A general approach to dynamic gain adaptation of sliding mode control for robotic arms with parameter uncertainty
Abstract
Facing parameter uncertainty is inevitable in control systems. Sliding mode control (SMC) is robust to uncertainty. To lead the system’s states towards a sliding surface and keep them there, the control input is required and it must include an additional discontinuous part. This part has a gain where its magnitude defines as the rate of this action. Setting the gain more than enough produces undesirable effects such as extra pressure and chattering on actuators. Hence, computing the precise gain is essential based on the sliding condition. In this paper, a general approach was introduced to specify adaptive gains of the SMC, regarding the sliding condition for multi-input multi-output (MIMO) systems. Adaptation of control gains, results in control effort reduction and weakening of the chattering phenomenon. To minimize the chattering even more, inverse tangent was used instead of sign function in control law and the structure of adaptive gain with this change is presented. The proposed formulation was applied on a planar arm and 6R robot to show precision and control effort reduction of the adaptive gain of the sliding mode controller. A comparison between the proposed method and conventional SMC was carried out to confirm the statement; and at the end, the proposed method is conducted on 6R robot experimentally.
References
[2] F.-C. Sun, Z.-Q. Sun, and G. Feng, "An adaptive fuzzy controller based on sliding mode for robot manipulators," Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 29, pp. 661-667, 1999.
[3] M. H. Korayem, A. Khademi, and S. R. Nekoo, "A comparative study on SMC, OSMC and SDRE for robot control," in Robotics and Mechatronics (ICRoM), 2014 Second RSI/ISM International Conference on, 2014, pp. 013-018.
[4] L. Wong, F. Leung, and P. Tam, "A chattering elimination algorithm for sliding mode control of uncertain non-linear systems," Mechatronics, vol. 8, pp. 765-775, 1998.
[5] S. Zeghlache, D. Saigaa, K. Kara, A. Harrag, and A. Bouguerra, "Fuzzy sliding mode control with chattering elimination for a quadrotor helicopter in vertical flight," in Hybrid Artificial Intelligent Systems, ed: Springer, 2012, pp. 125-136.
[6] M. Ertugrul, O. Kaynak, and F. Kerestecioglu, "Gain adaptation in sliding mode control of robotic manipulators," International Journal of Systems Science, vol. 31, pp. 1099-1106, 2000.
[7] J.-S. Park, G.-S. Han, H.-S. Ahn, and D.-H. Kim, "Adaptive approaches on the sliding mode control of robot manipulators," Transactions on Control, Automation and Systems Engineering, vol. 3, pp. 15-20, 2001.
[8] M. M. Abdelhameed, "Enhancement of sliding mode controller by fuzzy logic with application to robotic manipulators," Mechatronics, vol. 15, pp. 439-458, 2005.
[9] Y.-J. Huang, T.-C. Kuo, and S.-H. Chang, "Adaptive sliding-mode control for nonlinearsystems with uncertain parameters," Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 38, pp. 534-539, 2008.
[10] T. Sun, H. Pei, Y. Pan, H. Zhou, and C. Zhang, "Neural network-based sliding mode adaptive control for robot manipulators," Neurocomputing, vol. 74, pp. 2377-2384, 2011.
[11] M. Korayem, H. Ghariblu, and A. Basu, "Maximum allowable load of mobile manipulators for two given end points of end effector," The International Journal of Advanced Manufacturing Technology, vol. 24, pp. 743-751, 2004.
[12] M. Korayem, A. Heidari, and A. Nikoobin, "Maximum allowable dynamic load of flexible mobile manipulators using finite element approach," The International journal of advanced manufacturing technology, vol. 36, pp. 606-617, 2008.
[13] M. Korayem, V. Azimirad, A. Nikoobin, and Z. Boroujeni, "Maximum load-carrying capacity of autonomous mobile manipulator in an environment with obstacle considering tip over stability," The International Journal of Advanced Manufacturing Technology, vol. 46, pp. 811-829, 2010.
[14] M. Korayem and A. Nikoobin, "Maximum payload path planning for redundant manipulator using indirect solution of optimal control problem," The International Journal of Advanced Manufacturing Technology, vol. 44, pp. 725-736, 2009.
[15] M. Korayem and A. Nikoobin, "Maximum payload for flexible joint manipulators in point-to-point task using optimal control approach," The International Journal of Advanced Manufacturing Technology, vol. 38, pp. 1045-1060, 2008.
[16] J.-J. E. Slotine and W. Li, Applied nonlinear control vol. 60: Prentice-Hall Englewood Cliffs, NJ, 1991.
[17] M. H. Korayem and S. R. Nekoo, "Nonlinear optimal control via finite time horizon state-dependent Riccati equation," in Robotics and Mechatronics (ICRoM), 2014 Second RSI/ISM International Conference on, 2014, pp. 878-883.
[18] M. Korayem and S. Nekoo, "Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control," ISA transactions, vol. 54, pp. 125-144, 2015.
[19] M. Korayem and S. Nekoo, "State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities," ISA transactions, 2015.
