Controlling the Double Rotary Inverted Pendulum with Multiple Feedback Delays

  • V. Casanova Departamento de Ingeniería de Sistemas y Automática Instituto Universitario de Automática e Informática Industrial Universitat Politécnica de Valencia Camino de Vera s/n 46022 Valencia (Spain)
  • J. Salt Departamento de Ingeniería de Sistemas y Automática Instituto Universitario de Automática e Informática Industrial Universitat Politécnica de Valencia Camino de Vera s/n 46022 Valencia (Spain)
  • R. Piza Departamento de Ingeniería de Sistemas y Automática Instituto Universitario de Automática e Informática Industrial Universitat Politécnica de Valencia Camino de Vera s/n 46022 Valencia (Spain)
  • A. Cuenca Departamento de Ingeniería de Sistemas y Automática Instituto Universitario de Automática e Informática Industrial Universitat Politécnica de Valencia Camino de Vera s/n 46022 Valencia (Spain)

Abstract

The aim of this work is the development and implementation of a control structure for the double rotary inverted pendulum, suitable to be used in a Networked Control System environment. Delays are quite common in this kind of systems and, when controlling multivariable plants, it is possible that different delays are applied to the multiple inputs and outputs of them. A control structure that allows compensating individually each one of the multiple loop delays would be useful when one of these delays changes. Inverted pendulums are quite sensitive to delays and for this reason are appropriated plants to be used in these conditions. The control structure is developed modifying the control in no-delay conditions with a generalized predictor able to deal with unstable and non-minimum plants as the chosen one is. The proposed structure has been simulated and implemented to control a real double rotary inverted pendulum.

References

[1] Y. Halevi, A. Ray, Integrated communication and control systems: Part I-Analysis, ournal of Dynamic Systems, Measurement and Control, vol. 110, pp. 367-373, 1988.
http://dx.doi.org/10.1115/1.3152698

[2] A. Ray, Y. Halevi, Integrated communication and control systems: Part II-Design onsiderations, Journal of Dynamic Systems, Measurement and Control, vol. 110, p. 374-381, 1988.
http://dx.doi.org/10.1115/1.3152699

[3] L.G. Bushnell, Networks and control, IEEE Control Systems Magazine, vol. 21, no., pp. 22-23, 2001.

[4] Y. Tipsuwan, M-Y. Chow, Control methodologies in networked control systems, ontrol Engineering Practice, vol. 11, no. 10, pp. 1099-1111, 2001.

[5] P.F. Hokayem, C.T. Abdallah, Inherent issues in networked control systems: A urvey, Proceedings of the 23rd American Control Conference, Boston (USA), vol.6, p. 4897-4902, 2004.

[6] T.C. Yang, Networked control systems: A brief survey, IEE Proceedings on Control heory and Applications, vol. 153, no. 4, pp. 403-412, 2006.

[7] V. Casanova, J. Salt, Multirate control implementation for an integrated communication nd control system, Control Engineering Practice, vol. 11, no. 11, pp. 1335- 348, 2003.
http://dx.doi.org/10.1016/S0967-0661(02)00256-3

[8] J. Nilsson, Real-time control systems with delays. PhD thesis, Lund Institute of echnology, Lund, Sweden, 1998.

[9] J. Nilsson, B. Bernhardsson, B. Wittenmark, Stochastic analysis and control of eal-time systems with random time delays, Automatica, vol. 34, no. 1, pp. 57-64, 998.
http://dx.doi.org/10.1016/S0005-1098(97)00170-2

[10] F.L. Lian, J.R. Moyne, D.M. Tilbury, Performance evaluation of control networks: thernet, ControlNet, and DeviceNet, IEEE Control Systems Magazine, vol. 21, p. 66-83, 2001.
http://dx.doi.org/10.1109/37.898793

[11] F.L. Lian, J.R. Moyne, D.M. Tilbury, Network design consideration for distributed ontrol systems, IEEE Transactions on Control Systems Technology, vol. 10, pp. 97-307, 2002.

[12] F.L. Lian, J.R. Moyne, D.M. Tilbury, Modelling and optimal controller design of etworked control systems with multiple delays, International Journal of Control, ol. 76, no. 6, pp. 591-606, 2003.
http://dx.doi.org/10.1080/0020717031000098426

[13] H. Gaoa, T. Chenb, J. Lamc, A new delay system approach to network-based control, utomatica, vol. 44, no. 1, pp. 39-52, 2008.

[14] A.V. Savkin, Analysis and synthesis of networked control systems: Topological ntropy, observability, robustness and optimal control, Automatica, vol. 42, no. 1, p. 51-62, 2006.
http://dx.doi.org/10.1016/j.automatica.2005.08.021

[15] D.S. Kim et al, Maximum allowable delay bounds of networked control systems, ontrol Engineering Practice, vol.11, no. 11, pp.1301-1313, 2003.

[16] H. Fanga, H. Yeb, M. Zhong, Fault diagnosis of networked control systems, Annual eviews in Control, vol.31, no. 1, pp. 55-68, 2007.

[17] O.E. Agamennoni, A.C. Desages, J.A. Romagnoli, A multivariable delay compensator cheme, Chemical Engineering Science, vol. 47, no. 5, pp. 1173-1185, 1992.
http://dx.doi.org/10.1016/0009-2509(92)80239-9

[18] B.A. Ogunnaike, W.H. Ray, Multivariable controller design for linear systems having ultiple time delays, AIChE Journal, vol. 25, no. 6, pp. 1043-1057, 1979.
http://dx.doi.org/10.1002/aic.690250616

[19] K. Watanabe, M. Ito, An observer for linear feedback control laws of multivariable ystems with multiple delays in controls and outputs, Systems & Control Letters, ol. 1, no. 1, pp. 54-59, 1981.

[20] S. Mori, H. Nishihara, K. Furuta, Control of unstable mechanical system: Control f pendulum, International Journal of Control, vol. 23 no. 5, pp. 673-692, 1976.
http://dx.doi.org/10.1080/00207177608922192

[21] K. Furuta, M. Yamakita, S. Kobayashi, M. Nishimura, A new inverted pendulum pparatus for education, IFAC Advances in Control Education Conference, pp. 191- 96, 1991.

[22] S. Yurkovich, M. Widjaja, Fuzzy controller synthesis for an inverted pendulum, ontrol Engineering Practice, vol. 4, no. 4, pp. 455-469, 1996.

[23] W. Zhong, H. Röck, Energy and passivity based control of the double inverted endulum on cart, IEEE Conference on Control Applications, pp. 896-901, 2001.

[24] J. Driver, D. Thorpe, Design, build and control of a single/double rotational inverted endulum, The University of Adelaide, School of Mechanical Engineering, Australia, 004.

[25] Quanser Consulting Inc, Rotary experiment #8: Double Inverted Pendulum (DBPEN), 2006.

[26] G. Alevisakis, D.E. Seborg, An extension of the Smith predictor method to multivariable inear systems containing time delays, International Journal of Control, ol. 17, no. 3, pp. 541- 551, 1973.
http://dx.doi.org/10.1080/00207177308932401

[27] K. Watanabe, Y. Ishiyama, M. Ito, Modified Smith predictor control for multivariable ystems with delays and unmeasurable step disturbances, International Journal f Control, vol. 37, no. 5, pp. 959-973, 1983.
http://dx.doi.org/10.1080/00207178308933022

[28] J.M. Maciejowski, Robustness of multivariable Smith predictors, Journal of Process ontrol, vol. 4, no. 1, pp. 29-32, 1994.

[29] A.M. De Paor, A modified Smith predictor and controller for unstable processes ith time delay, International Journal of Control, vol. 41, no. 4, pp. 1025-1036, 985.

[30] H.J. Kwak, S.W. Sung, I.B. Lee, A modified Smith predictor with a new structure or unstable processes, Industrial & Engineering Chemistry Research, vol. 38, no. 2, p. 405-411, 1999.
http://dx.doi.org/10.1021/ie980515n

[31] T. Liu, Y.Z. Cai, D.Y. Gu, W.D. Zhang, New modified Smith predictor scheme or integrating and unstable processes with time delay, IEE Proceedings on Control heory and Applications, vol. 152, no. 2, pp. 238-246, 2005.

[32] P. García, P. Albertos, T. Hägglund, Control of unstable non-minimum-phase delayed ystems, Journal of Process Control, vol. 16, no. 10, pp. 1099-1111, 2006
http://dx.doi.org/10.1016/j.jprocont.2006.06.007

[33] P. Albertos, P. García, Robust control design for long time-delay systems, Journal f Process Control, vol. 19, no. 10, pp. 1640-1648, 2009.
http://dx.doi.org/10.1016/j.jprocont.2009.05.006
Published
2012-03-01
How to Cite
CASANOVA, V. et al. Controlling the Double Rotary Inverted Pendulum with Multiple Feedback Delays. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 7, n. 1, p. 20-38, mar. 2012. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/1420>. Date accessed: 15 apr. 2021. doi: https://doi.org/10.15837/ijccc.2012.1.1420.

Keywords

Control applications, delay compensation, distributed control, multi-loop control, multi-variable feedback control, transport delay