Tuning of a Pix+iyD Fractional Complex Order Controller

This paper deals with Fractional Complex Order Controller FCOC tuning. The paper presents new structure of FCOC with the form PIx+iyD, in which x and y are the real and imaginary parts of the integral complex order, respectively. With the controller's five parameters, we can fulfil five design requirements. Design specifications are set to ensure robustness toward gain variations, noise on system output and disturbance. A tuning method for the Controller is presented to accomplish design requirements. The proposed design method is investigated with a Second Order Plus Time Delay resonant system. Frequency and time domain analysis are presented in this manuscript.

[1]  Mohamed Naceur Abdelkrim,et al.  Guaranteed frequency-domain identification of fractional order systems: application to a real system , 2012, Int. J. Model. Identif. Control..

[2]  A. Oustaloup,et al.  Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements , 2004 .

[3]  M. Amairi,et al.  Multi-objective optimization based design of fractional PID controller , 2015, 2015 IEEE 12th International Multi-Conference on Systems, Signals & Devices (SSD15).

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

[5]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[6]  J. Machado.  Optimal tuning of fractional controllers using genetic algorithms , 2010 .

[7]  Mohamed Naceur Abdelkrim,et al.  EIV methods for system identification with fractional models , 2012 .

[8]  Yangquan Chen,et al.  A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments , 2010, IEEE Transactions on Control Systems Technology.

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

[10]  Harold T. Davis,et al.  The theory of linear operators from the standpoint of differential equations of infinite order , 1936 .

[11]  N. Heymans,et al.  Fractional Calculus Description of Non-Linear Viscoelastic Behaviour of Polymers , 2004 .

[12]  José António Tenreiro Machado,et al.  Optimal Controllers with Complex Order Derivatives , 2013, J. Optim. Theory Appl..

[13]  Khaled Jelassi,et al.  Fractional order modeling of rotor skin effect in induction machines , 2013 .

[14]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[15]  Alain Oustaloup,et al.  Fractional Order Differentiation and Robust Control Design , 2015 .

[16]  Mohamed Aoun,et al.  Bode shaping-based design methods of a fractional order PID controller for uncertain systems , 2015 .

[17]  YangQuan Chen,et al.  Fractional order PID control of a DC-motor with elastic shaft: a case study , 2006, 2006 American Control Conference.

[18]  Alain Oustaloup,et al.  Robust factional order PID controllers: The first generation CRONE CSD approach , 2014, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014.

[19]  A. Ranjbar,et al.  New tuning design schemes of fractional complex-order PI controller , 2016 .

[20]  M. Aoun,et al.  Systèmes linéaires non entiers et identification par bases orthogonales non entières , 2005 .