LMI-based Multiobjective Integral Sliding Mode Control for Rotary Inverted Pendulum System Under Load Variations
DOI:
https://doi.org/10.11113/jt.v73.4444Keywords:
Integral sliding mode, multiobjective, linear matrix inequality, rotary inverted pendulum, extended linearizationAbstract
This paper presents a multiobjective integral sliding mode controller (ISMC) for a rotary inverted pendulum system under the influence of varying load. Firstly, the nonlinear system is approximated to facilitate the desired control design via extended linearization and deterministic approach. By using both of these techniques, the nonlinear system is formulated into a nonlinear state-space representation where the uncertainties are retained in the model. Next, the design objectives are formulated into linear matrix inequalities (LMI) which are then solved efficiently through convex optimization algorithms. With proper selection variables, numbers of the decision variables for LMIs are reduced. Hence, it will reduce the numerical burden and believes the calculated values more viable in practice. Finally, simulation works are conducted and comparison is made between the proposed controller, such as normal ISMC and LQR. The simulation results illustrate the effectiveness of the proposed controller and the performance is evaluated through integral of absolute-value error (IAE) performance index.Â
References
Furuta, K., M. Yamakita, and S. Kobayashi. 1992. Swing-up Control of Inverted Pendulum Using Pseudo-state Feedback. Proceedings of the Institution of Mechanical Engineers, Part I. Journal of Systems and Control Engineering. 206(4): 263–269.
Cazzolato, B. S., and Z. Prime. 2011. On the Dynamics of the Furuta Pendulum. Journal of Control Science and Engineering. 2011: 8.
Fantoni, I., and R. Lozano. 2002. Stabilization of the Furuta Pendulum Around Its Homoclinic Orbit. International Journal of Control. 75(6): 390–398.
Park, M. S., and D. Chwa. 2009. Swing-Up and Stabilization Control of Inverted-Pendulum Systems via Coupled Sliding-Mode Control Method. IEEE Transactions on Industrial Electronics. 56(9): 3541–3555.
Hassanzadeh, I., and S. Mobayen. 2011. Controller Design for Rotary Inverted Pendulum System Using Evolutionary Algorithms. Mathematical Problems in Engineering.
Muske, K. R., H. Ashrafiuon, S. Nersesov, and M. Nikkhah. 2012. Optimal Sliding Mode Cascade Control for Stabilization of Underactuated Nonlinear Systems. Journal of Dynamic Systems, Measurement, and Control. 134(2): 21020–21030.
Friedland, B. 1995. Advanced Control System Design. New Jersey: Prentice-Hall, Inc.
Wernli, A., and G. Cook. 1975. Suboptimal Control for the Nonlinear Quadratic Regulator Problem. Automatica. 11(1): 75–84.
Mracek, C. P., and J. R. Cloutier. 1998. Control Designs for the Nonlinear Benchmark Problem via the State-dependent Riccati Equation Method. International Journal of Robust and Nonlinear Control. 8(4–5): 401–433.
Çimen, T. 2010. Systematic and Effective Design of Nonlinear Feedback Controllers via the State-Dependent Riccati Equation (SDRE) method. Annual Reviews in Control. 34(1): 32–51.
Yang, W., N. Hammoudi, G. Herrmann, M. Lowenberg, and X. Chen. 2015. Dynamic Gain-scheduled Control and Extended Linearisation: Extensions, Explicit Formulae and Stability. International Journal of Control. 88(1): 163–179.
Lee, T. S. 2003. Nonlinear State Feedback Control Design for Three-phase PWM Boost Rectifiers Using Extended Linearisation. IEE Proceedings of Electric Power Applications. 150(5): 546–554.
Wang, J., and N. Sundararajan. 1996. Extended Nonlinear Flight Controller Design for Aircraft. Automatica. 32(8): 1187–1193.
Osman, J. H. S., and P. D. Roberts. 1995. A Two-level Control Strategy for Robot Manipulators. International Journal of Control. 61(6): 1201–1222.
Olalla, C., R. Leyva, A. El-Aroudi, and I. Queinnec. 2009. Robust LQR Control for PWM Converters: An LMI Approach. IEEE Transactions on Industrial Electronics. 56(7): 2548–2558.
Zhang, D., and D. Ionescu. 2006. Robust and Optimal Control of Packet Loss Probability. IEEE Global Telecommunications Conference (GLOBECOM ’06): 1–5.
Ge, M., M. S. Chiu, and Q. G. Wang 2002. Robust PID Controller Design via LMI Approach. Journal of Process Control. 12(1): 3–13.
Peaucelle, D. 2009. Integral Quadratic Separation Applied to Polytopic Systems. IFAC Symposium on Robust Control Design. Haifa.
Çimen, T. 2012. Survey of State-dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis. Journal of Guidance, Control, and Dynamics. 35(4): 1025–1047.
Utkin, V. I. 1992. Sliding Modes in Control and Optimization. Springer-Verlag.
Chilali, M., and P. Gahinet. 1996. H∞ Design with Pole Placement Constraints: An LMI approach. IEEE Transactions on Automatic Control. 41(3): 358–367.
Slotine, J. J. E., W. Li, and others. 1991. Applied Nonlinear Control. New Jersey: Prentice-Hall.
Hibbeler, R. C. 2013. Engineering Mechanics: Statics. New Jersey: Pearson Prentice Hall.
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