Control of Flexible Beam with Unmodelled Dynamics Using Second-Order Pole Placement and LQR Techniques

Abstract:

Control of a flexible beam such as that in flexible-link robot manipulators in many mechanical devices is very challenging, due in part to its intrinsic nature of unmodelled dynamics in a system. Such a system is said to be subjected to nonholonomic constraints, hence its feedback control is difficult to realize. This paper presents the application of control design based on second-order pole placement and LQR approaches to a single-link flexible robotic arm. In this case, a controller considering the flexibility of highly-flexible arm is employed to suppress the tip vibration of the manipulator. The effectiveness of the method is verified through computer simulations and consequently, the adequateness of the control performance and the feasibility of the system with a super-light link are shown.

• Periodical: Applied Mechanics and Materials (Volume 393)
• Pages: 675-682
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.393.675
• Online since: September 2013
• Authors: Z.A. Rahman, A.A. Mat Isa, Haydar H. Ali, M.A. Anuar
• Keywords: Flexible Beam, Linear Quadratic Regulator, Performance Index, Second-Order Pole Placement

References

[1] Martins, J.M., Mohamed, Z., Tokhi, M.O., Sá da Costa, J. and Botto, M.A., Approaches for dynamic modelling of flexible manipulator systems. IEEE Proceedings-Control Theory and Application, 2003. 150(4): pp.401-411.

DOI: 10.1049/ip-cta:20030496

[2] Mansour, T., A. Konno, and M. Uchiyama, Modified PID Control of a Single-Link Flexible Robot Advanced Robotics, 2008. 22(4): pp.433-449.

DOI: 10.1163/156855308x294671

[3] Cannon, R.H. and E. Schmitz, Initial experiment on the end-point control of a flexible one-link robot. International Journal of Robotics Research, 1984. 3(3): pp.62-75.

DOI: 10.1177/027836498400300303

[4] Hasting, G.G. and W.J. Book, A linear dynamic model for flexible robot manipulators. IEEE Control Systems Magazine, 1987. 7: pp.61-64.

[5] A. Arisoy, M.G., O.S. Bogosyan Partial Feedback Linearization Control of A Single Flexible Link Robot Manipulator in IEEE Proceedings of 2nd International Conference on Recent Advances in Space Technologies. (2005).

DOI: 10.1109/rast.2005.1512577

[6] Moser, A.N., Designing controllers for flexible structures with H-infinity/μ-synthesis IEEE Control Systems Magazine, 1993. 13(2): pp.79-89.

DOI: 10.1109/37.206989

[7] Feliu, V., Rattan, K.S. and Brown, H.B., Adaptive control of a single-link flexible manipulator. IEEE Control Systems Magazine, 1990. 10(2): pp.29-33.

DOI: 10.1109/37.45791

[8] Moallem, M., Khorasani, K. and Patel, R.V., Inversion-based sliding control of a flexible-link manipulator. International Journal of Control, 1998. 71(3): pp.477-490.

DOI: 10.1080/002071798221786

[9] Gutierrez, L.B., Lewis, P.L. and Lowe, J.A., Implementation of a neural network tracking controller for a single flexible link: comparison with PD and PID controllers. IEEE Transactions on Industrial Electronics, 1998. 45(3): pp.307-318.

DOI: 10.1109/41.681230

[10] Yuan-Gang T., F. -C.S., Zeng-Qi S., and Ting-Liang H., Tip Position Control of a Flexible-Link Manipulator with Neural Networks. International Journal of Control, Automation, and Systems, 2006. 4(3): pp.308-317.

[11] Moudgal, V.G., Passino, K.M. and Yurkovich, S., Rule-based control for a flexible-link robot. IEEE Transactions on Control Systems Technology, 1994. 2(4): pp.392-405.

DOI: 10.1109/87.338648

[12] Loudini, M., Timoshenko Beam Theory based Dynamic Modeling of Lightweight Flexible Link Robotic Manipulators, in Advances in Robot Manipulators, E.H. (Ed. ), Editor. 2010. pp.625-650.

DOI: 10.5772/9661

[13] Subudhi, B. a.M., A.S., Dynamic modelling, simulation and control of a manipulator with flexible links and joints. Robotics and Autonomous Systems, 2002. 41: pp.257-270.

DOI: 10.1016/s0921-8890(02)00295-6

[14] Azad, A.K.M., and Tokhi, M.O., Contro Engineering Series. Flexible Robot Manipulators: Modelling, simulation and control. Vol. 68. 2008, London, United Kingdom: The Institution of Engineering and Technology.

[15] Quanser, Student Handout. Rotary Flexible Joint Module.

[16] Franklin, G.F., J.D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems. 1987: Addison-Wesley Publishing Company Inc.

[17] Mariam B., M.S., Walid G., State-Feedback and Linear Quadratic Regulator Applied to a Single-Link Flexible Manipulator. Proceedings of the 2009 IEEE International Conference on Robotics and Biomimetics, 2009: pp.1381-1386.

DOI: 10.1109/robio.2009.5420822