. Inoue, M. Nakano, T. Kubo, S. Matsumoto, and H. Baba, “High Accuracy Control of a Proton Synchrotron Magnet Power Supply,” IFAC Proc. Vol., vol. 14, no. 2, pp. 3137–3142, 1981, doi: 10.1016/S1474-6670(17)63938-7.
B. A. Francis and W. M. Wonham, “The internal model principle for linear multivariable regulators,” Appl. Math. Optim., vol. 2, no. 2, pp. 170–194, 1975, doi: 10.1007/BF01447855.
R. L. McGrath and F. Sergi, “Repetitive Control of Knee Interaction Torque via a Lower Extremity Exoskeleton for Improved Transparency During Walking,” IEEE Trans. Med. Robot. Bionics, vol. 6, no. 4, pp. 1581–1590, 2024, doi: 10.1109/TMRB.2024.3464119.
K. Umeda, Y. Jiang, H. Yokoi, and S. Togo, "Repetitive Control of Robotic Joint With Variable Impedance Utilizing Agonist-Antagonist Muscle Pair Structure Based on Virtual Trajectories," in IEEE Access, vol. 13, pp. 16866-16878, 2025, doi: 10.1109/ACCESS.2025.3532633.
L. Li, X. Wang, W.-W. Huang, X. Zhang, and L. Zhu, “Design of General Parametric Repetitive Control Using IIR Filter With Application to Piezo-Actuated Nanopositioning Stages,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 2, pp. 2102–2112, 2024, doi: 10.1109/TASE.2023.3260340.
L. Li, W.-W. Huang, X. Wang, and L. Zhu, “Dual-Notch-Based Repetitive Control for Tracking Lissajous Scan Trajectories With Piezo-Actuated Nanoscanners,” IEEE Trans. Instrum. Meas., vol. 71, pp. 1–12, 2022, doi: 10.1109/TIM.2022.3169561.
L. Zhou, D. Gao, J. She, X.-M. Zhang, and H. Yan, “Adaptive Spatial Repetitive-Control for Time-Varying Periodic Signals in a Rotational System,” IEEE Trans. Automat. Contr., vol. 69, no. 6, pp. 4134–4141, 2024, doi: 10.1109/TAC.2023.3349316.
S. Tian et al., “Two-Dimensional Repetitive Control of Uncertain Takagi–Sugeno Systems Based on a New Equivalent-Input-Disturbance Estimator,” IEEE Trans. Fuzzy Syst., vol. 32, no. 4, pp. 2366–2377, 2024, doi: 10.1109/TFUZZ.2024.3350744.
E. Kurniawan, H. Wang, J. A. Prakosa, P. Purwowibowo, and E. B. Pratiwi, “An improved repetitive controller with fractional time-delay for discrete-time linear systems: Synthesis and comparison study,” ISA Trans., vol. 146, pp. 511–527, 2024, doi: 10.1016/j.isatra.2023.12.035.
E. Kurniawan et al., “Design of Fractional Order Odd-Harmonics Repetitive Controller for Discrete-Time Linear Systems with Experimental Validations,” Sensors, vol. 22, no. 22, 2022, doi: 10.3390/s22228873.
E. Kurniawan et al., “Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals,” Fractal and Fractional, vol. 9, no. 1, 2025, doi: 10.3390/fractalfract9010041.
E. Kurniawan et al., “Robust adaptive repetitive control for unknown linear systems with odd-harmonic periodic disturbances,” Sci. China Inf. Sci., vol. 65, no. 12, p. 222202, 2022, doi: 10.1007/s11432-022-3561-2.
X. Ye, X. Tang, K. Xing, H. Wang, J. Yao, and T. Zhang, “Repetitive Control for Vibration Suppression of Bearingless Induction Motor,” IEEE Access, vol. 12, pp. 60532–60540, 2024, doi: 10.1109/ACCESS.2024.3391292.
L.-W. Shih and C.-W. Chen, “Model-free repetitive control design and implementation for dynamical galvanometer-based raster scanning,” Control Eng. Pract., vol. 122, p. 105124, 2022, doi: 10.1016/j.conengprac.2022.105124.
P. Cui, H. Xu, Z. Liu, J. Li, and B. Han, “Improved Second-Order Repetitive Control With Parameter Optimization for Magnetically Suspended Rotor System,” IEEE Sens. J., vol. 20, no. 5, pp. 2294–2303, 2020, doi: 10.1109/JSEN.2019.2951764.
Y. Zhao, C. Xie, C. Peng, and J. Zou, “Passivity-Based Design of Frequency Adaptive Repetitive Controller for LCL-Type Grid-Connected Inverters,” IEEE Trans. Power Electron., vol. 39, no. 4, pp. 4017–4028, 2024, doi: 10.1109/TPEL.2023.3347723.
Q. Qian et al., “Coordinated Self-Tuning Implementation of Repetitive Control and Active Damping for 400 Hz Inverter against Filter Inductance Fluctuation,” IEEE Trans. Power Electron., vol. 39, no. 12, pp. 15520–15535, 2024, doi: 10.1109/TPEL.2024.3446833.
W. Xiong, Z. Wang, J. Na, B. Zhang, and S. Li, “Robust Predictive Disturbance Observer-Based Repetitive Control for Time-Delay Systems With Application to CVCF Inverters,” IEEE Trans. Ind. Electron., vol. 72, no. 2, pp. 1904–1913, 2025, doi: 10.1109/TIE.2024.3417982.
J. Zhang, Z. Sun, Q. Zhao, and H. Li, "Frequency Adaptive Proportional Feedforward Repetitive Control Based on Farrow Structure Filter for LCL Grid-Tied Inverters," in IEEE Access, vol. 12, pp. 191120-191128, 2024, doi: 10.1109/ACCESS.2024.3510881.
M. Zhu, Y. Ye, Y. Xiong, and Q. Zhao, “Multibandwidth Repetitive Control Resisting Frequency Variation in Grid-Tied Inverters,” IEEE J. Emerg. Sel. Top. Power Electron., vol. 10, no. 1, pp. 446–454, 2022, doi: 10.1109/JESTPE.2021.3077618.
Q. Chen, Y. Li, Y. Hong, and H. Shi, “Prescribed-Time Robust Repetitive Learning Control for PMSM Servo Systems,” IEEE Trans. Ind. Electron., vol. 71, no. 11, pp. 14753–14763, 2024, doi: 10.1109/TIE.2024.3363757.
B. Chen, Z. Huang, P. Sun, and G. Wei, “Harmonic Suppression for PMSM Applied to MSTMP Based on Virtual Even-Order Fractional Repetitive Controller,” IEEE Trans. Ind. Informatics, vol. 20, no. 4, pp. 6289–6299, 2024, doi: 10.1109/TII.2023.3345465.
Y.-H. Lan, J.-L. He, P. Li, and J.-H. She, “Optimal preview repetitive control with application to permanent magnet synchronous motor drive system,” J. Franklin Inst., vol. 357, no. 15, pp. 10194–10210, 2020, doi: 10.1016/j.jfranklin.2020.04.026.
S. Chalia, A. K. Seth, and M. Singh, “Frequency Adaptive Discrete Repetitive Controller Design for Electric Vehicle Charger,” IEEE J. Emerg. Sel. Top. Ind. Electron., vol. 6, no. 1, pp. 72–81, 2025, doi: 10.1109/JESTIE.2024.3469569.
N. Feng, Y. Ruan, and T. Tang, “Youla Parameterization-Based Fractional Repetitive Control of Arbitrary Frequency Disturbance Rejections for Line-of-Sight Stabilization,” IEEE Trans. Ind. Electron., vol. 71, no. 8, pp. 9460–9469, 2024, doi: 10.1109/TIE.2023.3317840.
X. Zhang and Z. Zheng, “Application of Repetitive Control in Electric Spring,” IEEE Access, vol. 8, pp. 216607–216616, 2020, doi: 10.1109/ACCESS.2020.3041648.
K. Zhou, C. Tang, Y. Chen, B. Zhang, and W. Lu, “A Generic Multi-Frequency Repetitive Control Scheme for Power Converters,” IEEE Trans. Ind. Electron., vol. 70, no. 12, pp. 12680–12688, 2023, doi: 10.1109/TIE.2023.3239855.
W. Lu, W. Wang, K. Zhou, and Q. Fan, “General High-Order Selective Harmonic Repetitive Control for PWM Converters,” IEEE J. Emerg. Sel. Top. Power Electron., vol. 10, no. 1, pp. 1178–1191, 2022, doi: 10.1109/JESTPE.2021.3101857.
E. Kurniawan et al., “Design and analysis of higher-order repetitive sliding mode controller for uncertain linear systems with time-varying periodic disturbances,” Trans. Inst. Meas. Control, vol. 45, no. 12, pp. 2219–2234, 2023, doi: 10.1177/01423312221146604.
G. Ramos, J. M. Olm, and R. Costa-Castelló, “Adaptive Compensation Strategy For The Tracking/Rejection of Signals with Time-Varying Frequency in Digital Repetitive Control Systems,” J. Process Control, vol. 20, Sep. 2009, doi: 10.1016/j.jprocont.2010.02.002.
E. Kurniawan, H. G. Harno, and H. Adinanta, “High-order repetitive model reference control for linear systems with uncertain periodic references and disturbances,” Int. J. Syst. Sci., vol. 53, no. 7, pp. 1456–1468, 2022, doi: 10.1080/00207721.2021.2008545.
C. Verrelli, “Repetitive Learning Control Design and Period Uncertainties,” Asian J. Control, vol. 17, Mar. 2015, doi: 10.1002/asjc.1125.
M. Steinbuch, S. Weiland, and T. Singh, “Design of noise and period-time robust high-order repetitive control, with application to optical storage,” Automatica, vol. 43, no. 12, pp. 2086–2095, 2007, doi: 10.1016/j.automatica.2007.04.011.
G. A. Ramos, R. Costa-Castelló, and J. M. Olm, "Odd-harmonic high order repetitive control," Digital Repetitive Control under Varying Frequency Conditions, pp. 37-64, 2013, doi: 10.1007/978-3-642-37778-5_5.
R. Chuei and Z. Cao, “Extreme learning machine-based super-twisting repetitive control for aperiodic disturbance, parameter uncertainty, friction, and backlash compensations of a brushless DC servo motor,” Neural Comput. Appl., vol. 32, no. 18, pp. 14483–14495, 2020, doi: 10.1007/s00521-020-04965-w.
Z. Zhao, S. Lin, D. Zhu, and G. Wen, “Vibration Control of a Riser-Vessel System Subject to Input Backlash and Extraneous Disturbances,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 67, no. 3, pp. 516–520, 2020, doi: 10.1109/TCSII.2019.2914061.
W. Lin et al., “Adaptive Extended State Observer-Based Velocity-Free Servo Tracking Control With Friction Compensation,” IEEE Trans. Syst. Man, Cybern. Syst., vol. 54, no. 1, pp. 2–11, 2024, doi: 10.1109/TSMC.2023.3299953.
A. H. M. Sayem, Z. Cao, and Z. Man, “Model Free ESO-Based Repetitive Control for Rejecting Periodic and Aperiodic Disturbances,” IEEE Trans. Ind. Electron., vol. 64, no. 4, pp. 3433–3441, 2017, doi: 10.1109/TIE.2016.2606086.
M. Nordin and P.-O. Gutman, “Controlling mechanical systems with backlash—a survey,” Automatica, vol. 38, no. 10, pp. 1633–1649, 2002, doi: 10.1016/S0005-1098(02)00047-X.
M. Çetin, B. Bahtiyar, and S. Beyhan, “Adaptive uncertainty compensation-based nonlinear model predictive control with real-time applications,” Neural Comput. Appl., vol. 31, no. 2, pp. 1029–1043, 2019, doi: 10.1007/s00521-017-3068-7.
H. Yan and Y. Li, “Adaptive NN prescribed performance control for nonlinear systems with output dead zone,” Neural Comput. Appl., vol. 28, no. 1, pp. 145–153, 2017, doi: 10.1007/s00521-015-2043-4.
İ. Eski and Ş. Yıldırım, “Neural network-based fuzzy inference system for speed control of heavy duty vehicles with electronic throttle control system,” Neural Comput. Appl., vol. 28, pp. 907–916, 2017, doi: 10.1007/s00521-016-2362-0.
Q. Li, T. Zhang, G. Li, Z. Li, H. Xia, and C.-Y. Su, “Neural-Dynamics Optimization and Repetitive Learning Control for Robotic Leg Prostheses,” IEEE/ASME Trans. Mechatronics, vol. 27, no. 2, pp. 811–822, 2022, doi: 10.1109/TMECH.2021.3071936.
V. H. Duenas, C. A. Cousin, C. Rouse, E. J. Fox, and W. E. Dixon, “Distributed Repetitive Learning Control for Cooperative Cadence Tracking in Functional Electrical Stimulation Cycling,” IEEE Trans. Cybern., vol. 50, no. 3, pp. 1084–1095, 2020, doi: 10.1109/TCYB.2018.2882755.
M. Yang, Y. Zhang, Z. Zhang, and H. Hu, “6-Step Discrete ZNN Model for Repetitive Motion Control of Redundant Manipulator,” IEEE Trans. Syst. Man, Cybern. Syst., vol. 52, no. 8, pp. 4969–4980, 2022, doi: 10.1109/TSMC.2021.3107898.
C. Xu, S. Xie, and Q. Chen, “Neural-network-based adaptive repetitive learning control for a class of non-parametric uncertain systems,” Gaojishu Tongxin/Chinese High Technol. Lett., vol. 32, no. 8, pp. 859–865, 2022, doi: 10.3772/j.issn.1002-0470.2022.08.008.
E. Tatlicioglu, N. Cobanoglu, and E. Zergeroglu, “Neural network-based repetitive learning control of euler lagrange systems: An output feedback approach,” IEEE Control Syst. Lett., vol. 2, no. 1, pp. 13–18, 2018, doi: 10.1109/LCSYS.2017.2720735.
Z. B. Duranay, “Extreme Learning Machine-Based Power Forecasting in Photovoltaic Systems,” IEEE Access, vol. 11, pp. 128923–128931, 2023, doi: 10.1109/ACCESS.2023.3333667.
K. Xu, H. Yang, C. Zhu, X. Jin, B. Fan, and L. Hu, “Deep Extreme Learning Machines Based Two-Phase Spatiotemporal Modeling for Distributed Parameter Systems,” IEEE Trans. Ind. Informatics, vol. 19, no. 3, pp. 2919–2929, 2023, doi: 10.1109/TII.2022.3165870.
H. D. P. De Carvalho, R. Fagundes, and W. Santos, “Extreme Learning Machine Applied to Software Development Effort Estimation,” IEEE Access, vol. 9, pp. 92676–92687, 2021, doi: 10.1109/ACCESS.2021.3091313.
Z. Wang, Y. Zeng, Y. Liu, and D. Li, “Deep Belief Network Integrating Improved Kernel-Based Extreme Learning Machine for Network Intrusion Detection,” IEEE Access, vol. 9, pp. 16062–16091, 2021, doi: 10.1109/ACCESS.2021.3051074.
M. Nahiduzzaman et al., “A Novel Method for Multivariant Pneumonia Classification Based on Hybrid CNN-PCA Based Feature Extraction Using Extreme Learning Machine With CXR Images,” IEEE Access, vol. 9, pp. 147512–147526, 2021, doi: 10.1109/ACCESS.2021.3123782.
R. Alasbahi and X. Zheng, “An Online Transfer Learning Framework With Extreme Learning Machine for Automated Credit Scoring,” IEEE Access, vol. 10, pp. 46697–46716, 2022, doi: 10.1109/ACCESS.2022.3171569.
J. Li, C. Hai, Z. Feng, and G. Li, “A Transformer Fault Diagnosis Method Based on Parameters Optimization of Hybrid Kernel Extreme Learning Machine,” IEEE Access, vol. 9, pp. 126891–126902, 2021, doi: 10.1109/ACCESS.2021.3112478.
M. Nahiduzzaman, M. R. Islam, S. M. R. Islam, M. O. F. Goni, M. S. Anower, and K.-S. Kwak, “Hybrid CNN-SVD Based Prominent Feature Extraction and Selection for Grading Diabetic Retinopathy Using Extreme Learning Machine Algorithm,” IEEE Access, vol. 9, pp. 152261–152274, 2021, doi: 10.1109/ACCESS.2021.3125791.
H. Lin, X. He, S. Wang, and P. Yang, “Wavefront Distortion Correction for the Non-Uniform-Intensity Light Based on Extreme Learning Machine,” IEEE Photonics J., vol. 13, no. 3, pp. 1–10, 2021, doi: 10.1109/JPHOT.2021.3086005.
K. Zheng, J. Yang, Q. Gong, S. Zhou, L. Zeng, and S. Li, “Multivariate Extreme Learning Machine Based AutoEncoder for Electricity Consumption Series Clustering,” IEEE Access, vol. 9, pp. 148665–148675, 2021, doi: 10.1109/ACCESS.2021.3124009.
J. M. Melchor-Leal and J. A. Cantoral-Ceballos, “Force profile characterization for thermostatic bimetal using extreme learning machine,” IEEE Lat. Am. Trans., vol. 19, no. 2, pp. 208–216, 2021, doi: 10.1109/TLA.2021.9443062.
P. P. Játiva, R. Becerra, C. A. Azurdia-Meza, D. Zabala-Blanco, I. Soto, and M. R. Cañizares, “Extreme Learning Machine Based Channel Estimator and Equalizer for Underground Mining VLC Systems,” in 2021 IEEE Latin-American Conference on Communications (LATINCOM), pp. 1–6, 2021, doi: 10.1109/LATINCOM53176.2021.9647737.
F. Luo, G. Liu, W. Guo, G. Chen, and N. Xiong, “ML-KELM: A Kernel Extreme Learning Machine Scheme for Multi-Label Classification of Real Time Data Stream in SIoT,” IEEE Trans. Netw. Sci. Eng., vol. 9, no. 3, pp. 1044–1055, 2022, doi: 10.1109/TNSE.2021.3073431.
J. Zhang, H. Wang, M. Ma, M. Yu, A. Yazdani, and L. Chen, “Active Front Steering-Based Electronic Stability Control for Steer-by-Wire Vehicles via Terminal Sliding Mode and Extreme Learning Machine,” IEEE Trans. Veh. Technol., vol. 69, no. 12, pp. 14713–14726, 2020, doi: 10.1109/TVT.2020.3036400.
H. Gao, W. Tang, and R. Fu, “Sliding Mode Control for Hypersonic Vehicle Based on Extreme Learning Machine Neural Network Disturbance Observer,” IEEE Access, vol. 10, no. June, pp. 69333–69345, 2022, doi: 10.1109/ACCESS.2022.3185256.
Y. Yang, Y. Wang, X. Yuan, Y. Chen, and L. Tan, “Neural network-based self-learning control for power transmission line deicing robot,” Neural Comput. Appl., vol. 22, no. 5, pp. 969–986, 2013, doi: 10.1007/s00521-011-0789-x.
Z. Wang et al., “Sensor Drift Compensation of E-Nose Systems with Discriminative Domain Reconstruction Based on an Extreme Learning Machine,” IEEE Sens. J., vol. 21, no. 15, pp. 17144–17153, 2021, doi: 10.1109/JSEN.2021.3081923.
Y. Zheng, Z. Cao, S. Wang, Z. Man, and R. Chuei, “Extreme learning machine-based field-oriented feedback linearization speed control of permanent magnetic synchronous motors,” Neural Comput. Appl., vol. 34, no. 7, pp. 5267–5282, 2022, doi: 10.1007/s00521-021-06722-z.
L. Chen, B. Yan, H. Wang, K. Shao, E. Kurniawan, and G. Wang, “Extreme-learning-machine-based robust integral terminal sliding mode control of bicycle robot,” Control Eng. Pract., vol. 121, p. 105064, 2022, doi: 10.1016/j.conengprac.2022.105064.
Y. Hu et al., “Extreme-learning-machine-based FNTSM control strategy for electronic throttle,” Neural Comput. Appl., vol. 32, no. 18, pp. 14507–14518, 2020, doi: 10.1007/s00521-019-04446-9.
D. Wu, H. Chen, Y. Huang, and S. Chen, “Online Monitoring and Model-Free Adaptive Control of Weld Penetration in VPPAW Based on Extreme Learning Machine,” IEEE Trans. Ind. Informatics, vol. 15, no. 5, pp. 2732–2740, 2019, doi: 10.1109/TII.2018.2870933.
H. J. Rong and G. S. Zhao, “Direct adaptive neural control of nonlinear systems with extreme learning machine,” Neural Comput. Appl., vol. 22, no. 3–4, pp. 577–586, 2013, doi: 10.1007/s00521-011-0805-1.
C. Yang, K. Huang, H. Cheng, Y. Li, and C. Y. Su, “Haptic Identification by ELM-Controlled Uncertain Manipulator,” IEEE Trans. Syst. Man, Cybern. Syst., vol. 47, no. 8, pp. 2398–2409, 2017, doi: 10.1109/TSMC.2017.2676022.
Quanser, Rotary Experiment 01: SRV02 Modeling using QuaRC. Markham, Ontario: Quanser Inc., 2011.
Y. Chen, K. Zhou, C. Tang, Y. Shu, and Y. Yang, “Fractional-Order Multiperiodic Odd-Harmonic Repetitive Control of Programmable AC Power Sources,” IEEE Trans. Power Electron., vol. 37, no. 7, pp. 7751–7758, 2022, doi: 10.1109/TPEL.2022.3147062.
C. Lin et al., “Output Voltage Ripple Suppression of PPSS-LCC Converter for Medical X-Ray Application Based on Repetitive Control,” IEEE J. Emerg. Sel. Top. Ind. Electron., vol. 5, no. 4, pp. 1688–1697, 2024, doi: 10.1109/JESTIE.2024.3435005.
M. S. Ali, L. Wang, H. Alquhayz, O. U. Rehman, and G. Chen, “Performance Improvement of Three-Phase Boost Power Factor Correction Rectifier Through Combined Parameters Optimization of Proportional-Integral and Repetitive Controller,” IEEE Access, vol. 9, pp. 58893–58909, 2021, doi: 10.1109/ACCESS.2021.3073004.
J. Ye, L. Liu, J. Xu, and A. Shen, “Frequency Adaptive Proportional-Repetitive Control for Grid-Connected Inverters,” IEEE Trans. Ind. Electron., vol. 68, no. 9, pp. 7965–7974, 2021, doi: 10.1109/TIE.2020.3016247.
Z. Chen, H. Zha, K. Peng, J. Yang, and J. Yan, “A Design Method of Optimal PID-Based Repetitive Control Systems,” IEEE Access, vol. 8, pp. 139625–139633, 2020, doi: 10.1109/ACCESS.2020.3012506.
M. Jamil, A. Waris, S. O. Gilani, B. A. Khawaja, M. N. Khan, and A. Raza, “Design of Robust Higher-Order Repetitive Controller Using Phase Lead Compensator,” IEEE Access, vol. 8, pp. 30603–30614, 2020, doi: 10.1109/ACCESS.2020.2973168.
A. Straś, B. Ufnalski, M. Michalczuk, A. Gałecki, and L. Grzesiak, “Design of fractional delay repetitive control with a dead-beat compensator for a grid-tied converter under distorted grid voltage conditions,” Control Eng. Pract., vol. 98, p. 104374, 2020, doi: 10.1016/j.conengprac.2020.104374.
H. Zhou. Extreme learning machine for classification and regression. Doctoral thesis, Nanyang Technological University, Singapore, 2013.
G. Bin Huang, Q. Y. Zhu, and C. K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing, vol. 70, no. 1–3, pp. 489–501, 2006, doi: 10.1016/j.neucom.2005.12.126.
E. Kurniawan. Robust Repetitive Control and Applications. Swinburne University of Technology, Melbourne, Australia, 2013.
G.-B. Huang, L. Chen, and C. Siew, “Universal Approximation Using Incremental Constructive Feedforward Networks With Random Hidden Nodes,” IEEE Trans. Neural Netw., vol. 17, pp. 879–892, Jul. 2006, doi: 10.1109/TNN.2006.875977.
W. Cao, J. Gao, Z. Ming, and S. Cai, “Some Tricks in Parameter Selection for Extreme Learning Machine,” IOP Conf. Ser. Mater. Sci. Eng., vol. 261, no. 1, p. 12002, 2017, doi: 10.1088/1757-899X/261/1/012002.
L. Hua, C. Zhang, T. Peng, C. Ji, and M. Shahzad Nazir, “Integrated framework of extreme learning machine (ELM) based on improved atom search optimization for short-term wind speed prediction,” Energy Convers. Manag., vol. 252, p. 115102, 2022, doi: 10.1016/j.enconman.2021.115102.
X. Zheng and G. Xu, “Extreme learning machine with incremental hidden layers,” in Third International Conference on Electronic Information Engineering, Big Data, and Computer Technology (EIBDCT 2024), vol. 13181, pp. 2105-2110, 2024, doi: 10.1117/12.3031279.
C. Y. Lin and C. M. Chang, “Hybrid proportional derivative/repetitive control for active vibration control of smart piezoelectric structures,” JVC/Journal Vib. Control, vol. 19, no. 7, pp. 992–1003, 2013, doi: 10.1177/1077546312436749.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Enggar Banifa Pratiwi, Prawito Prajitno, Edi Kurniawan
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This journal is based on the work at https://journal.umy.ac.id/index.php/jrc under license from Creative Commons Attribution-ShareAlike 4.0 International License. You are free to:
- Share – copy and redistribute the material in any medium or format.
- Adapt – remix, transform, and build upon the material for any purpose, even comercially.
The licensor cannot revoke these freedoms as long as you follow the license terms, which include the following:
- Attribution. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- ShareAlike. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Creative Commons Attribution-ShareAlike (CC BY-SA)
JRC is licensed under an International License
