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

ABSTRACT This paper deals with a comparative analysis of the performances of sliding mode controller (SMC) and fractional-order sliding mode controller (FOSMC) when applied to the problem of trajectory control of ball in a ball and plate (BP) system. Owing to the open-loop instability, inherent nonlinearity, and under actuation, the BP system is considered a benchmark platform for testing the efficacies of different control algorithms. In this work, a robust cascaded SMC is initially designed to track the desired trajectory and tackle the uncertainties present in the system. In order to improve the speed of response, an FOSMC is designed thereafter. The two-control algorithms are simulated on MATLAB-Simulink environment and the experimental validation is later carried out on a BP laboratory set-up (Feedback Instruments Model No. 033-240). The simulation results and experimental validation convey that FOSMC performs better than SMC in regard to speed of response and tracking accuracy without increasing the level of chattering and control effort.

[1]  Thomas Parisini,et al.  Switching-Driving Lyapunov Function and the Stabilization of the Ball-and-Plate System , 2009, IEEE Transactions on Automatic Control.

[2]  D. Yuan,et al.  Modelling and control scheme of the ball-plate trajectory-tracking pneumatic system with a touch screen and a rotary cylinder , 2010 .

[3]  S. Das.  Functional Fractional Calculus , 2011 .

[4]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[5]  YangQuan Chen,et al.  Fractional-order systems and control : fundamentals and applications , 2010 .

[6]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[7]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[8]  Muhammad Shafi,et al.  Fractional order adaptive fuzzy sliding mode controller for a position servo system subjected to aerodynamic loading and nonlinearities , 2015 .

[9]  Shouming Zhong,et al.  Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems , 2014, Autom..

[10]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[11]  Prasanta Roy,et al.  Fractional order PI control applied to level control in coupled two tank MIMO system with experimental validation , 2016 .

[12]  Sadegh Ebrahimkhani,et al.  Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines. , 2016, ISA transactions.

[13]  Sui Zhen,et al.  Nonlinear control for output regulation of ball and plate system , 2008, 2008 27th Chinese Control Conference.

[14]  Marvin K. Bugeja,et al.  Application of sliding mode control to the ball and plate problem , 2015, 2015 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO).

[15]  Jason Jianjun Gu,et al.  On the interval type-2 fuzzy logic control of ball and plate system , 2013, 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO).

[16]  Maria Letizia Corradini,et al.  On the adoption of a fractional-order sliding surface for the robust control of integer-order LTI plants , 2015, Autom..

[17]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[18]  M. Shafiei,et al.  Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach , 2013 .

[19]  Rong Tyai Wang,et al.  Tracking and balance control of ball and plate system , 2007 .

[20]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[21]  YangQuan Chen,et al.  Tuning and auto-tuning of fractional order controllers for industry applications , 2008 .

[23]  Prasanta Roy,et al.  Trajectory Control of a Ball in a Ball and Plate System Using Cascaded PD Controllers Tuned by PSO , 2014, SocProS.

[24]  Naiyao Zhang,et al.  Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme , 2004, Fuzzy Sets Syst..

[25]  Marco A. Moreno-Armendáriz,et al.  Indirect hierarchical FCMAC control for the ball and plate system , 2010, Neurocomputing.

[26]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[27]  Yanyang Liang,et al.  Trajectory tracking sliding mode control of ball and plate system , 2010, 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR 2010).

[28]  Chirdpong Deelertpaiboon,et al.  Ball and plate position control based on fuzzy logic with adaptive integral control action , 2013, 2013 IEEE International Conference on Mechatronics and Automation.

[29]  Dongli Zhang,et al.  Fractional order sliding mode controller design for antilock braking systems , 2013, Neurocomputing.

[30]  R. Svecko,et al.  Modeling and control design for the ball and plate system , 2003, IEEE International Conference on Industrial Technology, 2003.

[31]  Sara Dadras,et al.  Fractional‐Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional‐Order Nonlinear Systems , 2014 .

[32]  S. Sankaranarayanan,et al.  Fractional-Order Sliding Mode Controller Design for a Modified Quadruple Tank Process via Multi-Level Switching , 2015, Comput. Electr. Eng..