Reducing the mast vibration of single-mast stacker cranes by gain-scheduled control

Hajdu, S. ; Gáspár, P.

International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) no. 4, pp. 791-802.

Résumé

In the frame structure of stacker cranes harmful mast vibrations may appear due to the inertial forces of acceleration or the braking movement phase. This effect may reduce the stability and positioning accuracy of these machines. Unfortunately, their dynamic properties also vary with the lifted load magnitude and position. The purpose of the paper is to present a controller design method which can handle the effect of a varying lifted load magnitude and position in a dynamic model and at the same time reveals good reference signal tracking and mast vibration reducing properties. A controller design case study is presented step by step from dynamic modeling through to the validation of the resulting controller. In the paper the dynamic modeling possibilities of single-mast stacker cranes are summarized. The handling of varying dynamical behavior is realized via the polytopic LPV modeling approach. Based on this modeling technique, a gain-scheduled controller design method is proposed, which is suitable for achieving the goals set. Finally, controller validation is presented by means of time domain simulations.

Détail

Keywords: robust control, LPV systems, gain scheduling, stacker cranes
Mots-clés : sterowanie odporne, szeregowanie zadań, układnica

Bibliographie

[1] Apkarian, P. and Adams, R.J. (1998). Advanced gain-scheduling techniques for uncertain systems, IEEE Transactions on Control Systems Technology 6(1): 21–32.

[2] Apkarian, P., Gahinet, P. and Becker, G. (1995). Self-scheduled H∞ control of linear parameter-varying systems: A design example, Automatica 31(9): 1251–1261.

[3] Aschemann, H., Schindele, D. and Ritzke, J. (2011). Modeling, Design, and Simulation of Systems with Uncertainties, Springer, Berlin/Heidelberg, pp. 333–351.

[4] Bachmayer, M. Schipplick, M., Th¨ummel, T., Kessler, S., Ulbrich, H. and Günthner, W.A. (2008). Nachschwingungsfreie Positionierung elastischer Roboter durch numerische und analytische Trajektorienplanung am Beispiel Regalbediengerät, VDE/VDI-Tagung: Elektrisch-mechanische Antriebssysteme—Innovationen—Trends—Mechatronik, Böblingen, Germany, pp. 1–7.

[5] Bachmayer, M., Zander, R. and Ulbrich, H. (2009). Numerical approaches for residual vibration free positioning of elastic robots, Materialwissenschaft und Werkstofftechnik 40(3): 161–168.

[6] Benner, P. Quintana-Orti, E.S. and Quintana-Orti, G. (2003). State-space truncation methods for parallel model reduction of large-scale systems, Parallel Computing 29(11–12): 1701–1722.

[7] Bokor, J. and Balas, G. (2005). Linear parameter varying systems: A geometric theory and applications, 16th IFAC World Congress, Prague, Czech Republic, pp. 12–22.

[8] Caigny, J.D., Pintelon, R., Camino, J.F. and Swevers, J. (2014). Interpolated modeling of LPV systems, IEEE Transactions on Control Systems Technology 22(6): 2232–2246.

[9] Chilali, M. and Gahinet, P. (1995). H∞ design with pole placement constraints: An LMI approach, IEEE Transactions on Automatic Control 41(3): 358–367.

[10] Dietzel, M. (1999). Beeinflussung des Schwingungsverhaltens von Regalbedienger¨aten durch Regelung des Fahrantriebs, dissertation, Institut für Fördertechnik Karlsruhe, Karlsruhe.

[11] Fang, H., Yueting, C. and Shouhua, Z. (2008). Application of fuzzy control in the stacker crane of an AS/RS, 5th International Conference on Fuzzy Systems and Knowledge Discovery, Jinan, Shandong, China, pp. 508–512.

[12] Gahinet, P. and Apkarian, P. (1994). A linear matrix inequality approach to H∞ control, International Journal of Robust and Nonlinear Control 4(4): 421–448.

[13] Görges, D., Kroneis, J. and Liu, S. (2009). Active vibration control of storage and retrieval machines, Proceedings of the ASME 2008 International Design Engineering Technical Conferences Computers and Information in Engineering Conference, New York, NY, USA, pp. 1037–1046.

[14] Hassanabadi, A.H., Shafiee, M. and Puig, V. (2016). Robust fault detection of singular LPV systems with multiple time-varying delays, International Journal of Applied Mathematics and Computer Science 26(1): 45–61, DOI: 10.1515/amcs-2016-0004.

[15] Heptner, K. (1970). Dynamisches Fahrverhalten von Regalförderzeugen und Dämpfung ihrer Schwingungen, Fördern und Heben 20(16): 918–922.

[16] Hoffmann, C. and Werner, H. (2015a). LFT-LPV modeling and control of a control moment gyroscope, 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, pp. 5328–5333.

[17] Hoffmann, C. and Werner, H. (2015b). A survey of linear parameter-varying control applications validated by experiments or high-fidelity simulations, IEEE Transactions on Control Systems Technology 23(2): 416–433.

[18] Leith, D. and Leithead, W. (2000). Survey of gain-scheduling analysis and design, International Journal of Control 73(11): 1001–1025.

[19] Nowakowski, C., Kürschner, P., Eberhard, P. and Benner, P. (2013). Model reduction of an elastic crankshaft for elastic multibody simulations, Journal of Applied Mathematics and Mechanics 93(4): 198–216.

[20] Packard, A. and Balas, G. (1997). Theory and application of linear parameter varying control techniques, American Control Conference, Albuquerque, NM, USA, Workshop I.

[21] Péni, T., Vanek, B., Szabó, Z. and Bokor, J. (2015). Supervisory fault tolerant control of the GTM UAV using LPV methods, International Journal of Applied Mathematics and Computer Science 25(1): 117–131, DOI: 10.1515/amcs-2015-0009.

[22] Poussot-Vassal, C. and Demourant, F. (2012). Dynamical medium (large)-scale model reduction and interpolation with application to aircraft systems, Aerospace Lab 4(1): 1–11.

[23] Poussot-Vassal, C. and Roos, C. (2011). Flexible aircraft reduced-order LPV model generation from a set of large-scale LTI models, Proceedings of the IEEE American Control Conference, San Francisco, CA, USA, pp. 745–750.

[24] Sasaki, M., Shimizu, T., Ikai, K. and Ito, S. (2009). Two-degree-of-freedom control of a stacker crane, ICROSSICE International Joint Conference, Fukuoka, Japan, pp. 874–878.

[25] Scherer, C. (1995). Mixed H2/H∞ control, in A. Isidori (Ed.), Trends in Control: A European Perspective, Springer-Verlag, London, pp. 173–216.

[26] Scherer, C., Gahinet, P. and Chilali, M. (1997). Multiobjective output-feedback control via LMI optimization, IEEE Transaction on Automatic Control 42(7): 896–911.

[27] Schindele, D. and Aschemann, H. (2014). Adaptive LQR-control design and friction compensation for flexible high-speed rack feeders, Journal of Computational and Nonlinear Dynamics 9(1): 1–9.

[28] Schumacher, M. (1994). Untersuchung des Schwingungsverhaltens von Einmast-Regalbediengeräten, Dissertation, Institut für Fördertechnik Karlsruhe, Karlsruhe.

[29] Shamma, J.S. (1988). Analysis and Design of Gain Scheduled Control Systems, Ph.D. thesis, Laboratory for Information and Decision Systems, Cambridge, MA.

[30] Staudecker, M., Schlacher, K. and Hansl, R. (2008). Passivity based control and time optimal trajectory planning of a single mast stacker crane, Proceedings of the 17th IFAC World Congress (IFAC’08), Seoul, Korea, pp. 875-880.

[31] Theis, J., Takarics B., Pfifer H., Balas G. and Werner H. (2015). Modal matching for LPV model reduction of aeroservoelastic vehicles, AIAA Atmospheric Flight Mechanics Conference, Kissimmee, FL, USA, pp. 1–12.

[32] Wu, F. (1996). Induced L2 norm model reduction of polytopic uncertain linear systems, Automatica 32(10): 1417–1426.

[33] Zhou, K., Doyle, J.C. and Glover, K. (1996). Robust and Optimal Control, Prentice Hall, Upper Saddle River, NJ.