Neural inverse control of a rotary flexible link

Main Article Content

Carlos Alberto Saldaña Enderica
José Ramón Llata
Carlos Torre-Ferrero

Abstract

This paper presents a data-driven inverse-model control scheme for a rotary flexible-link (RFL) system,
with (θ) denoting the base angular position and (α) the relative tip deflection. The plant is identified from experimental data and represented as a continuoustime fourth-order state-space model. On this basis, an inverse-model controller is designed and implemented using an artificial neural network (ANN) of the multilayer perceptron (MLP) type, trained on regressors composed of delayed states and inputs. Validation relies on quantitative error metrics, transientresponse analysis, and an indirect discrete-time BIBO (Bounded Input–Bounded Output) stability certification obtained by identifying an equivalent closed-loop linear model. Six MLP architectures are compared under three reference scenarios. The selected configuration achieves the best trade-off between (θ) tracking and (α) vibration attenuation, with bounded closedloop signals and competitive settling times. The work integrates, into a single workflow, data-driven identification of the RFL, systematic MLP architecture selection, and discrete-time BIBO stability analysis, providing a reproducible framework for designing and objectively comparing inverse-model neural controllers in subactuated flexible systems.

Article Details

Section
Scientific Paper

References

[1] D. Subedi, I. Tyapin, and G. Hovland, “Review on modeling and control of flexible link manipulators,” Modeling, Identification and Control: A Norwegian Research Bulletin, vol. 41, no. 3, pp. 141–163, 2020. [Online]. Available: https://doi.org/10.4173/mic.2020.3.2

[2] W. Tang and P. Daoutidis, “Data-driven control: Overview and perspectives,” in 2022 American Control Conference (ACC). IEEE, 2022, pp. 1048–1064. [Online]. Available: https://doi.org/10.23919/ACC53348.2022.9867266

[3] K. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, Mar. 1990. [Online]. Available: https://doi.org/10.1109/72.80202

[4] S. Haykin, Neural Networks and Learning Machines, 3rd ed. Upper Saddle River, NJ, USA: Pearson Education, 2009, accessed: 2026-05-19. [Online]. Available: https://upsalesiana.ec/ing36ar8r4

[5] S. Shin, M. Kang, and J. Baek, “Dynamic model learning and control of robot manipulator based on multi-layer perceptron neural network,” Transactions of the Korean Society of Mechanical Engineers - A, vol. 47, no. 12, pp. 945–957, Dec. 2023. [Online]. Available: https://doi.org/10.3795/KSME-A.2023.47.12.945

[6] M. Deja and A. P. Markopoulos, “Advances and trends in non-conventional, abrasive and precision machining,” Machines, vol. 9, no. 2, p. 37, Feb. 2021. [Online]. Available: https://doi.org/10.3390/machines9020037

[7] M. Suzuki and O. Kaneko, “Data-driven control by using data-driven prediction and LASSO for FIR typed inverse controller,” Electronics and Communications in Japan, vol. 106, no. 3, Aug. 2023. [Online]. Available: https://doi.org/10.1002/ecj.12405

[8] S. Yahagi and M. Suzuki, “Direct datadriven design for a sparse feedback controller based on VRFT and LASSO regression,” IFAC-PapersOnLine, vol. 55, no. 25, pp. 229–234, 2022. [Online]. Available: https://doi.org/10.1016/j.ifacol.2022.09.351

[9] E. Garrabe, H. Jesawada, C. D. Vecchio, and G. Russo, “On convex data-driven inverse optimal control for nonlinear, non-stationary and stochastic systems,” Automatica, vol. 173, p. 112015, Mar. 2025. [Online]. Available: https://doi.org/10.1016/j.automatica.2024.112015

[10] Marji, A. M. Widodo, Marjono, W. Firdaus Mahmudy, and A. Maulana Muhamad, “Comparison of multi-layer perceptron and support vector machine methods on rainfall data with optimal parameter tuning,” International Journal of Advanced Computer Science and Applications, vol. 14, no. 7, 2023. [Online]. Available: https://dx.doi.org/10.14569/IJACSA.2023.0140745

[11] N. V. Thieu, S. Mirjalili, H. Garg, and N. T. Hoang, “Metaperceptron: A standardized framework for metaheuristic-driven multi-layer perceptron optimization,” Computer Standards & Interfaces, vol. 93, p. 103977, Apr. 2025. [Online]. Available: https://doi.org/10.1016/j.csi.2025.103977

[12] C. Saldaña Enderica, J. R. Llata, and C. Torre-Ferrero, “Guided reinforcement learning with twin delayed deep deterministic policy gradient for a rotary flexible-link system,” Robotics, vol. 14, no. 6, p. 76, May 2025. [Online]. Available: https://doi.org/10.3390/robotics14060076

[13] J. G. Guarnizo Marin, N. Díaz Aldana, and C. Trujillo Rodríguez, “Design and implementation of an inverse neural network controller applied to VSC converter for active and reactive power flow, based on regions of work,” Revista Facultad de Ingeniería Universidad de Antioquia, no. 72, pp. 20–34, Aug. 2014. [Online]. Available: https://doi.org/10.17533/udea.redin.15045

[14] V. A. Rodríguez-Toro, J. E. Garzón, and J. A. López, “Control neuronal por modelo inverso de un servosistema usando algoritmos de aprendizaje levenberg-marquardt y bayesiano,” arXiv, 2011. [Online]. Available: https://doi.org/10.48550/arXiv.1111.4267

[15] M. Sasaki, M. Takeda, J. Muguro, and W. Njeri, “Trajectory control of flexible manipulators using forward and inverse models with neural networks,” Vibration, vol. 8, no. 3, p. 48, Aug. 2025. [Online]. Available: https://doi.org/10.3390/vibration8030048

[16] M. T. Hagan, H. B. Demuth, M. H. Beale, and O. D. Jesús, Neural Network Design, 2nd ed. Stillwater, OK, USA: Martin Hagan, 2024, free eBook available online, Accessed: 2026-05-19. [Online]. Available: https://upsalesiana.ec/ing36ar8r16

[17] M. Hagan and M. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Transactions on Neural Networks, vol. 5, no. 6, pp. 989–993, 1994. [Online]. Available: https://doi.org/10.1109/72.329697

[18] J. Capa López, Control de un manipulador flexible de un único segmento. Universidad de Cantabria, 2022. [Online]. Available: https://upsalesiana.ec/ing36ar8r18

[19] C. A. Saldaña Enderica, J. R. Llata, and C. Torre-Ferrero, “Optimization of Q and R matrices with genetic algorithms to reduce oscillations in a rotary flexible link system,” Robotics, vol. 13, no. 6, p. 84, May 2024. [Online]. Available: https://doi.org/10.3390/robotics13060084

[20] Quanser. (2021) Rotary flexible link system identification and LQR design. MATLAB Central File Exchange. [Online]. Available: https://upsalesiana.ec/ing36ar8r20