Multi-objective Fractional Order PID Controller Optimization for Kid's Rehabilitation Exoskeleton

(1) * Intissar Zaway Mail (University of Sfax, Tunisia)
(2) Rim Jallouli-Khlif Mail (University of Sfax, Tunisia)
(3) Boutheina Maaleja Mail (University of Sfax, Tunisia)
(4) Hanene Medhaffar Mail (University of Sfax, Tunisia)
(5) Nabil Derbela Mail (University of Sfax, Tunisia)
*corresponding author

Abstract


Fractional order Controllers have been used in several industrial cases to achieve better performance of the systems. This paper proposes a Fractional Order Proportional Integral Derivative (FOPID) controller. It is synthesized using Oustaloup approximation, and its parameters are tuned using the Genetic Algorithm (GA) optimization method. The aim is to minimize the error, the energy and the startup torques using two objective functions to improve the control performances and the robustness. The validity of the proposed controller is shown via simulation by controlling a two-link exoskeleton for children's gait rehabilitation, and the results are compared to an Integer order PID (IOPID) controller. Simulation results clearly indicate the superiority of the optimized FOPID in terms of trajectory tracking and the used torques. Moreover, the FOPID controller is tested with parameter uncertainties. Its robustness is proven against thigh and shank masses variation. Both controllers are simulated under the same frequency conditions using Simulink MATLAB R2018a.

Keywords


Rehabilitation Robot; Fractional order PID Controller; PID Controller; Optimization; Genetic Algorithm;Robustness

   

DOI

https://doi.org/10.31763/ijrcs.v3i1.840
      

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References


[1] V. Cimolin, C. Germiniasi, M. Galli, C. Condoluci, E. Beretta, L. Piccinini, “Robot-Assisted upper limb training for hemiplegic children with cerebral palsy,” Journal of Developmental and Physical Disabilities, vol. 31, no. 1, pp. 89-101, 2019, https://doi.org/10.1007/s10882-018-9632-y.

[2] J. A. Buitrago, A. M. Bolanos, E. Caicedo Bravo, “A motor learning therapeutic intervention for a child with cerebral palsy through a social assistive robot,” Disability and Rehabilitation: Assistive Technology, vol. 15, no. 3, pp. 357-362, 2020, https://doi.org/10.1080/17483107.2019.1578999.

[3] A. A. Lins, J. M. de Oliveira, J. J. Rodrigues, V. H. C. de Albuquerque, “Robot-assisted therapy for rehabilitation of children with cerebral palsy-a complementary and alternative approach,” Computers in Human Behavior, vol. 100, pp. 152-167, 2019 https://doi.org/10.1016/j.chb.2018.05.012.

[4] R. M. Andrade, S. Sapienza, P. Bonato, “Development of a transparent operation mode for a lower-limb exoskeleton designed for children with cerebral palsy,” IEEE 16th International Conference on Rehabilitation Robotics (ICORR), pp. 512-517, 2019, https://doi.org/10.1109/ICORR.2019.8779432.

[5] G. Zeilig, H. Weingarden, M. Zwecker, I. Dudkiewicz, A. Bloch, A. Esquenazi, “Safety and tolerance of the ReWalk exoskeleton suit for ambulation by people with complete spinal cord injury: A pilot study,” The journal of spinal cord medicine, vol. 35, no. 2, pp. 96-101, 2012, https://doi.org/10.1179/2045772312Y.0000000003.

[6] A. Tsukahara, R. Kawanishi, Y. Hasegawa, Y. Sankai, “Sit-to-stand and stand-to-sit transfer support for complete paraplegic patients with robot suit HAL,” Advanced robotics, vol. 24, no. 11, pp. 1615-1638, 2010, https://doi.org/10.1163/016918610X512622.

[7] K. A. Strausser and H. Kazerooni, “The development and testing of a human machine interface for a mobile medical exoskeleton,” IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4911-4916, 2011, https://doi.org/10.1109/IROS.2011.6095025.

[8] M. Bortole, A. Venkatakrishnan, F. Zhu, J. C. Moreno, G. E. Francisco, J. L. Pons, J. L. Contreras-Vidal, “The H2 robotic exoskeleton for gait rehabilitation after stroke: early findings from a clinical study,” Journal of neuroengineering and rehabilitation, vol. 12, no. 1, pp. 1-14, 2015, https://doi.org/10.1186/s12984-015-0048-y.

[9] Y. Sun, Y. Tang, J. Zheng, D. Dong, X. Chen, L. Bai, “From sensing to control of lower limb exoskeleton: a systematic review,” Annual Reviews in Control, 2022, https://doi.org/10.1016/j.arcontrol.2022.04.003.

[10] Z. Shen, J. Zhou, J. Gao, R. Song, “Fuzzy logic based PID control of a 3 DOF lower limb rehabilitation robot,” IEEE 8th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), pp. 818-821, 2018, https://doi.org/10.1109/CYBER.2018.8688089.

[11] Y. Yang, D. Huang, X. Dong, “Enhanced neural network control of lower limb rehabilitation exoskeleton by add-on repetitive learning,” Neurocomputing, vol. 323, pp. 256-264, 2019, https://doi.org/10.1016/j.neucom.2018.09.085.

[12] S. K. Hasan and A. K. Dhingra, “An adaptive controller for human lower extremity exoskeleton robot,” Microsystem Technologies, pp. 1-18, 2021, https://doi.org/10.1007/s00542-020-05207-8.

[13] A. Riani, T. Madani, A. Benallegue, K. Djouani, “Adaptive integral terminal sliding mode control for upper-limb rehabilitation exoskeleton,” Control Engineering Practice, vol. 75, pp. 108-117, 2018, https://doi.org/10.1016/j.conengprac.2018.02.013.

[14] Munadi, M. S. Nasir, M. Ariyanto, N. Iskandar, J. D. Setiawan, “Design and simulation of PID controller for lower limb exoskeleton robot,” AIP Conference Proceedings, vol. 1983, p. 060008, 2018, https://doi.org/10.1063/1.5046300.

[15] E. H. Dulf, “Simplified fractional order controller design algorithm,” Mathematics, vol. 7, no. 12, p. 1166, 2019, https://doi.org/10.3390/math7121166.

[16] P. Shah and S. Agashe, “Review of fractional PID controller,” Mechatronics, vol. 38, pp. 29-41, 2016, https://doi.org/10.1016/j.mechatronics.2016.06.005.

[17] H. Hamidian and M. T. Beheshti, “A robust fractional-order PID controller design based on active queue management for TCP network,” International Journal of Systems Science, vol. 49, no. 1, pp. 211-216, 2018, https://doi.org/10.1080/00207721.2017.1397801.

[18] H. H. Ammar and A. T. Azar, “Robust path tracking of mobile robot using fractional order PID controller,” International Conference on Advanced Machine Learning Technologies and Applications, pp. 370-381, 2019, https://doi.org/10.1007/978-3-030-14118-9_37.

[19] A. N. Sharkawy and P. Koustoumpardis, “Dynamics and computed-torque control of a 2-DOF manipulator: Mathematical analysis,” International Journal of Advanced Science and Technology, vol. 28, no. 12, pp. 201-212, 2019, https://hal.archives-ouvertes.fr/hal-03598924.

[20] M. Z. Othman and E. A. Al-Sabawi, “Design of Fractional Order PID Controller Based on Genetic Algorithms,” Al-Rafadain Engineering Journal, vol. 20, no. 4, 2012, http://dx.doi.org/10.33899/rengj.2012.54151.

[21] B. Hekimoglu, “Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm,” IEEE Access, vol. 7, pp. 38100-38114, 2019, https://doi.org/10.1109/ACCESS.2019.2905961.

[22] K. Vanchinathan and N. Selvaganesan, “Adaptive fractional order PID controller tuning for brushless DC motor using artificial bee colony algorithm,” Results in Control and Optimization, vol. 4, p. 100032, 2021, https://doi.org/10.1016/j.rico.2021.100032.

[23] S. M. A. Altbawi, A. S. B. Mokhtar, T. A. Jumani, I. Khan, N. N. Hamadneh, and A. Khan, “Optimal design of Fractional order PID controller based Automatic voltage regulator system using gradient-based optimization algorithm,” Journal of King Saud University-Engineering Sciences, 2021, https://doi.org/10.1016/j.jksues.2021.07.009.

[24] R. Jallouli-Khlif, B. Maalej, P. Melchior, and N. Derbel, “Control of Prosthetic Hand Based on Input Shaping Combined to Fractional PI Controller,” 9th International Conference on Systems and Control (ICSC), pp. 449-454, 2021, https://doi.org/10.1109/ICSC50472.2021.9666537.

[25] Y. Zhang and J. Li, “Fractional-order PID controller tuning based on genetic algorithm,” International Conference on Business Management and Electronic Information, pp. 764-767, 2011, https://doi.org/10.1109/ICBMEI.2011.5920371.

[26] S. Mirjalili, J. S. Dong, A. S. Sadiq, and H. Faris, “Genetic algorithm: Theory, literature review, and application in image reconstruction,” Nature-inspired optimizers, pp. 69-85, 2020, https://doi.org/10.1007/978-3-030-12127-3_5.

[27] D. Doval, S. Mancoridis, B. S. Mitchell, “Automatic clustering of software systems using a genetic algorithm,” Proceedings Ninth International Workshop Software Technology and Engineering Practice, pp. 73-81, 1999, https://doi.org/10.1109/STEP.1999.798481.

[28] M. K. Amjad, S. I. Butt, R. Kousar, R. Ahmad, M. H. Agha, Z. Faping, N. Anjum, and U. Asgher, “Recent research trends in genetic algorithm based flexible job shop scheduling problems,” Mathematical Problems in Engineering, 2018, https://doi.org/10.1155/2018/9270802.

[29] L. B. Booker, D. E. Goldberg, J. H. Holland, “Classifier systems and genetic algorithms,” Artificial intelligence, vol. 40, no. 1-3, pp. 235-282, 1989, https://doi.org/10.1016/0004-3702(89)90050-7.

[30] H. F. Ho, Y. K. Wong, A. B. Rad, “Robust fuzzy tracking control for robotic manipulators,” Simulation Modelling Practice and Theory, vol. 15, no. 7, pp. 801-816, 2007, https://doi.org/10.1016/j.simpat.2007.04.008.

[31] M. Ghezal, M. Guiatni, I. Boussioud, and C. S. Renane, “Design and Robust Control of a 2 DOFs Lower Limb Exoskeleton,” International Conference on Communications and Electrical Engineering (ICCEE), pp. 1-6, 2018, https://doi.org/10.1109/CCEE.2018.8634540.

[32] A. Oustaloup and B. Mathieu, La commande CRONE: du scalaire au multivariable, Hermes Editions: Paris, 1999, https://books.google.co.id/books?id=ccBbAAAACAAJ.

[33] B. Maalej, R. J. Khlif, C. Mhiri, M. H. Elleuch, N. Derbel, “Adaptive fractional control optimized by genetic algorithms with application to polyarticulated robotic systems,” Mathematical Problems in Engineering, 2021, https://doi.org/10.1155/2021/5579541.

[34] I. Petras, ”Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab,” Engineering Education and Research Using MATLAB, 2011, https://doi.org/10.5772/19412.

[35] R. Al-Aomar, “Incorporating robustness into genetic algorithm search of stochastic simulation outputs,” Simulation modelling practice and theory, vol. 14, no. 3, pp. 201-223, 2006, https://doi.org/10.1016/j.simpat.2005.05.001.

[36] B. Maalej, A. Chemori, and N. Derbel, “Intelligent Tuning of Augmented L1 Adaptive Control for Cerebral Palsy Kids Rehabilitation,” 16th International Multi-Conference on Systems, Signals Devices (SSD), pp. 231-237, 2019, https://doi.org/10.1109/SSD.2019.8893237.


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International Journal of Robotics and Control Systems
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