Fractional order adaptive fuzzy terminal sliding mode controller design for a knee joint orthosis

Document Type : Research Article

Authors

1 Department of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran

2 Department of Electrical Engineering, Hamedan University of Technology

Abstract

Rehabilitation and assistive robots have drawn a large amount of interest, related to the increase of the elderly and the increase in diseases such as stroke and spinal cord injuries as well as the high cost of rehabilitation. In this paper, a fractional order adaptive fuzzy terminal sliding mode control is proposed for a knee joint orthosis. A model integrating the human lower-limb and orthosis based on the Lagrange equations is used. To overcome the uncertainties and external disturbances, a fractional order terminal sliding mode control is designed, then in order to remove the undesirable chattering phenomenon in control signal, a fractional order adaptive fuzzy controller is designed. To improve the precision and speed of tracking and to decrease the effect of the uncertainties in muscular torque modeling on the system control, a nonlinear disturbance observer is combined with fractional order terminal sliding mode control. The stability of closed loop system is proved by new fractional order extention of Lyapunov theorem. The PSO algorithm is used to determine the coefficients of the adaptive fuzzy terminal sliding mode control and the fuzzy membership functions. Finally, the performance of the proposed controller is compared with conventional sliding mode control and PID control.

Keywords

Main Subjects

References

[1]Yan, T., Cempini, M., Oddo, C. M., Vitelo, N. 2015. "Review of assistive strategies in powered lower-limb orthoses and exoskeletons". Robotics and Autonomous Systems, 64,pp. 120-136.
[2]Sadeghian, H., Shokrani, S., Ghorbani, L., 2017. “Imitating Sound Ankle Behavior with a Powered Below-Knee Prosthesis and Validation of its Mechanical Performance”. Amirkabir Journal of Mechanical Engineering, (DOI): 10.22060/mej.2017.12099.5258(in persian).
[3]DÍAZ, I., GIL, J. J. & SÁNCHEZ, E., 2011. "Lower-limb robotic rehabilitation: literature review and challenges". Journal of Robotics, 2011.
[4]Lalami, M. E., Rifaï, H., Mohammed, S., Hassani, W., Amirat, Y., 2013. "Output feedback control of an actuated lower limb orthosis with bounded input," Industrial Robot: An International Journal, 40, pp. 541-549.
[5]Sui, P., Yao, L., Z. Lin, Yan H., 2009. "Analysis and synthesis of ankle motion and rehabilitation robots," in Robotics and Biomimetics (ROBIO), 2009 IEEE International Conference on. pp. 2533-2538.
[6]Hassani, W., Mohammed, S., Rifaï, H., 2014. "Powered orthosis for lower limb movements assistance and rehabilitation," Control Engineering Practice , 26, pp. 245-253.
[7]Daachi, M., Madani, T., Daachi, B., and Djouani, K., 2015. "A radial basis function neural network adaptive controller to drive a powered lower limb knee joint orthosis," Applied Soft Computing ,34, pp. 324-336,.
[8]Mohammed, S., Huo, W., Huang, J., Rifaï, H., and Amirat, Y., 2016."Nonlinear disturbance observer based sliding mode control of a human-driven knee joint orthosis". Robotics and Autonomous Systems, 75, pp. 41-49,.
[9]Barghandan, S., Badamchizadeh, M. A., Jahed-Motlagh, M. R., 2017." Single-rod electro-hydraulic servo system control with sliding mode controller improved by parallel fuzzy compensators". Modares Mechanical Engineering, 17( 2), pp. 377-384, (in Persian).
[10]Shahmohamadi, A., Abolmasomi, A. H., Soleimani, M., 2016. “Design and Implementation of Fast Terminal Sliding Mode Control for Vehicle Lane Keeping by Using Virtual Prototyping Simulations”. Amirkabir Journal of Mechanical Engineering, (DOI): 10.22060/mej.2016.667 (in persian)
[11]Delavari H., 2012." A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty ". International Journal of Dynamics and Control, 5, pp. 102–114.
[12] Nasimullah, M., Khan, K., Wang, S.,2015. "Fractional order adaptive fuzzy sliding mode controller for a position servo system subjected to aerodynamics loading and nonlinearities," Aerosp Sci Technol, 43, pp. 381-387                                                                                                                                                        
[13]Mefoued, S., 2015. "A second order sliding mode control and a neural network to drive a knee joint actuated orthosis," Neurocomputing, 155, pp. 71-79.
[14]Shafiei, S. E., Soltanpour, M. R.,2011. "Neural network sliding-mode-PID controller design for electrically driven robot manipulators," International Journal of Innovative Computing, Information and Control, 7, pp. 511-524.
[15]Guo, Y., Woo, P.-Y., 2003. " An adaptive fuzzy sliding mode controller for robotic manipulators", IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 33, pp. 149-159.
[16]Shakki, S., Zakerzadeh, M. R.,2016." Modeling and control of a shape memory alloy actuator using fuzzy sliding mode controller". Modares Mechanical Engineering, 16( 7), pp. 353-360 (in Persian).
[17]Yousefi, F., Alipour, Kh., Tarvirdizadeh, B., Hadi, A.,2016." Control of knee rehabilitation robot based on combination of backstepping and admittance algorithms". Modares Mechanical Engineering, 16(12), pp. 135-143 (in Persian).
[18]Rifai, H., Mohammed, S., Daachi, B., Amirat, Y.,2012. "Adaptive control of a human-driven knee joint orthosis," in Robotics and Automation (ICRA), 2012 IEEE International Conference on , pp. 2486-2491.
[19] Daachia, Madanib, M.E., Daachib, B., 2015. "A radial basis function neural network adaptive controller to drivea powered lower limb knee joint orthosis". Applied Soft Computing, 34, pp. 324–336.
[20] Rifai, H., Mohammed, S., Daachi, B., Amirat, Y., 2016."  Toward Lower Limbs Functional Rehabilitation Through a Knee-Joint Exoskeleton". IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, pp. 1063-6536.
[21]Benbrahim M., Essounbouli N., Hamzaoui A., Betta A.,2013. "Adaptive type-2 fuzzy sliding mode controller for SISO nonlinear systems subject to actuator faults". International Journal of Automation and Computing, 10, pp. 335-342.
[22]Chang, M.-K., 2010."An adaptive self-organizing fuzzy sliding mode controller for a 2-DOF rehabilitation robot actuated by pneumatic muscle actuators". Control Engineering Practice, 18, pp. 13-22.
[23]Trelea, I. C.,2003. "The particle swarm optimization algorithm: convergence analysis and parameter selection," Information processing letters , 85, pp. 317-325.
[24]Nejat, A., Kaviani, H. R., 2016. "Aerodynamic optimization of a megawatt class horizontal axis wind turbine blade with particle swarm optimization algorithm". Modares Mechanical Engineering, 99, pp. 9-99  (in Persian).
[25]Mohammed, S., Huo, W., Rifaï, H., Hassani, W., Amirat, Y., 2015. "Robust Control of an Actuated Orthosis for Lower Limb Movement Restoration," in Intelligent Assistive Robots, ed: Springer , pp. 385-400.
[26]Mefoued, S., 2014. "A robust adaptive neural control scheme to drive an actuated orthosis for assistance of knee movements" .Neurocomputing, 140, pp. 27-40.
[27] Chen, W-H., Ballance, D., Gawthrop, P., Gribble, J., 1999." A Nonlinear Disturbance Observer for Two Link Robotic Manipulators". Proceedings of the 38th Conference on Decision & Control, pp. 3410-3415.
[28] Chen, W-H., 2004."  Disturbance Observer Based Control for Nonlinear Systems". IEEE/ASME TRANSACTIONS ON MECHATRONICS, 9(4), pp.706-710.
[29]Xing, K., Huang, J., Wang, Y., Wu, J., Xu, Q., He, J., 2010."Tracking control of pneumatic artificial muscle actuators based on sliding mode and non-linear disturbance observer".IET control theory & applications, 4, pp. 2058-2070.
[30]Huo, W., Mohammed, S., Amirat, Y., 2015. " Observer-Based Active Impedance Control of a Knee-Joint Assistive Orthosis". IEEE International Conference on Rehabilitation Robotics (ICORR), pp. 313-318.
[31]Li, C., Deng, W, 2007. "Remarks on fractional derivatives," Applied Mathematics and Computation, 187, pp. 777-784.
[32]Park, K. B., Tsuji, T., 1999. "Terminal sliding mode control of second‐order nonlinear uncertain systems". International Journal of Robust and Nonlinear Control, 9, pp. 769-780.
[33]Aguila-Camacho, N., Duarte-Mermoud, M. A., Gallegos, J. A.,2014 "Lyapunov functions for fractional order systems". Communications in Nonlinear Science and Numerical Simulation, 19, pp. 2951-2957.
[34]  Mohadeszadeh M., Delavari H., A. 2017." Synchronization of uncertain fractional-order hyper-chaotic systems via a novel adaptive interval type-2 fuzzy active sliding mode controller". International Journal of Dynamics and Control, 5, pp. 135–144.
[35]Mottahedi, A., Akbarzadeh Kalat, A., 2016. "Adaptive robust sliding mode control of quadrotor in the presence of wind/ disturbance". Modares Mechanical Engineering, 16(12), pp. 95-102 (in Persian)
[36]Pourmahmood Aghababa M., 2014. "Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach". Journal of Computational and Nonlinear Dynamics 9(3)pp.1-22 doi: 10.1115/1.4025771.
[37]Chiang, C.-C., Hu, C.-C., 1999. "Adaptive fuzzy controller for nonlinear uncertain systems." in Intelligent Processing and Manufacturing of Materials, 1999. IPMM'99. Proceedings of the Second International Conference on, pp. 1131-1136.
[38]Temeltas, H., 1998. "A fuzzy adaptation technique for sliding mode controllers," in Industrial Electronics. Proceedings. ISIE'98. IEEE International Symposium on,pp. 110-115.
[39]Yang Y., Yang C., Lee K.-M., Yu H., 2009. "Model-based fuzzy adaptation for control of a lower extremity rehabilitation exoskeleton". in Advanced Intelligent Mechatronics. AIM 2009. IEEE/ASME International Conference on, pp. 350-355 [40]    Wang, L., 1997."A course in Fuzzy Systems and Control. New Jersey: Pretice-Hall Internacional". ed: Inc.
[41] Mahmoodabadi, M.J., Taherkhorsandi, M., Bagheri A.,2014. " Optimal Robust Sliding Mode Tracking Control of a Biped Robot Based on Ingenious Multi-objective PSO". Neurocomputing, 124, pp. 194-209.
[42]Allouani1, A., Boukhetala, D.,  Boudjema, F., 2012." Particle swarm optimization based fuzzy sliding mode controller for the Twin Rotor MIMO system". Nonlinear Dynamic, 74, pp. 467–478.
[43]Atyabi, A., Phon-Amnuaisuk, S., Ho, C. K., 2010. "Applying area extension PSO in robotic swarm," Journal of Intelligent & Robotic Systems, 58, pp. 253-285.
[44]Shi, Y., Eberhart, R., 1998."A modified particle swarm optimizer". in Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on, pp. 69-73.
[45]Faieghi, M. R., Delavari, H., Baleanu, D., 2012." A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations ", 17, pp. 1021-1030.
Amirkabir Journal of Mechanical Engineering
Volume 51, Issue 3
July and August 2019
Pages 151-160

Files

Share

How to cite

Statistics