A performance analysis of fractional order based MARC controller over optimal fractional order PID controller on inverted pendulum

  • Authors

    • Deep Mukherjee
    • Palash Kumar Kundu
    • Apurba Ghosh
    2018-04-20
    https://doi.org/10.14419/ijet.v7i2.21.11830
  • Inverted pendulum, optimal fractional order PID controller, MARC controller, fractional order, MIT rule.

  • Abstract

    This paper presents a new way to design MIT rule as an advanced technique of MARC (Model Adaptive Reference Controller) for an integer order inverted pendulum system. Here, our work aims to study the performance characteristics of fractional order MIT rule of MARC controller followed by optimal fractional order PID controller in MATLAB SIMULINK environment with respect to time domain specifications. Here, to design fractional order MIT rule Grunwald-Letnikov fractional derivative calculus method has been considered and based on Grunwald-Letnikov fractional calculus rule fractional MIT rule has been designed in SIMULINK. The proposed method aims finally to analyze overall desired closed loop dynamic performance on inverted pendulum with different performance criteria and to show the desired nature of an unstable system over optimal fractional order PID controller.

     

  • References

    1. [1] Annaswamy AM, “Model reference adaptive controlâ€, Control systems, Robotics & Automation.

      [2] Kurdekar V & Borkar S, “Inverted pendulum control: A brief overviewâ€, International Journal of Modern Engineering Research, Vol.3, No.5, (2013), pp.2924-2927.

      [3] Jain P & Nigam MJ, “Design of a Model Reference Adaptive Controller Using Modified MIT Rule for a Second Order Systemâ€, Advance in Electronic and Electrical Engineering, Vol.3, (2013), pp.477-484.

      [4] Vinagre BM, Petráš I, Podlubny I & Chen YQ, “Using fractional order adjustment rules and fractional order reference models in model-reference adaptive controlâ€, Nonlinear Dynamics, Vol.29, No.1-4, (2002), pp.269-279.

      [5] Eizadiyan MA & Naseriyan M, “Control of Inverted Pendulum Cart System by Use of PID Controllerâ€, Science International, Vol.27, No.2, (2015).

      [6] Moghaddas M & Dastranj MR, “Design of Optimal PID Control for Inverted Pendulum Using Genetic Algorithmâ€, IJIMT, Vol.3, (2012), pp.234-240.

      [7] Duka AV, Oltean SE & Dulau M, “Model reference adaptive control and fuzzy model reference learning control for the inverted pendulum. Comparative analysisâ€, Proceedings of WSEAS International Conference on Dynamical Systems and Control, (2005), pp.168-173.

      [8] Boubaker O, “The inverted pendulum: A fundamental benchmark in control theory and roboticsâ€, International conference on Education and e-Learning Innovations (ICEELI), (2012), pp.1-6.

      [9] Ladaci S & Charef A, “Model reference adaptive control with fractional derivativeâ€, Proceedings of International Conference on Tele-Communication Systems, Medical Electronics and Automation, Algeria, (2003).

      [10] Adrian C & Corneliu A, “The Simulation of Adaptive System Using MIT Ruleâ€, 10th WSEAS Int. Conf. on Mathematical methods and computational techniques in Electrical Engineering, (2008).

      [11] Bensafia Y, Ladaci S & Khettab K, “Using a fractionalized integrator for control performance enhancementâ€, Int. Journal of Innovative Computing, Information and Control, IJICIC, Vol.11, No.6, (2015), pp.2013-2028.

      [12] Loverro A, “Fractional calculus: history, definitions and applications for the engineer. Rapport techniqueâ€, University of Notre Dame: Department of Aerospace and Mechanical Engineering, (2004), pp.1-28.

      [13] Abedini M, Nojoumian MA, Salarieh H & Meghdari A, “Model reference adaptive control in fractional order systems using discrete-time approximation methodsâ€, Communications in Nonlinear Science and Numerical Simulation, Vol.25, No.1-3, (2015), pp.27-40.

      [14] Ladaci S & Khettab K, “Using the Fractional Model Reference for Tracking Trajectory in Adaptive Controlâ€, 2nd International conference on networking and advanced system , (2015).

      [15] Podlubny I, “Fractional order system and PIλDµ controllersâ€, IEEE Transactions on Automatic Control, (1999), pp.208-214.

      [16] Tepljakov A, Petlenkov E, Belikov J & Finajev J, “Fractional-order controller design and digital implementation using FOMCON toolbox for MATLABâ€, IEEE Conference on Computer Aided Control System Design (CACSD), (2013), pp.340-345.

      [17] Moraglio A & Johnson CG, “Geometric generalization of the nelder-mead algorithmâ€, European Conference on Evolutionary Computation in Combinatorial Optimization, (2010), pp.190-201.

      [18] Wei Y & Sun Z, “On Fractional Order Composite Model Reference Adaptive Controlâ€, International Journal of Systems, Vol.47, (2016).

  • Downloads

  • How to Cite

    Mukherjee, D., Kumar Kundu, P., & Ghosh, A. (2018). A performance analysis of fractional order based MARC controller over optimal fractional order PID controller on inverted pendulum. International Journal of Engineering & Technology, 7(2.21), 29-33. https://doi.org/10.14419/ijet.v7i2.21.11830

    Received date: 2018-04-21

    Accepted date: 2018-04-21

    Published date: 2018-04-20