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

 
 
 
  • Abstract
  • Keywords
  • References
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  • 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.

     


  • Keywords


    Inverted pendulum, optimal fractional order PID controller, MARC controller, fractional order, MIT rule.

  • References


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

      [2] Kurdekar V & Borkar S, “Inverted pendulum control: A brief overview”, 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 System”, 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 control”, 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 Controller”, Science International, Vol.27, No.2, (2015).

      [6] Moghaddas M & Dastranj MR, “Design of Optimal PID Control for Inverted Pendulum Using Genetic Algorithm”, 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 analysis”, 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 robotics”, International conference on Education and e-Learning Innovations (ICEELI), (2012), pp.1-6.

      [9] Ladaci S & Charef A, “Model reference adaptive control with fractional derivative”, 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 Rule”, 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 enhancement”, 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 technique”, 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 methods”, 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 Control”, 2nd International conference on networking and advanced system , (2015).

      [15] Podlubny I, “Fractional order system and PIλDµ controllers”, 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 MATLAB”, IEEE Conference on Computer Aided Control System Design (CACSD), (2013), pp.340-345.

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

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


 

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Article ID: 11830
 
DOI: 10.14419/ijet.v7i2.21.11830




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