# zbMATH — the first resource for mathematics

A new efficient adaptive control of torsional vibrations induced by switched nonlinear disturbances. (English) Zbl 1430.93123
Summary: Torsional vibrations induced in drilling systems are detrimental to the condition of the machine and to the effectiveness of the engineering process. The cause of vibrations is a nonlinear and unknown friction between a drill string and the environment, containing jumps in its characteristics. Nonlinear behaviour of the friction coefficient results in self-excited vibration and causes undesirable stick-slip oscillations. The aim of this paper is to present a novel adaptive technique of controlling vibrating systems. The scheme is based on the linear quadratic regulator and uses direct measurements of the friction torque to synthesize its linear dynamic approximation. This approach allows generating a control law that takes into account the impact of the friction on the system dynamics and optimally steers the system to the desired trajectory. The controller’s performance is examined via numerical simulations of the stabilization of the drilling system. The proposed solution outperforms the comparative LQG regulator in terms of the minimization of the assumed cost functional and the overall stability of the control system under the nonlinear disturbance.
##### MSC:
 93C40 Adaptive control/observation systems 93C73 Perturbations in control/observation systems 74H50 Random vibrations in dynamical problems in solid mechanics
Full Text:
##### References:
 [1] Alin, A. (2010). Multicollinearity, Wiley Interdisciplinary Reviews: Computational Statistics2(3): 370-374, DOI: 10.1002/wics.84.; [2] Bailey, J.R. and Remmert, S.M. (2010). Managing drilling vibrations through BHA design optimization, SPE Drilling & Completion25(4): 458-471, DOI: 10.2118/139426-PA.; [3] Bajer, C.I., Pisarski, D., Szmidt, T. and Dyniewicz, B. (2017). Intelligent damping layer under a plate subjected to a pair of masses moving in opposite directions, Journal of Sound and Vibration394: 333-347, DOI: 10.1016/j.jsv.2017.01.046.; [4] Christoforou, A.P. and Yigit, A.S. (2003). Fully coupled vibrations of actively controlled drillstrings, Journal of Sound and Vibration267(5): 1029-1045, DOI: 10.1016/S0022-460X(03)00359-6.; [5] Davis, J.E., Smyth, G.F., Bolivar, N. and Pastusek, P.E. (2012). Eliminating stick-slip by managing bit depth of cut and minimizing variable torque in the drillstring, IADC/SPE Drilling Conference and Exhibition, San Diego, CA, USA, pp. 402-410, DOI: 10.2118/151133-MS.; [6] Farrar, D.E. and Glauber, R.R. (1967). Multicollinearity in regression analysis: The problem revisited, The Review of Economics and Statistics49(1): 92-107, DOI: 10.2307/1937887.; [7] Fear, M.J. and Abbassian, F. (1994). Experience in the detection and suppression of torsional vibration from mud logging data, European Petroleum Conference, London, UK, pp. 433-448, DOI: 10.2118/28908-MS.; [8] Hernandez-Suarez, R., Puebla, H., Aguilar-Lopez, R. and Hernandez-Martinez, E. (2009). An integral high-order sliding mode control approach for stick-slip suppression in oil drillstrings, Petroleum Science and Technology27(8): 788-800, DOI: 10.1080/10916460802455483.; [9] Hillsley, K.L. and Yurkovich, S. (1991). Vibration control of a two-link flexible robot arm, 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, USA, Vol. 3, pp. 212-216, DOI: 10.1109/ROBOT.1991.131941.; · Zbl 0800.93825 [10] Jansen, J.D. and van den Steen, L. (1995). Active damping of self-excited torsional vibrations in oil well drillstrings, Journal of Sound and Vibration179(4): 647-668, DOI: 10.1006/jsvi.1995.0042.; [11] Kar, I.N., Miyakura, T. and Seto, K. (2000a). Bending and torsional vibration control of a flexible plate structure using $$H_∞$$-based robust control law, IEEE Transactions on Control Systems Technology8(3): 545-553, DOI: 10.1109/87.845884.; [12] Kar, I.N., Seto, K. and Doi, F. (2000b). Multimode vibration control of a flexible structure using $$H_∞$$-based robust control, IEEE/ASME Transactions on Mechatronics5(1): 23-31, DOI: 10.1109/3516.828586.; [13] Kreuzer, E. and Steidl, M. (2012). Controlling torsional vibrations of drill strings via decomposition of traveling waves, Archive of Applied Mechanics82(4): 515-531, DOI: 10.1007/s00419-011-0570-8.; · Zbl 1293.74187 [14] Kucuk, I., Yildirim, K., Sadek, I. and Adali, S. (2013). Active control of forced vibrations in a beam via Maximum principle, 2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), Hammamet, Tunisia, pp. 1-4, DOI: 10.1109/ICMSAO.2013.6552558.; [15] Li, X., Agarwal, R.K. and Shue, S.-P. S.-P. (1994). Optimal control and $$H_∞$$ filter for control of Timoshenko beam vibrations using piezoelectric material, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA, Vol. 2, pp. 1566-1571, DOI: 10.1109/CDC.1998.758513.; [16] Michajłow, M., Jankowski, Ł., Szolc, T. and Konowrocki, R. (2017). Semi-active reduction of vibrations in the mechanical system driven by an electric motor, Optimal Control Applications and Methods38(6): 2-8, DOI: 10.1002/oca.2297.; · Zbl 1386.49057 [17] Mihajlović, N., van Veggel, A.A., van de Wouw, N. and Nijmeijer, H. (2004). Analysis of friction-induced limit cycling in an experimental drill-string system, Journal of Dynamic Systems, Measurement, and Control126(4): 709-720, DOI: 10.1115/1.1850535.; [18] Mohamed, Z., Chee, A.K., Hashim, A.W.I.M., Tokhi, M.O., Amin, S.H.M. and Mamat, R. (2006). Techniques for vibration control of a flexible robot manipulator, Robotica24(4): 499-511, DOI: 10.1017/S0263574705002511.; [19] Monteiro, H.L.S. and Trindade, M.A. (2017). Performance analysis of proportional-integral feedback control for the reduction of stick-slip-induced torsional vibrations in oil well drillstrings, Journal of Sound and Vibration398: 28-38, DOI: 10.1016/j.jsv.2017.03.013.; [20] Orlowska-Kowalska, T., Kaminski, M. and Szabat, K. (2010). Implementation of a sliding-mode controller with an integral function and fuzzy gain value for the electrical drive with an elastic joint, IEEE Transactions on Industrial Electronics57(4): 1309-1317, DOI: 10.1109/TIE.2009.2030823.; [21] Pisarski, D. and Bajer, C.I. (2010). Semi-active control of 1D continuum vibrations under a travelling load, Journal of Sound and Vibration329(2): 140-149, DOI: 10.1016/j.jsv.2009.09.006.; [22] Pisarski, D. and Canudas-de-Wit, C. (2016). Nash game-based distributed control design for balancing traffic density over freeway networks, IEEE Transactions on Control of Network Systems3(2): 149-161, DOI: 10.1109/TCNS.2015.2428332.; · Zbl 1370.90079 [23] Pisarski, D. and Myśliński, A. (2017). Online adaptive algorithm for optimal control of structures subjected to travelling loads, Optimal Control Applications and Methods38(6): 1168-1186, DOI: 10.1002/oca.2321.; · Zbl 1386.49050 [24] Priesner, R. and Jakubek, S. (2014). Mechanical impedance control of rotatory test beds, IEEE Transactions on Industrial Electronics61(11): 6264-6274, DOI: 10.1109/TIE.2014.2308159.; [25] Serrarens, A.F.A., Van De Molengraft, M.J.G., Kok, J.J. and Van Den Steen, L. (1998). $$h_∞$$ control for suppressing stick-slip in oil well drillstrings, IEEE Control Systems Magazine18(2): 19-30, DOI: 10.1109/37.664652.; [26] Singhose, W. (2009). Command shaping for flexible systems: A review of the first 50 years, International Journal of Precision Engineering and Manufacturing10(4): 153-168, DOI: 10.1007/s12541-009-0084-2.; [27] Symans, M.D. and Constantinou, M.C. (1999). Semi-active control systems for seismic protection of structures: a state-of-the-art review, Engineering Structures21(6): 469-487, DOI: 10.1016/S0141-0296(97)00225-3.; [28] Szabat, K., Tran-Van, T. and Kaminski, M. (2015). A modified fuzzy Luenberger observer for a two-mass drive system, IEEE Transactions on Industrial Informatics11(2): 531-539, DOI: 10.1109/TII.2014.2327912.; [29] Tzes, A. and Yurkovich, S. (1993). An adaptive input shaping control scheme for vibration suppression in slewing flexible structures, IEEE Transactions on Control Systems Technology1(2): 114-121, DOI: 10.1109/87.238404.; [30] van de Vrande, B.L., van Campen, D.H. and de Kraker, A. (1999). An approximate analysis of dry-friction-induced stick-slip vibrations by a smoothing procedure, Nonlinear Dynamics19(2): 159-171, DOI: 10.1023/A:1008306327781.; · Zbl 0966.70013 [31] Wang, S., Ren, X. and Na, J. (2016). Adaptive dynamic surface control based on fuzzy disturbance observer for drive system with elastic coupling, Journal of the Franklin Institute353(8): 1899-1919, DOI: 10.1016/j.jfranklin.2016.03.006.; · Zbl 1347.93157 [32] Young, K. (1998). A polar coordinate based sliding mode design for vibration control, IEEE International Workshop on Variable Structure Systems, VSS’96, Tokyo, Japan, Vol. 8, pp. 181-186, DOI: 10.1109/VSS.1996.578606.; [33] Zhu, X., Tang, L. and Yang, Q. (2015). A literature review of approaches for stick-slip vibration suppression in oilwell drillstring, Advances in Mechanical Engineering6: 1-17, DOI: 10.1155/2014/967952.;
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.