Abstract
Balancing inverted pendulum along a vertical position with or without cart is a benchmark control problem owing to the fact that out of two equilibrium points, inverted one is open-loop unstable. In this paper, an attempt has been made to stabilize the system with delayed state feedback control strategy using T-S fuzzy modeling in an linear matrix inequality (LMI) framework. Then, by Lyapunov–Krasovskii (L-K) theory, it is proved that the closed-loop system is locally asymptotically stable around its unstable equilibrium point. The result of the control design is validated through closed-loop simulation carried out in MATLAB Simulink.
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Prasad, L.B., Tyagi, B., Gupta, H.O.: Optimal control of nonlinear inverted pendulum dynamical system with disturbance input using PID controller & LQR. In: IEEE International Conference on Control System, Computing and Engineering (ICCSCE), pp. 540–545 (2011)
Cannon, R.H.: Dynamics of Physical Systems. Courier Corporation (2003)
Ogata, K., Yang, Y.: Modern Control Engineering, vol. 4. Prentice Hall India (2002)
Faizan, F., Farid, F., Rehan, M., Mughal, S., Qadri, M.T.: Implementation of discrete PID on Inverted pendulum. In: 2nd International Conference on Education Technology and Computer (ICETC), vol. 1, pp. V1–48 (2010)
Liu, Y., Chen, Z., Xue, D., Xu, X.: Real-time controlling of inverted pendulum by fuzzy logic. In: IEEE International Conference on Automation and Logistics, ICAL’09, pp. 1180–1183 (2009)
Huang, C.H., Wang, W.J., Chiu, C.H.: Design and implementation of fuzzy control on a two-wheel inverted pendulum. IEEE Trans. Ind. Electron. 58(7), 2988–3001 (2011)
Lan, Y., Fei, M.: Design of state-feedback controller by pole placement for a coupled set of inverted pendulums. In: 10th International Conference on Electronic Measurement & Instruments (ICEMI), vol. 3, pp. 69–73 (2011)
Huang, C.E., Li, D.H., Su, Y.: Simulation and robustness studies on an inverted pendulum. In: 30th Chinese Control Conference (CCC), pp. 615–619 (2011)
Prasad, L.B., Gupta, H.O., Tyagi, B.: Intelligent control of nonlinear inverted pendulum dynamical system with disturbance input using fuzzy logic systems. In: International Conference on Recent Advancements in Electrical, Electronics and Control Engineering (ICONRAEeCE), pp. 136–141 (2011)
Khalil, H.K.: Noninear Systems. Prentice-Hall, New Jersey (1999)
Tagaki, T., Sugeno, M.: Fuzzy identification of systems and its application to modelling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory, vol. 15. Siam (1994)
Gahinet, P., Nemirovskii, A., Laub, A.J., Chilali, M.: The LMI control toolbox. In: Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 3, pp. 2038–2041 (1994)
Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2004)
Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9), 2860–2866 (2013)
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Datta, R., Dey, R., Bhattacharya, B., Chakrabarti, A. (2019). Delayed State Feedback Controller Design for Inverted Pendulum Using T-S Fuzzy Modeling: An LMI Approach. In: Deb, D., Balas, V., Dey, R. (eds) Innovations in Infrastructure. Advances in Intelligent Systems and Computing, vol 757. Springer, Singapore. https://doi.org/10.1007/978-981-13-1966-2_6
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DOI: https://doi.org/10.1007/978-981-13-1966-2_6
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