Abstract
An X − Y inverted pendulum, also known as a spherical or a two-dimensional inverted pendulum consists of a thin cylindrical rod attached to a base through a universal joint. The control objective is to place the pendulum in the upright position while keeping the base at some desired reference trajectory. This paper presents an adaptive gain scheduling method in designing PID controllers for the stabilization of an X − Y inverted pendulum. The variations in PID gains depend upon the transient and the steady-state part of the response. The performance of the proposed scheme has been compared with the conventional PID scheme given in the literature. The effectiveness of the proposed scheme under the effect of disturbance, noise and friction in the inverted pendulum system has also been studied. Simulation results show that the proposed controllers provide better performance than the conventional PID controllers in terms of various performance specifications.
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References
Angeli, D. (2001). Almost global stabilization of the inverted pendulum via continuous state feedback, Automatica, 37, 1103–1108.
Astrom, K.J. & Furuta K. (1999). Swinging up a pendulum by energy control, Automatica, 3, 287-295.
Astrom, K. J. & Hagglund, T. (1995). PID Controllers: Theory, Design and Tuning, Instrument Society of America, 2, USA.
Bloch, A.M., Leonard, N.E. & Marsden, J.E. (2000). Controlled lagrangians and the stabilization of mechanical Systems I: the first matching theorem, IEEE Transactions on Automatic Control, 45, 2253–2270.
Champbell, S.A. (2004). Friction and the Inverted Pendulum Stabilization Problem, Department of Applied Mathematics, University of Waterloo, Canada, 1-21.
Chang, L.H. & Lee, A.C. (2007) Design of nonlinear controller for bi-axial inverted pendulum system, IET Control Theory and Application, 1, 979–986.
Ghosh, A. , Krishnan, T.R. & Subudhi, B. (2012). Robust PID compensation of an inverted cartpendulum system: an experimental study, IET Control Theory and Applications, 6, 1145-1152
Ibanez, C.A. , Gutierrez, O. & Sossa-Azuela, H. (2006). Lyapunov Approach for the stabilization of the Inverted Spherical Pendulum, 45th IEEE Conference on Decision & Control , 6133-6137
Kumar,V. & Jerome, J. (2013). Robust LQR Controller Design for Stabilizing and Trajectory Tracking of Inverted Pendulum, Procedia Engineering, 64, 169-178.
Liu, G.Y., Nesic, D. & Mareels, I. (2008). Non-linear stable inversion-based output tracking control for a spherical inverted pendulum, International Journal of Control, 81, 116–133.
Maravall, D. (2004). Control and stabilization of the inverted pendulum via vertical forces, Robotic welding, intelligence and automation. Lecture notes in control and information sciences, Berlin: Springer-Verlag, 299, 190–211.
Mason, P., Broucke, M. & Piccoli, B. (2008). Time optimal swing-up of the planar pendulum, IEEE Transactions on Automatic Control, 53, 1876–1886.
Muskinja, N. & Tovornik, B. (2006). Swinging up and stabilization of a real inverted pendulum, IEEE Transaction on Industrial Electronics, 53, 631-639.
Nagar, A., Bardini, M. & Rabaie, N.M. (2014). Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller, Alexandria Engineering Journal, 53, 23-32.
Nasir, A. (2007). Modeling and controller design for an inverted pendulum system, Master of Technology Degree, Faculty of Electrical Engineering, Universiti Teknologi Malaysia.
Prasad, L.B. , Tyagi, B. & Gupta, H.O. (2011). Optimal Control of Nonlinear Inverted Pendulum Dynamical System with Disturbance Input using PID Controller & LQR, IEEE International Conference on Control System, Computing and Engineering, 540-545.
Tsai, C.C., Yu,C.C. & Chang, C.S. (2011). Aggregated hierarchical sliding-mode control for spherical inverted Pendulum, Proceedings of 2011 8th Asian Control Conference (ASCC), 914-919.
Wai R.J. & Chang, L.J. (2006). Adaptive stabilizing and tracking control for a nonlinear invertedpendulum system via sliding-mode technique, IEEE Transactions on Industrial Electronics, 53, 674-692.
Wang, J.J. (2011). Simulation studies of inverted pendulum based on PID controllers, Simulation Modelling Practice and Theory, Elsevier 19 , 440-449.
Wang, J.J. (2012). Stabilization and tracking control of X–Z inverted pendulum with sliding-mode control, ISA Transactions, 51, 763-770.
Zhao, J. & Spong, M.W. (2001). Hybrid control for global stabilization of the cart-pendulum system, Automatica, 37, 1941-1951.
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Chopra, V., Singla, S. & Dewan, L. Stabilization of an X-Y inverted pendulum using adaptive gain scheduling PID controllers. J Engin Res 3, 14 (2015). https://doi.org/10.7603/s40632-015-0014-7
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DOI: https://doi.org/10.7603/s40632-015-0014-7