Position Control Of A Stewart Platform using Dynamic Matrix Control

  • Soheil Sheikh Ahmadi Mechatronics Research Laboratory, School of Engineering Emerging Technologies, University of Tabriz, Iran.
  • Arash Rahmani Faculty of Mechanical Engineering, Urmia University of Technology, Iran.
Keywords: Dynamic Matrix Control, Model Predictive Control, Cost Function, Stewart Platform

Abstract

This paper presents a Dynamic Matrix Controller (DMC) for six-degree-of-freedom (6-DOF) Stewart platform based on the parallel mechanism in order to track the reference trajectory in the mechanism workspace. Dynamic matrix control is a particular type of model predictive control (MPC), which are framed as advanced controllers. This controller is an industrial controller that is utilized based on the system step response coefficients. The DMC showed robust performance for different size of input signals, and prediction and control windows. This method is a generalization of pole placement methods and optimal control. In addition, this method showed good tracking performance and benefit when considering input or output constraints, which is often the case in real industrial systems.

References

[1] Stewart, D., A platform with six degrees of freedom, In Proc. Inst. Mech. Eng., London, Vol. 180, No. 15, pp. 371-386, 1965. [2] F. Persson, H. Hvittfeldt, J. Larsson and P. Mikaelsson, Industrial Robot., United states patent No. 7,188, 544 B2, 2007.
[3] Lars Grüne, Jürgen Pannek, “Nonlinear Model Predictive Control: Theory and Algorithms”, Publisher, Springer Science & Business Media, 2011,ISBN 0857295012, 9780857295019
[4] James Blake Rawlings, David Q. Mayne, “Model Predictive Control: Theory and Design”, Publisher Nob Hill Pub., 2009, ISBN 0975937707, 9780975937709
[5] Liuping Wang,” Model Predictive Control System Design and Implementation Using MATLAB®”,
[6] Pedrammehr Siamak, Mahboubkhah Mehran, Khani Navid, “Improved dynamic equations for the generally configured Stewart platform manipulator”, Journal of Mechanical Science and Technology, Vol 26, pp. 711-721,2012
[7] R. Oftadeh, M. M. Aref and H. D. Taghirad, "Explicit Dynamics Formulation of Stewart-Gough Platform: A Newton-Euler Approach ", IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, 2010.
[8] Zhaoqi He, Xigeng Song, Dongxin Xue, Comments to the: “Closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach” and “A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator”, Mechanism and Machine Theory, Volume 102, August 2016, Pages 229-231, ISSN 0094-114X,
[9] Kalani Hadi, Rezaei Amir, Akbarzadeh Alireza, “Improved general solution for the dynamic modeling of Gough–Stewart platform podd on principle of virtual work”, Journal of Nonlinear Dynamics, pp. 1-26, 2015
[10] Hu B et al (2012) Analyses of inverse kinematics, statics and workspace of a novel 3RPS-3SPR serial–parallel manipulator. Open Mech Eng. J 6:65–72
[11] Gallardo-Alvarado J et al (2008) Kinematics and dynamics of 2 (3-RPS) manipulators by means of screw theory and the principle of virtual work. Mech Mach Theory 43(10):1281–1294
[12] Lung-Wen Tsai, “Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work”, J. Mech. 1999,7 pages doi:10. 1115/1. 533540
[13] FU Shao-wen, YAO Yu, “Adaptive robust control design with inverse dynamic compensation for Stewart platform manipulator”, Journal of Electric Machines and Control, 2007
[14] Guo, H., and Li, H., 2006, “Dynamic Analysis and Simulation of a Six Degree of Freedom Stewart Platform Manipulator,” Proc. Inst. Mech. Eng., Part C, 220(1), pp. 61–72.
[15] Ghosh BB, Sarkar BK, Saha R. Realtime performance analysis of different combinations of fuzzy-PID and bias controllers for a two degree of freedom electrohydraulic parallel manipulator. Robot Cim-Int Manuf 2015; 34: 62–69.
[16] S.-H. Lee, J.-B. Song, W.-C. Choi, and D. Hong, "Position control of a Stewart platform using inverse dynamics control with approximate dynamics," MECHATRONICS, 2003.
[17] P. Kumar, A. Chalanga, B. Bandyopadhyay, "Position control of Stewart platform using continuous higher order sliding mode control", Asian Control Conference (ASCC), vol. 10, pp. 1-6, May 2015.
[18] Qian Men, Tao Zhang, Xiang Gao, Jing-yen Song, "Adaptive Sliding Mode Fault-Tolerant Control of the Uncertain Stewart Platform Podd on Offline Multibody Dynamics", Mechatronics IEEE/ASME Transactions on, vol. 19, pp. 882-894, 2014, ISSN 1083-4435.
[19] Ramesh Kumar P., Asif Challenge, B. Bandyopadhyay, "Smooth integral sliding mode controller for the position control of Stewart platform", ISA Transactions, pp., 2015, ISSN 00190578.
[20] S. Chen, L. Fu, "Output feedback sliding mode control for a Stewart platform with a nonlinear observer-podd forward kinematics solution", IEEE Trans. Control Syst. Technol., vol. 21, no. 1, pp. 176-185, Jan. 2013.
[21] H. S. Kim, Y. M. Cho, K. Lee, "Robust nonlinear task space control for 6 DOF parallel manipulator", Automatic a, vol. 41, no. 9, pp. 1591-1600, 2005.
[22] Mauricio Becerra-Vargas, Eduardo Morgado Belo, “Application of H∞ theory to a 6 DOF flight simulator motion pod”, J. Braz. Soc. Mech. Sci. & Eng. vol. 34 no. 2 Rio de Janeiro Apr June 2012
[23] Zude Zhou, Wei Meng, Qingsong Ai, Quan Liu, Xiang Wu, “Practical Velocity Tracking Control of a Parallel Robot Podd on Fuzzy Adaptive Algorithm”, Journal of Advances in Mechanical Engineering vol. 5 574896, 2013
[24] Rahmani Arash, Ghanbari Ahmad, “Application of neural network training in forward kinematics simulation for a novel modular hybrid manipulator with experimental validation”, Journal of Intelligent Service Robotics, Vol 9, pp. 79-91, 2016
[25] C. R. Cutler, B. L. Ramaker, "Dynamic matrix control—a computer control algorithm", AIChE National Meeting, 1979-Apr.
[26] E. Camacho, C. Bordons, Model Predictive Control, New York: Springer-Verlag, 1999.
[27] Daniel Martins Lima, Julio Elias Normey-Rico, Tito Luís Maia Santos, “Temperature control in a solar collector field using Filtered Dynamic Matrix Control”, ISA Transactions, Volume 62, May 2016, Pages 39-49, ISSN 0019-0578
[28] Peyman Bagheri, Ali Khaki-Sedigh, Tuning of Dynamic Matrix Controller for FOPDT Models Using Analysis of Variance, IFAC Proceedings Volumes, Volume 44, Issue 1, 2011, Pages 12319-12324, ISSN 1474-6670,
[29] Clemente Manzanera Reverter, Julio Ibarrola, José-Manuel Cano-Izquierdo, Tuning rules for a quick start up in Dynamic Matrix Control, ISA Transactions, Volume 53, Issue 2, March 2014, Pages 612-627, ISSN 0019-0578,
[30] Peyman Bagheri, Ali Khaki Sedigh, Robust tuning of dynamic matrix controllers for first order plus dead time models, Applied Mathematical Modelling, Volume 39, Issue 22, 15 November 2015, Pages 7017-7031, ISSN 0307-904X,
Published
2020-03-01
How to Cite
Sheikh Ahmadi, S., & Rahmani, A. (2020). Position Control Of A Stewart Platform using Dynamic Matrix Control. Majlesi Journal of Mechatronic Systems, 9(1), 37-46. Retrieved from http://journals.iaumajlesi.ac.ir/ms/index/index.php/ms/article/view/437
Section
Articles