A Numerical Study for Plant-Independent Evaluation of Fractional-order PID Controller Performance 1 1This study is based upon works from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).

Abstract A stunning outcome of fractional calculus for control practice are fractional-order PID (FOPID) controllers. Based on their experimental and numerical results, several studies have reported improvements in control performance of closed loop control systems by FOPID controllers compared to classical PID controllers. However, the industry at large is still cautious about adopting FOPID controllers because of the lack of concrete data about the related cost-benefit trade-off. Main concerns arise at the point that there have not been a quantitative evaluation scheme that clearly demonstrates for which concrete cases FOPID controllers can provide considerable improvements in control. Therefore, there is a need for more thorough theoretical and quantitative demonstrations. To that end, this study presents a plant function independent evaluation methodology to reveal inherent advantages of FOPID control. Impacts of two additional controller coefficients, namely fractional orders of differentiator and integrator, are analyzed in the frequency domain and their contributions to open loop gain maximization, phase margin and Reference to Disturbance Rate (RDR) performance are investigated.

[1]  Eduard Petlenkov,et al.  Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop. , 2016, ISA transactions.

[2]  Cemal Keles,et al.  Disturbance rejection performance analyses of closed loop control systems by reference to disturbance ratio. , 2015, ISA transactions.

[3]  Antonio Visioli,et al.  On the fragility of fractional-order PID controllers for IPDT processes , 2017, 2017 25th Mediterranean Conference on Control and Automation (MED).

[4]  Yangquan Chen,et al.  Two direct Tustin discretization methods for fractional-order differentiator/integrator , 2003, J. Frankl. Inst..

[5]  Antonio Visioli,et al.  Tuning rules for optimal PID and fractional-order PID controllers , 2011 .

[6]  Víctor M Alfaro.  PID controllers' fragility. , 2007, ISA transactions.

[7]  Wenlong Fu,et al.  An adaptively fast fuzzy fractional order PID control for pumped storage hydro unit using improved gravitational search algorithm , 2016 .

[8]  Y. Chen,et al.  Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review , 2004 .

[9]  Baris Baykant Alagoz,et al.  Implicit disturbance rejection performance analysis of closed loop control systems according to communication channel limitations , 2015 .

[10]  N. Macon,et al.  A continued fraction for , 1955 .

[11]  YangQuan Chen,et al.  Fractional order control - A tutorial , 2009, 2009 American Control Conference.

[12]  Igor Podlubny,et al.  On Fractional Derivatives, Fractional-Orlder Dynamic Systems and PIXD~-controllei~s , 1997 .

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