Previous |  Up |  Next


rotary inverted pendulum; sliding mode control; dynamical systems
The rotary inverted pendulum (RIP) system is one of the fundamental, nonlinear, unstable and interesting benchmark systems in the field of control theory. In this paper, two nonlinear control strategies, namely hierarchical sliding mode control (HSMC) and decoupled sliding mode control (DSMC), are discussed to address the stabilization problem of the RIP system. We introduced HSMC with state-dependent switching gain for stabilization of the RIP system. Numerical simulations are performed to analyze the performance of the hierarchical sliding mode controllers with the decoupled sliding mode controller and the controller obtained from the pole placement technique. We proposed HSMC with state-dependent switching gain as it shows better performance as compared to HSMC with constant switching gain, DSMC, and the state feedback controller based on pole placement technique. The stability analysis of proposed HSMC is also discussed by using Lyapunov stability theory.
[1] Antonio-Toledo, M. E., Sanchez, E. N., Alanis, A. Y., Florez, J., Perez-Cisneros, M. A.: Real-time integral backstepping with sliding mode control for a quadrotor UAV. IFAC-Papers Online 51 (2018), 549-554. DOI 10.1016/j.ifacol.2018.07.337
[2] Butt, Y. A.: Robust stabilization of a class of nonholonomic systems using logical switching and integral sliding mode control. Alexandria Engrg. J. 57 (2018), 1591-1596. DOI 10.1016/j.aej.2017.05.017
[3] Baker, G. J., Blackburn, J. A.: The Pendulum: A Case Study in Physics. Oxford University Press, New York 2002. MR 2155144
[4] Chen, Y. F., Huang, A. C.: Adaptive control of rotary inverted pendulum system with time-varying uncertainties. Nonlinear Dynamics 76 (2014), 95-102. DOI 10.1007/s11071-013-1112-4 | MR 3189156
[5] Choi, J. J., Kim, J. S.: Robust control for rotational inverted pendulums using output feedback sliding mode controller and disturbance observer. KSME Int. J. 17 (2003), 1466-1474. DOI 10.1007/bf02982326
[6] Coban, R., Ata, B.: Decoupled sliding mode control of an inverted pendulum on a cart: An experimental study. In: IEEE International Conference on Advanced Intelligent Mechatronics, Germany 2017. DOI 10.1109/aim.2017.8014148
[7] Furuta, K., Yamakita, M., Kobayashi, S.: Swing-up control of inverted pendulum using pseudo-state feedback. J. Systems Control Engrg. 206 (1992), 263-269. DOI 10.1243/pime_proc_1992_206_341_02
[8] Gao, W., Hung, J. C.: Variable structure control of nonlinear systems: A new approach. IEEE Trans. Industr. Electronics 40 (1993), 45-55. DOI 10.1109/41.184820 | MR 3860982
[9] Grasser, F., D{$^\prime$}Arrigo, A., Colombi, S., Rufer, A. C.: Joe: a mobile, inverted pendulum. IEEE Trans. Industr. Electron. 49 (2002), 107-114. DOI 10.1109/41.982254
[10] Hassanzadeh, I., Mobayen, S.: Controller design for rotary inverted pendulum system using evolutionary algorithms. Math. Problems Engrg. 2011 (2011), 1-17. DOI 10.1155/2011/572424
[11] Irfan, J., Rehan, J., Zhao, J., Rizwan, J., Abdus, S.: Mathematical model analysis and control algorithms design based on state feedback method of rotary inverted pendulum. Int. J. Research Engrg. Technol. 1 (2013), 41-50.
[12] Jia, Z., Yu, J., Mei, Y., Chen, Y., Shen, Y., Ai, X.: Integral backstepping sliding mode control for quadrotor helicopter under external uncertain disturbances. Aerospace Science Technol. 68 (2017), 299-307. DOI 10.1016/j.ast.2017.05.022
[13] Jadlovska, S., Sarnovsky, J.: Modelling of classical and rotary inverted pendulum systems: A generalized approach. J. Electr. Engrg. 64 (2013), 12-19. DOI 10.2478/jee-2013-0002
[14] Jose, A., Augustine, C., Malola, S. M., Chacko, K.: Performance study of PID controller and LQR technique for inverted pendulum. World J. Engrg. Technol. 3 (2015), 76-81. DOI 10.4236/wjet.2015.32008
[15] Kchaou, A., Naamane, A., Koubaa, Y., M'sirdi, N.: Second order sliding mode-based MPPT control for photovoltaic applications. Solar Energy 155 (2017), 758-769. DOI 10.1016/j.solener.2017.07.007
[16] Kaynak, O., Erbatur, K., Ertugrul, M.: The fusion of computationally intelligent methodologies and sliding mode control-A survey. IEEE Trans. Industr. Electron. 48 (2001), 4-17. DOI 10.1109/41.904539
[17] Kurode, S., Chalanga, A., Bandyopadhyay, B.: Swing-up and stabilization of rotary inverted pendulum using sliding modes. In: Preprints of the 18th IFAC World Congress, Milano 2011. DOI 10.3182/20110828-6-it-1002.02933
[18] Khanesar, M. A., Teshnehlab, M., Shoorehdeli, M. A.: Fuzzy sliding mode control of rotary inverted pendulum. In: Proc. 5th IEEE International Conference on Computational Cybernetics, Tunisia 2007. DOI 10.1109/icccyb.2007.4402019
[19] Khanesar, M. A., Teshnehlab, M., Shoorehdeli, M. A.: Sliding mode control of rotary inverted pendulum. In: Proc. 15th Mediterannean Conference on Control and Automation, Greece 2007. DOI 10.1109/med.2007.4433653
[20] Liu, X., Vargas, A. N., Yu, X., Xu, L.: Stabilizing two-dimensional stochastic systems through sliding mode control. J. Franklin Inst. 354 (2017), 5813-5824. DOI 10.1016/j.jfranklin.2017.07.015 | MR 3692085
[21] Lu, B., Fang, Y., Sun, N.: Sliding mode control for underactuated overhead cranes suffering from both matched and unmatched disturbances. Mechatronics 47 (2017), 116-125. DOI 10.1016/j.mechatronics.2017.09.006
[22] Lin, X., Nie, J., Jiao, Y., Liang, K., Li, H.: Adaptive fuzzy output feedback stabilization control for the underactuated surface vessel. Appl. Ocean Res. 74 (2018), 40-48. DOI 10.1016/j.apor.2018.01.015
[23] Lo, J. C., Kuo, Y. H.: Decoupled fuzzy sliding-mode control. IEEE Trans. Fuzzy Systems 6 (1998), 426-435. DOI 10.1109/91.705510
[24] Muskinja, N., Tovornik, B.: Swinging up and stabilization of a real inverted pendulum. IEEE Trans. Industr. Electron. 53 (2006), 631-639. DOI 10.1109/tie.2006.870667
[25] Mei, H., He, Z.: Study on stability control for single link rotary inverted pendulum. In: Proc. International Conference on Mechanic Automation and Control Engineering, Wuhan 2010. DOI 10.1109/mace.2010.5536653
[26] Mon, Y. J., Lin, C. M.: Hierarchical fuzzy sliding-mode control. In: Proc. IEEE International Conference on Fuzzy Systems, Greece 2002. DOI 10.1109/fuzz.2002.1005070
[27] Ngo, Q. H., Nguyen, N. P., Nguyen, C. N., Tran, T. H., Ha, Q. P.: Fuzzy sliding mode control of an offshore container crane. Ocean Engrg. 140 (2017), 125-134. DOI 10.1016/j.oceaneng.2017.05.019
[28] Nagarale, R., Patre, B.: Decoupled neural fuzzy sliding mode control of nonlinear systems. In: IEEE International Conference on Fuzzy Systems, Hyderabad 2013. DOI 10.1109/fuzz-ieee.2013.6622321
[29] Oltean, S. E.: Swing-up and stabilization of the rotational inverted pendulum using PD and fuzzy-PD controllers. Procedia Technol. 12 (2014), 57-64. DOI 10.1016/j.protcy.2013.12.456
[30] Phuong, N., Loc, H., Tuan, T.: Control of two wheeled inverted pendulum using sliding mode technique. Int. J. Engrg. Res. Appl. 3 (2013), 1276-1282.
[31] Perruquetti, W., Barbot, J. P.: Sliding Mode Control in Engineering. CRC Press, 2002. DOI 10.1201/9780203910856
[32] Qian, D., Yi, J.: Hierarchical Sliding Mode Control for Under-actuated Cranes. Springer-Verlag, Berlin 2015. DOI 10.1007/978-3-662-48417-3 | MR 3408614
[33] Qureshi, M. S., Swarnkar, P., Gupta, S.: A supervisory on-line tuned fuzzy logic based sliding mode control for robotics: An application to surgical robots. Robotics Autonom. Systems 109 (2018), 68-85. DOI 10.1016/j.robot.2018.08.008
[34] Qian, D., Yi, J., Zhao, D.: Hierarchical sliding mode control for a class of simo under-actuated systems. Control Cybernet. 37 (2008), 159-175. MR 2440728
[35] Qian, D., Yi, J., Zhao, D., Hao, Y.: Hierarchical sliding mode control for series double inverted pendulums system. In: Proc. International Conference on Intelligent Robots and Systems, Beijing 2006. DOI 10.1109/iros.2006.282521
[36] Song, Z., Sun, K., Ling, S.: Stabilization and synchronization for a mechanical system via adaptive sliding mode control. ISA Trans. 68 (2017), 353-366. DOI 10.1016/j.isatra.2017.02.013
[37] Solanes, J. E., Gracia, L., Munoz-Benavent, P., Miro, J. V., Girbes, V., Tornero, J.: Human-robot cooperation for robust surface treatment using non-conventional sliding mode control. ISA Trans. 80 (2018), 528-541. DOI 10.1016/j.isatra.2018.05.013
[38] Slotine, J. J. E.: Sliding controller design for nonlinear systems. Int. J. Control 40 (1984), 421-434. DOI 10.1080/00207178408933284
[39] Sirisha, V., Junghare, A. S.: A comparative study of controllers for stabilizing a rotary inverted pendulum. Int. J. Chaos, Control, Modell. Simul. 3 (2014), 1-13. DOI 10.5121/ijccms.2014.3201
[40] Slotine, J. J. E., Li, W.: Applied Nonlinear Control. Prentice Hall International Inc., 1991. Zbl 0753.93036
[41] Tapia, A., Bernal, M., Fridman, L.: Nonlinear sliding mode control design: An LMI approach. Systems Control Lett. 104 (2017), 38-44. DOI 10.1016/j.sysconle.2017.03.011 | MR 3652391
[42] Tuan, L. A., Lee, S. G., Nho, L. C., Cuong, H. M.: Robust controls for ship-mounted container cranes with viscoelastic foundation and flexible hoisting cable. Proc. Inst. Mechan. Engineers, Part I: J. Systems Control Engrg. 229 (2015), 662-674. DOI 10.1177/0959651815573903
[43] Tuan, L. A., Cuong, H. M., Lee, S. G., Nho, L. C., Moon, K.: Nonlinear feedback control of container crane mounted on elastic foundation with the flexibility of suspended cable. J. Vibration Control 22 (2016), 3067-3078. DOI 10.1177/1077546314558499 | MR 3527669
[44] Utkin, V. I., Korovin, S. K.: Application of sliding mode to static optimization. Automatic Remote Control 4 (1972), 570-579. MR 0738683
[45] Utkin, V. I., Yagn, K. D.: Methods for construction of discontinuity planes in multidimensional variable structure systems. Automat. Remote Control 39 (1978), 72-77. MR 0533368
[46] Utkin, V. I., Yagn, K. D.: Variable structure systems with sliding modes. IEEE Trans. Automat. Control 22 (1997), 212-222. DOI 10.1109/tac.1977.1101446 | MR 0484664
[47] Utkin, V. I., Guldner, J., Shi, J.: Sliding Mode Control in Electro-Mechanical Systems. CRC Press, 2009. DOI 10.1201/9781420065619 | MR 2455618
[48] Wu, Y. J., Li, G. F.: Adaptive disturbance compensation finite control set optimal control for PMSM systems based on sliding mode extended state observer. Mechan. Systems Signal Process. 98 (2018), 402-414. DOI 10.1016/j.ymssp.2017.05.007
[49] Wu, A., Zhang, X., Zhang, Z.: A control system based on the Lagrange modeling method for a single link rotary inverted pendulum. Engrg. Sci. 7 (2005), 11-15.
[50] Wen, J., Shi, Y., Lu, X.: Stabilizing a rotary inverted pendulum based on logarithmic Lyapunov function. J. Control Science Engrg. 2017 (2017), 1-11. DOI 10.1155/2017/4091302 | MR 3622180
[51] Yigit, I.: Model free sliding mode stabilizing control of a real rotary inverted pendulum. J. Vibration Control 23 (2017), 1645-1662. DOI 10.1177/1077546315598031 | MR 3659607
[52] Yue, M., An, C., Du, Y., Sun, J.: Indirect adaptive fuzzy control for a nonholonomic/underactuated wheeled inverted pendulum vehicle based on a data-driven trajectory planner. Fuzzy Sets Systems 290 (2016), 158-177. DOI 10.1016/j.fss.2015.08.013 | MR 3460256
[53] Zhang, J., Zhang, Q., Wang, Y.: A new design of sliding mode control for Markovian jump systems based on stochastic sliding surface. Inform. Sci. 391 (2017), 9-27. DOI 10.1016/j.ins.2017.02.005
[54] Zhao, Y., Huang, P., Zhang, F.: Dynamic modeling and super-twisting sliding mode control for tethered space robot. Acta Astronautica 143 (2018), 310-321. DOI 10.1016/j.actaastro.2017.11.025
Partner of
EuDML logo