Optimal Controller with Backstepping and BELBIC for Single-Link Flexible Manipulator

Authors: Ali Reza Sahab, Amir Gholami Pastaki

Abstract:

In this paper, backstepping method (BM) is proposed for a single-link flexible mechanical manipulator. In each step of this method a positive value is obtained. Selections of the gain factor values are very important because controller will have different behavior for each different set of values. Improper selection of these gains can lead to instability of the system. In order to choose proper values for gains BELBIC method has been used in this work. Finally, to prove the efficiency of this method, the obtained results of proposed model are compared with robust controller one. Results show that the combination of backstepping and BELBIC that is presented here, can stabilized the system with higher speed, shorter settling time and lower overshoot in than robust controller.

Keywords: single-link flexible manipulator, backstepping, BELBIC

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1086239

References:

[1] Vicente Feliu, Emiliano Pereira, Iv'an M. D'─▒az, Pedro Roncero, "Feed forward control of multimode single-link flexible manipulators based on an optimal mechanical design", Robotics and Autonomous Systems 54 (2006) 651-666.
[2] M.S. Alam, M.O. Tokhi, "Designing feed forward command shapers with multi-objective genetic optimization for vibration control of a single-link flexible manipulator", Engineering Applications of Artificial Intelligence 21 (2008) 229-246.A. Alpher. Frobnication. Journal of Foo, 12(1):234-778, 2002.
[3] M.S. Alam_, M.O. Tokhi, "Hybrid fuzzy logic control with genetic optimization for a single-link flexible manipulator", Engineering Applications of Artificial Intelligence 21 (2008) 858-873.
[4] Kerem Gurses, Bradley J. Buckham, Edward J. Park, "Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators", Mechatronics 19 (2009) 167-177.
[5] Dong Sun, James K. Mills, Jinjun Shan, S.K. Tso, "A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement", Mechatronics 14 (2004) 381-401.
[6] Barun Pratiher, Santosha K. Dwivedy, "Non-linear vibration of a single link viscoelastic Cartesian manipulator", International Journal of Non- Linear Mechanics 43 (2008) 683-696.
[7] Ho-Cheol Shin, Seung-Bok Choi, "Position control of a two-link flexible manipulator featuring piezoelectric actuators and sensors", Mechatronics 11 (2001) 707-729.
[8] Ismael Payo, Vicente Feliu, Osvaldo Daniel Cortazar, "Force control of a very lightweight single-link flexible arm based on coupling torque feedback", Mechatronics 19 (2009) 334-347.
[9] K. Liu and X.sun, "System Identification and Model Reduction For A Single-link Flexible Manipulator" , Journal of Sound and vibration (2001) 242(5), 867-891.
[10] S.B. Choi, J.W. Cheon, "Vibration control of a single-link flexible arm subjected to disturbances", Journal of Sound and Vibration 271 (2004) 1147-1156.
[11] V. Feliu, F. Ramos, "Strain gauge based control of single-link flexible very lightweight robots robust to payload changes", Mechatronics 15 (2005) 547-571.
[12] S.S. Ge, T.H.Lee, J.Q.Gong, "A robust distributed controller of a singlelink SCARA/Cartesian smart materials robot", Mechatronics 9 (1999) 65-93.
[13] Y. Cao, V.J. Modi, C.W. de Silva, M. Chu, Y. Chen, A.K. Misra, "Trajectory tracking experiments using a novel manipulator", Acta Astronautica 52 (2003) 523 - 540.
[14] Jhih-Wei Huang, Jung-Shan Lin, "Backstepping Control Design of a Single-Link Flexible Robotic Manipulator", Proceedings of the 17th World Congress, The International Federation of Automatic Control, Seoul, Korea, July 6-11, 2008.
[15] Jong H. Oh, Gin S. Lee, "Control of Flexible Joint Robot system by Backstepping Design Approach", International Conference on Robotics and Automation, Albuquerque, New Mexico, April 1997.
[16] S.S. Mokri, H. Husain, W. Martono and A. Shafie, "Real Time Implementation of NARMA-L2 Control of a Single Link Manipulator", American Journal of Applied Sciences 5 (12): 1642-1649, 2008.
[17] Jinjun Shan, Hong-Tao Liu, Dong Sun, "Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF)", Mechatronics 15 (2005) 487-503.
[18] H. R. Karimi, M. J. Yazdanpanah, "A new modeling approach to singlelink flexible manipulator using singular perturbation method", Electrical Engineering (2006) 88: 375-382.
[19] Woosoon Yim, "Adaptive Control of a Flexible Joint Manipulator", Proceedings of the 2001 IEEE, International Conference on Robotics & Automation, Seoul, Korea. May 21-26, 2001.
[20] An-Chyau Huang and Yuan-Chih Chen, "Adaptive Sliding Control for Single-Link Flexible-Joint Robot with Mismatched Uncertainties", IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 12, NO. 5, SEPTEMBER 2004.
[21] B.A. Md Zain, M. O. Tokhi, and S.F. Toha, "PID-based Control of a Single-Link Flexible Manipulator in Vertical Motion with Genetic Optimisation", 2009 Third UKSim European Symposium on Computer Modeling and Simulation.
[22] B.A. Md Zain, M. O. Tokhi and S. Md Salleh, "Dynamic Modelling of a Single-Link Flexible Manipulator Using Parametric Techniques with Genetic Algorithms", 2009 Third UKSim European Symposium on Computer Modeling and Simulation.
[23] Emiliano Pereira, Sumeet S Aphalet, Vicente Feliu and S O Reza Moheimanit, "A hybrid control strategy for vibration damping and precise tip-positioning of a single-link flexible manipulator", Proceedings of the 2009 IEEE International Conference on Mechatronics. Malaga, Spain, April 2009.
[24] Emiliano Pereira, Sumeet S. Aphale, Vicente Feliu and S. O. Reza Moheimani, "Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator", IEEE/ASME TRANSACTIONS ON MECHATRONICS.
[25] M.-T. Ho and Y.-W. Tu, "Position control of a single-link flexible manipulator using H∞-based PID control", IEE Proc.-Control Theory Appl., Vol. 153, No. 5, September 2006.
[26] G. Surya Kiran, Amit Kumar, Pushparaj M. Pathak, and N. Sukavanam, "Trajectory Control of Flexible Space Robot", Proceedings of 2008 IEEE International Conference on, Mechatronics and Automation.
[27] Withit Chatlatanagulchai and Peter H. Meckl, "Backstepping High- Order Differential Neural Network Control of Flexible-Joint Manipulator", 2005 American Control Conference, June 8-10, 2005. Portland, OR, USA.
[28] Ali Reza Mehrabian, and Caro Lucas, "Emotional Learning based Intelligent Robust Adaptive Controller for Stable Uncertain Nonlinear Systems", INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE VOLUME 2 NUMBER 4 2005 ISSN 1304-4508.
[29] Ali Reza Mehrabian, Caro Lucas, Jafar Roshanian, "Aerospace launch vehicle control: an intelligent adaptive approach", Aerospace Science and Technology 10 (2006) 149-155.
[30] Saeed Jafarzadeh, Rooholah Mirheidari, Mohammad Reza Jahed Motlagh, Mojtaba Barkhordari, "Designing PID and BELBIC Controllers in Path Tracking Problem", Int. J. of Computers, Communications & Control, ISSN 1841-9836, E-ISSN 1841-9844,Vol. III (2008), Suppl. issue: Proceedings of ICCCC 2008, pp. 343-348.
[31] Saeed Jafarzadeh, Rooholah Mirheidari, Mohammad Reza Jahed Motlagh, Mojtaba Barkhordari, "Intelligent Autopilot Control Design for a 2-DOF Helicopter Model", Int. J. of Computers, Communications & Control, ISSN 1841-9836, E-ISSN 1841-9844, Vol. III (2008), Suppl. issue: Proceedings of ICCCC 2008, pp. 337-342.
[32] Ghorbel, F., J. Hung, and M.W. Spong, "Adaptive control of flexiblejoint manipulators". IEEE Control Systems Mag. 9, 1989: p. 9-13.
[33] Sira-Ramirez, H., S. Ahmad, and M. Zribi, "Dynamical feedback control of robot manipulators with joint flexibility". IEEE Trans. Systems Man Cybernet. 22, 1992: p. 736-747.
[34] Ali Reza Sahab, Mohammad Haddad Zarif, "Improve backstepping method to GBM". World Applied Sciences Journal 6 (10): 1399-1403, 2009.
[35] Jeng Tze Huang, "A New Approach to Parametric Identification of a Single-Link Flexible-Joint Manipulator", Journal of Intelligent and Robotic Systems. 37, 3. P.273-284. 2003.