Polytopic Linear Models-Based Output Tracking Control of a Single-Link Flexible Joint Robot Manipulator

Document Type : Research Article

Authors

Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran.

Abstract

In this paper, to solve the output tracking problem of a single-link flexible joint manipulator, Polytopic Linear Models (PLMs) of the dynamics are made to take advantage of this method. Although linear control methods are very useful due to their powerful theories and simplicity, they can only be used in a neighborhood of the equilibrium point. One way to solve this problem is a PLMs-based method that linearizes the dynamics around several operating points. Therefore, in this paper, after calculating the PLMs of the manipulator, a state feedback control is applied to the derived linear dynamics that are augmented with the dynamics of the output tracking error. An extended method is used to decompose the scheduling space to construct PLMs, which is the segregation method improved with an extra aggregation. In order to avoid creating a large number of local models, an axis-oblique decomposition strategy is used instead of an axis-orthogonal decomposition. In addition, the scheduling functions of the PLMs are determined such that overlaps between the regions are avoided. By this selection, the output tracking problem becomes as a Linear Matrix Inequality (LMI) problem instead of a bilinear matrix inequality problem, which is more difficult to solve and may not lead to an optimal global solution.

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Main Subjects


[1] D. Meng, Y. She, W. Xu, W. Lu, and B. Liang, "Dynamic modeling and vibration characteristics analysis of flexible-link and flexible-joint space manipulator," Multibody System Dynamics, vol. 43, no. 4, pp. 321-347, 2018.
[2] M. A. Mabrok, "New results on negative imaginary systems theory with application to flexible structures and nano-positioning," Australian Defence Force Academy, 2013.
[3] I. H. Akyuz, E. Yolacan, H. M. Ertunc, and Z. Bingul, "PID and state feedback control of a single-link flexible joint robot manipulator," in IEEE International Conference on Mechatronics, 2011, pp. 409-414.
[4] Y. Li, S. S. Ge, Q. Wei, T. Gan, and X. Tao, "An online trajectory planning method of a flexible-link manipulator aiming at vibration suppression," IEEE Access, vol. 8, pp. 130616-130632, 2020.
[5] O. A. Garcia-Perez, G. Silva-Navarro, and J. F. Peza-Solis, "Flexible-link robots with combined trajectory tracking and vibration control," Applied Mathematical Modelling, vol. 70, pp. 285-298, 2019.
[6]  L. Sun, W. Yin, M. Wang, and J. Liu, "Position control for flexible joint robot based on online gravity compensation with vibration suppression," IEEE Transactions on Industrial Electronics, vol. 65, no. 6, pp. 4840-4848, 2017.
[7]  D. Subedi, I. Tyapin, and G. Hovland, "Review on modeling and control of flexible link manipulators," Modeling, Identification and Control, vol. 41, no. 3, pp. 141-163, 2021.
[8] S. Ozgoli and H. Taghirad, "A survey on the control of flexible joint robots," Asian Journal of Control, vol. 8, no. 4, pp. 332-344, 2006.
[9] O. Khan, M. Pervaiz, E. Ahmad, and J. Iqbal, "On the derivation of novel model and sophisticated control of flexible joint manipulator," Revue Roumaine des Sciences Techniques - Serie Électrotechnique et Énergétique, vol. 62, pp. 103-108, 2017.
[10] N. Razmjooy, M. Ramezani, and A. Namadchian, "A new LQR optimal control for a single-link flexible joint robot manipulator based on grey wolf optimizer," vol. 10, p. 53, 2016.
[11] K. Ibrahim and A. B. Sharkawy, "A hybrid PID control scheme for flexible joint manipulators and a comparison with sliding mode control," Ain Shams Engineering Journal, vol. 9, no. 4, pp. 3451-3457, 2018.
[12] L. L. Tien, A. A. Schaffer, and G. Hirzinger, "MIMO state feedback controller for a flexible joint robot with strong joint coupling," in IEEE International Conference on Robotics and Automation, 2007, pp. 3824-3830.
[13]K. Khorasani, "Adaptive control of flexible joint robots," in IEEE International Conference on Robotics and Automation, 1991, pp. 2127-2134.
[14]  G. Yang, Y. Liu, M. Jin, and H. Liu, "A robust and adaptive control method for flexible-joint manipulator capturing a tumbling satellite," IEEE Access, vol. 7, pp. 159971-159985, 2019.
[15]H. Ma, H. Li, H. Ren, and Q. Zhou, "Adaptive fuzzy control for a single-link flexible-joint robotic manipulator with output constraint," in 7th International Conference on Information, Cybernetics, and Computational Social Systems, 2020, pp. 46-51.
[16] J. Tavoosi and F. Mohammadi, "A new type-II fuzzy system for flexible-joint robot arm control," in 6th International Conference on Control, Instrumentation and Automation, 2019, pp. 1-4.
[17] X. Cheng, H. Liu, and W. Lu, "Chattering-suppressed sliding mode control for flexible-joint robot manipulators," Actuators, vol. 10, no. 11, p. 288, 2021.
[18] S. zaare, M. R. Soltanpour, and M. Moattari, "Voltage based sliding mode control of flexible joint robot manipulators in presence of uncertainties," Robotics and Autonomous Systems, vol. 118, pp. 204-219, 2019.
[19] K. Rsetam, Z. Cao, and Z. Man, "Hierarchical sliding mode control applied to a single-link flexible joint robot manipulator," in International Conference on Advanced Mechatronic Systems, 2016, pp. 476-481.
[20] W. He, Z. Yan, Y. Sun, Y. Ou, and C. Sun, "Neural-learning-based control for a constrained robotic manipulator with flexible joints," IEEE Transactions on Neural Networks and Learning Systems, vol. 29, pp. 5993-6003, 2018.
[21] X. Liu, C. Yang, Z. Chen, M. Wang, and C.-Y. Su, "Neuro-adaptive observer based control of flexible joint robot," Neurocomputing, vol. 275, pp. 73-82, 2018.
[22] M. B. A. Jabali and M. H. Kazemi, "Uncertain polytopic LPV modelling of robot manipulators and trajectory tracking," International Journal of Control, Automation and Systems, vol. 15, no. 2, pp. 883-891, 2017/04/01 2017, doi: 10.1007/s12555-015-1432-1.
[23]A. Fazli and M. H. Kazemi, "Manipulator Dynamic Nonlinearity Approximation Based on Polytopic LPV Modeling for Robot Tracking Control Problem," Iranian Journal of Science and Technology, Transactions of Electrical Engineering, vol. 46, no. 2, pp. 537-547, 2022/06/01 2022, doi: 10.1007/s40998-021-00477-y.
[24]H. S. Ali, M. Darouach, L. Boutat-Baddas, and Y. Becis-Aubry, "ℋ<inf>∞</inf> state feedback LPV control of a SCARA robot," in 2007 European Control Conference (ECC), 2-5 July 2007 2007, pp. 4222-4227, doi: 10.23919/ECC.2007.7068605.
[25]  A. GZ, System analysis, modeling and control with Polytopic Linear Models. Universiteitsdrukkerij TU Eindhoven, Eindhoven, The Netherlands, 2003.
[26]  O. Nelles, Nonlinear system identification from classical approaches to neural networks and fuzzy models. Springer Nature, 2020.