Improved Performance of Cascaded Fractional-Order SMC over Cascaded SMC for Position Control of a Ball and Plate System

REFERENCES

• Ball and Plate Control System manual for model no. 33-240 using LabView. East Sussex: Feedback Instruments, 2011.
   Google Scholar
• A. Knuplez, A. Chowdhury, and R. Svecko, “Modeling and control design for the ball and plate system,” in 2003 IEEE International Conference on Industrial Technology, Maribor, Vol. 2, Dec. 2003, pp. 1064–7.
   Google Scholar
• X. Fan, N. Zhang, and S. Teng, “Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme,” Fuzzy Sets and Systems, Vol. 144, pp. 297–312, Mar. 2004.
   Web of Science ®Google Scholar
• C. A.-O. Moreno-Armendariz, “Indirect hierarchical FCMAC for the ball and plate system,” Neurocomputing, Vol. 73, pp. 2454–63, Jun. 2010.
   Web of Science ®Google Scholar
• Y. Pattanapong and C. Deelertpaiboon, “Ball and plate position control based on fuzzy logic with adaptive integral control action,” in International Conference on Mechatronics and Automation (ICMA), IEEE, Takamatsu, Vol. 1, Aug. 2013, pp. 1513–7.
   Google Scholar
• U. Farooq, J. Gu, and J. Luo, “On the interval type-2 fuzzy logic control of ball and plate system,” in 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenzhen, Dec. 2013, pp. 2250–6.
   Google Scholar
• C. C. Ker, C. E. Lin, and R. T. Wang, “Tracking and balance control of ball and plate system,” Journal of the Chinese Institute of Engineers, Vol. 30, pp. 459–470, Mar. 2007.
   Web of Science ®Google Scholar
• W. Hongrui, T. Yantao, F. Siyan, and S. Zhen, “Nonlinear control for output regulation of ball and plate system,” in Proceedings of 27th Chinese Control Conference, 2008. CCC 2008, Kunming, Jul. 2008, pp. 382–7.
   Google Scholar
• D. Casagrande, A. Astolfi, and T. Parisini, “Switching-driving Lyapunov function and the stabilization of the ball-and-plate system,” IEEE Transactions on Automatic Control, Vol. 54, pp. 1881–6, Aug. 2009.
   Web of Science ®Google Scholar
• H. Liu and Y. Liang, “Trajectory tracking sliding mode control of ball and plate system,” in 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR), Wuhan, Vol. 3, Mar. 2010, pp. 142–5.
   Google Scholar
• D. Debono and M. Bugeja, “Application of sliding mode control to the ball and plate problem,” in 2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO), Colmar, Vol. 1, pp. 412–9, Jul. 2015.
   Google Scholar
• P. Roy, B. Kar, and I. Hussain, “Trajectory control of a ball in a ball and plate system using cascaded PD controllers tuned by PSO,” in Proceedings of Fourth International Conference on Soft Computing for Problem Solving: SocProS 2014, Vol. 2, Silchar: Springer India, Dec. 2014, pp. 53–65.
   Google Scholar
• H. Wang, Y. Tian, C. Ding, Q. Gu, and F. Guo, “Output regulation of the ball and plate system with a nonlinear velocity observer,” in 7th World Congress on Intelligent Control and Automation, 2008. WCICA 2008, Chongqing, Jun. 2008, pp. 2164–9.
   Google Scholar
• D. Yuan and Z. Zhang, “Modelling and control scheme of the ball-plate trajectory-tracking pneumatic system with a touch screen and a rotary cylinder,” Control Theory Applications, IET, Vol. 4, pp. 573–89, Apr. 2010.
   Web of Science ®Google Scholar
• T. Binazadeh and M. Shafiei, “Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach,” Mechatronics, Vol. 23, pp. 888–92, Apr. 2013.
   Web of Science ®Google Scholar
• Y. Tang, X. Zhang, D. Zhang, G. Zhao, and X. Guan, “Fractional order sliding mode controller design for antilock braking systems,” Neurocomputing, Vol. 111, pp. 122–30, Jan. 2013.
   Web of Science ®Google Scholar
• M. L. Corradini, R. Giambó, and S. Pettinari, “On the adoption of a fractional-order sliding surface for the robust control of integer-order LTI plants,” Automatica, Vol. 51, pp. 364–71, Nov. 2014.
   Web of Science ®Google Scholar
• S. Sutha, P. Lakshmi, and S. Sankaranarayanan, “Fractional-order sliding mode controller design for a modified quadruple tank process via multi-level switching,” Computers & Electrical Engineering, Vol. 45, pp. 10–21, Apr. 2015.
   Web of Science ®Google Scholar
• N. Ullah, W. Shaoping, M. I. Khattak, and M. Shafi, “Fractional order adaptive fuzzy sliding mode controller for a position servo system subjected to aerodynamic loading and nonlinearities,” Aerospace Science and Technology, Vol. 43, pp. 381–7, Mar. 2015.
   Web of Science ®Google Scholar
• S. Dadras and H. R. Momeni, “Fractional-order dynamic output feedback sliding mode control design for robust stabilization of uncertain fractional-order nonlinear systems,” Asian Journal of Control, Vol. 16, pp. 489–97, Mar. 2014.
   Web of Science ®Google Scholar
• S. Ebrahimkhani, “Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines,” ISA Transactions, Vol. 63, pp. 343–54, Mar. 2016.
   PubMed Web of Science ®Google Scholar
• C. Yin, Y. Chen, and S.-m. Zhong, “Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems,” Automatica, Vol. 50, pp. 3173–81, Jul. 2014.
   Web of Science ®Google Scholar
• Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation. London: Springer, Oct. 2010.
   Google Scholar
• V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, Vol. 22, pp. 212–22, Apr. 1977.
   Web of Science ®Google Scholar
• S. Das, Functional Fractional Calculus, 2nd ed. Berlin Heidelberg: Springer-Verlag, Sept. 2011.
   Google Scholar
• K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order. New York: Academic Press, mathematics in science and engineering, Feb. 1974.
   Google Scholar
• C. Monje, Y. Chen, B. Vinagre, D. Xue, and V. Feliu, Fractional-Order Systems and Controls: Fundamentals and Applications. London: Springer Verlag, Nov. 2010.
   Google Scholar
• C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Engineering Practice, Vol. 16, pp. 798–812, Jul. 2008.
   Web of Science ®Google Scholar
• I. Podlubny, “Fractional-order systems and PIλ Dμ controllers,” IEEE Transactions on Automatic Control, Vol. 44, pp. 208–14, Jan. 1999.
   Web of Science ®Google Scholar
• P. Roy and B. K. Roy, “Fractional order PI control applied to level control in coupled two tank MIMO system with experimental validation,” Control Engineering Practice, Vol. 48, pp. 119–35, Jan. 2016.
   Web of Science ®Google Scholar
• A. Oustaloup, F. Levron, B. Mathieu, and F. Nanot, “Frequency-band complex noninteger differentiator: Characterization and synthesis,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 47, pp. 25–39, Jan. 2000.
   Web of Science ®Google Scholar