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TECHNICAL PAPERS

Block Control Principle for Mechanical Systems

[+] Author and Article Information
Vadim I. Utkin

Department of Electrical Engineering, The Ohio State University, Columbus, OH 43210e-mail: utkin@ee.eng.ohio-state.edu

De-Shiou Chen

Software and Calibration Tools Dept., Powertrain Operations Engine Engineering, Ford Motor Company, Dearborn, MI 48121e-mail: dchen10@ford.com

Hao-Chi Chang

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210e-mail: chang@rcltel.eng.ohio-state.edu

J. Dyn. Sys., Meas., Control 122(1), 1-10 (Nov 02, 1998) (10 pages) doi:10.1115/1.482422 History: Received November 02, 1998
Copyright © 2000 by ASME
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References

Luk’yanov,  A. G., and Utkin,  V. I., 1981, “Methods of Reducing Equations for Dynamic Systems to A Regular Form,” Autom. Remote Control (Engl. Transl.), 42, pp. 413–420.
Drakunov,  S. V., Izosimov,  D. B., Luk’yanov,  A. G., Utkin,  V. A., and Utkin,  V. I., 1990, “The Block Control Principle I,” Autom. Remote Control (Engl. Transl.), 51, pp. 601–608.
Drakunov,  S. V. , Izosimov,  D. B., Luk’yanov,  A. G., Utkin,  V. A., and Utkin,  V. I., 1990, “The Block Control Principle II,” Autom. Remote Control (Engl. Transl.), 51, pp. 737–746.
Luk’yanov, A. G., 1993, “Optimal Nonlinear Block-Control Method,” Proc. of the 2nd European Control Conference, Groningen, pp. 1853–1855.
Luk’yanov, A. G., and Dodds, S. J., 1996, “Sliding Mode Block Control of Uncertain Nonlinear Plants,” Proceedings of the 13th World Congress of the International Federation on Automatic Control (IFAC), San Francisco, CA, June 30–July 5.
Utkin, V. I., Chang, H., Kolmanovsky, I., and Chen, D., 1998, “Sliding Mode Control Design based on Block Control Principle,” The Fourth International Conference on Motion and Vibration Control (MOVIC), Zurich, Switzerland, Aug. 25–28.
Utkin, V. I., and Chen, D., 1998, “Sliding Mode Control of Pendulum Systems,” The Fourth International Conference on Motion and Vibration Control (MOVIC), Zurich, Switzerland, Aug. 25–28.
Rashevskii, P. K., 1947, Geometrical Theory of Partial Differential Equations, Gostekhiiizdat, Moscow (in Russian).
Utkin, V. I., 1992, Sliding Modes in Control and Optimization, Springer-Verlag, Berlin.
Utkin,  V. I., 1977, “Variable Structure Systems with Sliding Modes,” IEEE Trans. Autom. Control, AC-22, pp. 212–222.
Utkin, V. I., Drakunov, S. V., and Izosimov, D. B., 1984, “Hierarchical Principle of The Control System Decomposition Based on Motion Separation,” The 9th World IFAC Congress, Budapest, Hungary, July, 2–6.
Widjaja, M., 1994, “Intelligent Control for Swing Up and Balancing of an Inverted Pendulum System,” Master’s thesis, The Ohio State University, Columbus, OH.
Ordonez,  R., Zumberge,  J., Spooner,  J. T., and Passino,  K. M., 1997, “Adaptive Fuzzy Control: Experiments and Comparative Analyses,” IEEE Trans. Fuzzy Syst., 5, pp. 167–188.
Utkin, V. I., 1978, Sliding Modes and Their Applications in Variable Structure Systems, Moscow, Mir.
Kwatny, H. G., and Siu, T. L., 1987, “Chattering in Variable Structure Feedback Systems,” Proceedings of the 10th World Congress of the International Federation on Automatic Control (IFAC), Vol. 8, pp. 307–314.
Bartolini,  G., 1989, “Chattering Phenomena in Discontinuous Control Systems,” Int. J. Syst. Sci., 20, pp. 2471–2481.
Slotine,  J. J., and Sastry,  S. S., 1983, “Tracking Control of Nonlinear Systems Using Sliding Surfaces, with Application to Robot Manipulators,” Int. J. Control, 38, pp. 465–492.
Burton,  J. A., and Zinober,  A. S. I., 1986, “Continuous Approximation of Variable Structure Control,” Int. J. Syst. Sci., 17, pp. 875–885.
Bondarev, S. A., Kostyleva, N. E., and Utkin, V. I., 1985, “Sliding Modes in Systems with Asymptotic State Observers,” Moscow, Translated from Automatika I Telemekhanika, pp. 5–11.

Figures

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The rotational inverted pendulum system
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Hardware setup configuration of the pendulum system
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Simulation results by LQR
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Simulation results by SMC for case 1: stabilizing the pendulum
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Experimental results by SMC: no weight (case 1)
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Experimental results by SMC: sloshing water (case 1)
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Experimental results by SMC: metal bolts (case 1)
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Simulation results by SMC for case 2: stabilizing both the pendulum and the base
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Experimental results by SMC with small δ: no weight (case 2)
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Experimental results by SMC with larger δ: no weight (case 2)
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Experimental results by SMC: sloshing water (case 2)
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Experimental results by SMC: metal bolts (case 2)

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