End Point Force Control of a Flexible Timoshenko Arm

Minoru Sasaki¹, Kouki Nagaya¹, Takahiro Endo², Kojiro Matsushita¹, Satoshi Ito¹

¹Department of Mechanical Engineering, Gifu University, Gifu, Japan.
²Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto, Japan.

DOI: 10.4236/jcc.2015.311017                

Abstract

This paper discusses a force control problem for a flexible Timoshenko arm. The effect of shear deformation and the effect of rotary inertia are considered in Timoshenko beam theory. Most of the research about force control of the flexible arm is based on Euler Bernoulli beam theory. There are a few researches about force control of the flexible arm using Timoshenko beam theory. The aim of the force control is to control the contact force at the contact point. To solve this problem, we propose a simple controller using Timoshenko beam theory. Finally, we describe simulation results using a numerical inversion of Laplace transform carried out to investigate the validity of the proposed controller for the force control problem. The results of the time response show the transverse displacement, the angle of deflection, the slider position, the rotational angle and the contact force toward the desired their values.

Keywords

Flexible Arm, Timoshenko Beam Theory, Force Control, Distributed Parameter Systems Control, Laplace Transform

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Yuan, K. and Hu, C.-M. (1996) Nonlinear Modeling and Partial Linearizing Control of a Slewing Timoshenko-Beam. Trans. ASME Journal of Dynamic Systems, Measurement, and Control, 118, 75-83. http://dx.doi.org/10.1115/1.2801154
[2]	Tadi, M. (1997) Comparison of Two Finite-Element Schemes for Feedback Control of a Timoshenko Beam. Proceedings of the ASME Dynamic Systems and Control Division, 61, 587-596.
[3]	White, M.H.D. and Heppler, G.R. (1996) Vibration of a Rotating Timoshenko Beam. Trans. ASME Journal of Vibration and Acoustic, 118, 606-613. http://dx.doi.org/10.1115/1.2888341
[4]	Sasaki, M., Ueda, T., Inoue, Y. and Book, W.J. (2012) Passivity-Based Control of Rotational and Translational Timoshenko Arms. Advances in Acoustics and Vibration, 2012, Article ID: 174816. http://dx.doi.org/10.1155/2012/174816
[5]	Morgül, ?. (1992) Dynamic Boundary Control of the Timoshenko Beam. Automatica, 28, 1255-1260. http://dx.doi.org/10.1016/0005-1098(92)90070-V
[6]	Oguamanam, D.C.D. and Heppler, G.R. (1996) The Effect of Rotating Speed on the Flexural Vibration of a Timoshenko Beam. Proc. of the 1996 IEEE International Conference on Robotics and Automation, 2438-2443. http://dx.doi.org/10.1109/ROBOT.1996.506529
[7]	Zhang, F., Dawson, D.M., de Queiroz, M.S. and Vedagarbha, P. (1997) Boundary Control of the Timoshenko Beam with Free-End Mass/Inertial Dynamics. Proc. of the 36th IEEE Conference on Decision & Control, 245-250. http://dx.doi.org/10.1109/CDC.1997.650623
[8]	Taylor, S.W. and Yau, S.C.B. (2003) Boundary Control of a Rotating Timoshenko Beam. ANZIAM J., 44, E143-E184.
[9]	Rastgoftar, H., Mahmoodi, M., Eghtesad, M. and Kazemi, M. (2008) Stability Analysis of a Flexible Two-Link Timoshenko Manipulator Using Boundary Control Method. Proc. of ASME 2008 International Mechanical Engineering Congress and Exposition, 409-415.
[10]	Grobbelaar-Van Dalsen, M. (2010) Uniform Stability for the Timoshenko Beam with Tip Load. J. Math. Anal. Appl., 361, 392-400. http://dx.doi.org/10.1016/j.jmaa.2009.06.059
[11]	Han, Z.J. and Xu, G.Q. (2011) Dynamical Behavior of a Hybrid System of Nonhomogeneous Timoshenko Beam with Partial Non-Collocated Inputs. J. Dyn. Control Syst., 17, 77-121. http://dx.doi.org/10.1007/s10883-011-9111-6
[12]	Hosono, T. (1981) Numerical Inversion of Laplace Transform and Some Application to Wave Optics. Radio Science, 16, 1015. http://dx.doi.org/10.1029/RS016i006p01015
[13]	Endo, T., Matsuno, F. and Kawasaki, H. (2014) Force Control and Exponential Stabilisation of One-Link Flexible Arm. Int. J. Control, 87, 1794-1807. http://dx.doi.org/10.1080/00207179.2014.889854