Review of fractional PID controller

Abstract Fractional calculus has been studied for over three centuries, and it has multifarious applications in science and engineering. This review investigates its progress since the first reported use of control systems, covering the fractional PID proposed by Podlubny in 1994, and is presenting a state-of-the-art fractional PID controller, incorporating the latest contributions in this field. It highlights developments in the field of fractional PID controllers, including their design and tuning, as well as explores their various versions. Software tools associated to the design of fractional PID controllers are also discussed.

[1]  S. Das,et al.  Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power With a Robust ${\rm PI}^{\lambda} {\rm D} ^{\mu}$ Controller , 2011, IEEE Transactions on Nuclear Science.

[2]  Anissa Zergaïnoh-Mokraoui,et al.  State-space representation for fractional order controllers , 2000, Autom..

[3]  Sara Dadras,et al.  Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ , 2013 .

[4]  YangQuan Chen,et al.  Fractional-order modeling of permanent magnet synchronous motor speed servo system , 2016 .

[6]  Bing-Gang Cao,et al.  Optimization of fractional order PID controllers based on genetic algorithms , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[7]  Reza Ghaderi,et al.  Fractional order control of a coupled tank , 2010 .

[8]  A. P. Singh,et al.  Design of fractional order controller for undamped control system , 2013, 2013 Nirma University International Conference on Engineering (NUiCONE).

[9]  Mohammad Saleh Tavazoei,et al.  A note on the stability of fractional order systems , 2009, Math. Comput. Simul..

[10]  Yangquan Chen,et al.  Fractional order [proportional derivative] controller for a class of fractional order systems , 2009, Autom..

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

[12]  J. A. Tenreiro Machado,et al.  Control and Dynamics of Fractional Order Systems , 2009, SOCO 2009.

[13]  YangQuan Chen,et al.  Fractional-order integral and derivative controller design for temperature profile control , 2008, 2008 Chinese Control and Decision Conference.

[14]  C. Yeroglu,et al.  Note on fractional-order proportional–integral–differential controller design , 2011 .

[15]  Vicente Feliu-Batlle,et al.  Fractional order controller robust to time delay variations for water distribution in an irrigation main canal pool , 2009 .

[16]  Nasser Sadati,et al.  Design of a fractional order PID controller for an AVR using particle swarm optimization , 2009 .

[17]  I. Podlubny,et al.  On Fractional Derivatives, Fractional-Order Dynamic Systems and PIW-controllers , 1997 .

[18]  Y. Chen,et al.  Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers , 2008 .

[19]  Zhen Wang,et al.  Control of an uncertain fractional order economic system via adaptive sliding mode , 2012, Neurocomputing.

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

[21]  Manisha K. Bhole,et al.  A new and simple method to construct root locus of general fractional-order systems. , 2014, ISA transactions.

[22]  Y. Chen,et al.  A comparative introduction of four fractional order controllers , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[23]  Saptarshi Das,et al.  Chaotic multi-objective optimization based design of fractional order PIλDμ controller in AVR system , 2012, ArXiv.

[24]  José António Tenreiro Machado,et al.  Effect of fractional orders in the velocity control of a servo system , 2010, Comput. Math. Appl..

[25]  YangQuan Chen,et al.  Fractional-order [proportional derivative] controller for robust motion control: Tuning procedure and validation , 2009, 2009 American Control Conference.

[26]  A. J. Calderón,et al.  Fractional PID Controllers for Industry Application. A Brief Introduction , 2007 .

[27]  C. Hwang,et al.  Stabilization of unstable first‐order time‐delay systems using fractional‐order pd controllers , 2006 .

[28]  Mohamed Karim Bouafoura,et al.  PI λ D μ controller design for integer and fractional plants using piecewise orthogonal functions , 2010 .

[29]  O. Agrawal A General Formulation and Solution Scheme for Fractional Optimal Control Problems , 2004 .

[30]  Vicente Feliú Batlle,et al.  On the robust control of stable minimum phase plants with large uncertainty in a time constant. A fractional-order control approach , 2014, Autom..

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

[32]  YangQuan Chen,et al.  PRACTICAL TUNING OF FRACTIONAL ORDER PROPORTIONAL AND INTEGRAL CONTROLLER (II): EXPERIMENTS , 2007 .

[33]  Enrico Pisoni,et al.  Interactive tools for designing fractional-order PID controllers , 2012 .

[34]  M. E. Bise,et al.  Fractional calculus application in control systems , 1990, IEEE Conference on Aerospace and Electronics.

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

[36]  Vicente Feliu-Batlle,et al.  Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool , 2009 .

[37]  Eduard Petlenkov,et al.  Fractional-order controller design and digital implementation using FOMCON toolbox for MATLAB , 2013, 2013 IEEE Conference on Computer Aided Control System Design (CACSD).

[38]  Y. Chen,et al.  A fractional order PID tuning algorithm for a class of fractional order plants , 2005, IEEE International Conference Mechatronics and Automation, 2005.

[39]  Lu Liu,et al.  Variable-order fuzzy fractional PID controller. , 2015, ISA transactions.

[40]  Li Meng,et al.  Design of an optimal fractional-order PID controller using multi-objective GA optimization , 2009, 2009 Chinese Control and Decision Conference.

[41]  Ajith Abraham,et al.  Design of fractional-order PIlambdaDµ controllers with an improved differential evolution , 2009, Eng. Appl. Artif. Intell..

[42]  N. Sadati,et al.  An Optimal Fractional Order Controller for an AVR System Using Particle Swarm Optimization Algorithm , 2007, 2007 Large Engineering Systems Conference on Power Engineering.

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

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

[45]  Duarte Valério,et al.  Tuning of fractional PID controllers with Ziegler-Nichols-type rules , 2006, Signal Process..

[46]  I. Petras,et al.  The fractional - order controllers: Methods for their synthesis and application , 2000, math/0004064.

[47]  S. Manabe The non-integer integral and its application to control systems. , 1961 .

[48]  Mansouri Rachid,et al.  IMC-PID-fractional-order-filter controllers design for integer order systems. , 2014, ISA transactions.

[49]  Siddhartha Sen,et al.  Root locus method for any fractional order commensurate system , 2011, IEEE Technology Students' Symposium.

[50]  Ivo Petráš,et al.  Tuning and implementation methods for fractional-order controllers , 2012 .

[51]  A. Oustaloup,et al.  First generation CRONE control , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[52]  Mohammad Pourmahmood Aghababa,et al.  Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm , 2015, Soft Computing.

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

[54]  Serdar Ethem Hamamci An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers , 2007, IEEE Transactions on Automatic Control.

[55]  Ivo Petras,et al.  Control quality enhancement by fractional order controllers , 1998 .

[56]  Vicente Feliu-Batlle,et al.  Fractional robust control of main irrigation canals with variable dynamic parameters , 2007 .

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

[58]  S. Manabe A Suggestion of Fractional-Order Controller for Flexible Spacecraft Attitude Control , 2002 .

[59]  Dingyu Xue,et al.  PRACTICAL TUNING OF FRACTIONAL ORDER PROPORTIONAL AND INTEGRAL CONTROLLER (I): TUNING RULE DEVELOPMENT , 2007 .

[60]  Hung-Cheng Chen,et al.  Tuning of fractional PID controllers using adaptive genetic algorithm for active magnetic bearing system , 2009 .

[61]  Hyo-Sung Ahn,et al.  Fractional-order integral and derivative controller for temperature profile tracking , 2009 .

[62]  Lu Liu,et al.  A review and evaluation of numerical tools for fractional calculus and fractional order controls , 2015, Int. J. Control.

[63]  Ivo Petraÿs,et al.  FRACTIONAL - ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

[64]  Saptarshi Das,et al.  Handling Packet Dropouts and Random Delays for Unstable Delayed Processes in NCS by Optimal Tuning of PIλDμ Controllers with Evolutionary Algorithms , 2011, ISA transactions.

[65]  Shunji Manabe,et al.  EARLY DEVELOPMENT OF FRACTIONAL ORDER CONTROL , 2003 .

[66]  Vicente Feliú Batlle,et al.  Fractional order control strategies for power electronic buck converters , 2006, Signal Process..

[67]  Ching-Hung Lee,et al.  Fractional-order PID controller optimization via improved electromagnetism-like algorithm , 2010, Expert Syst. Appl..

[68]  D. Cafagna,et al.  Fractional calculus: A mathematical tool from the past for present engineers [Past and present] , 2007, IEEE Industrial Electronics Magazine.

[69]  Alain Oustaloup,et al.  The CRONE toolbox for Matlab , 2000, CACSD. Conference Proceedings. IEEE International Symposium on Computer-Aided Control System Design (Cat. No.00TH8537).

[70]  Chyi Hwang,et al.  A note on time-domain simulation of feedback fractional-order systems , 2002, IEEE Trans. Autom. Control..

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

[72]  De-Jin Wang,et al.  Hinfinity design with fractional-order PDU controllers , 2012, Autom..

[73]  Mohammad Haeri,et al.  Fractional order model reduction approach based on retention of the dominant dynamics: application in IMC based tuning of FOPI and FOPID controllers. , 2011, ISA transactions.

[74]  Antonio Visioli,et al.  Advances in Robust Fractional Control , 2014 .

[75]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[76]  Y. Chen,et al.  Tuning fractional order proportional integral controllers for fractional order systems , 2010 .

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

[78]  Haiyang Chao,et al.  Roll-channel fractional order controller design for a small fixed-wing unmanned aerial vehicle , 2010 .

[79]  Ferdinand Svaricek,et al.  Fractional order PID controller (FOPID)-Toolbox , 2013, 2013 European Control Conference (ECC).

[80]  Suman Saha,et al.  On the Selection of Tuning Methodology of FOPID Controllers for the Control of Higher Order Processes , 2011, ISA transactions.

[81]  Suman Saha,et al.  Design of a Fractional Order Phase Shaper for Iso-Damped Control of a PHWR Under Step-Back Condition , 2010, IEEE Transactions on Nuclear Science.

[82]  A. Luo,et al.  Fractional Dynamics and Control , 2011 .

[83]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[84]  Dominik Sierociuk,et al.  Comparison of variable fractional order PID controller for different types of variable order derivatives , 2013, Proceedings of the 14th International Carpathian Control Conference (ICCC).

[85]  J. Machado Analysis and design of fractional-order digital control systems , 1997 .

[86]  Eduard Petlenkov,et al.  FOMCON: Fractional-order modeling and control toolbox for MATLAB , 2011, Proceedings of the 18th International Conference Mixed Design of Integrated Circuits and Systems - MIXDES 2011.

[87]  Ying Luo,et al.  Lateral directional fractional order (PI) π control of a small fixed-wing unmanned aerial vehicles: controller designs and flight tests , 2011 .

[88]  Duarte Valério,et al.  Introduction to single-input, single-output fractional control , 2011 .

[89]  Enrico Pisoni,et al.  An interactive tool for fractional order PID controllers , 2009, 2009 35th Annual Conference of IEEE Industrial Electronics.

[90]  Luigi Fortuna,et al.  New results on the synthesis of FO-PID controllers , 2010 .

[91]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[92]  I. Petráš Stability of Fractional-Order Systems with Rational Orders , 2008, 0811.4102.

[93]  Margarita Rivero,et al.  Stability of Fractional Order Systems , 2013 .

[94]  Jun-yi Cao,et al.  Design of Fractional Order Controllers Based on Particle Swarm Optimization , 2006, 2006 1ST IEEE Conference on Industrial Electronics and Applications.

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

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

[97]  Serdar Ethem Hamamci Stabilization using fractional-order PI and PID controllers , 2007 .

[98]  Alexandra M. Galhano,et al.  Performance of Fractional PID Algorithms Controlling Nonlinear Systems with Saturation and Backlash Phenomena , 2007 .

[99]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[100]  Shantanu Das,et al.  Improved Model Reduction and Tuning of Fractional Order PIλDμ Controllers for Analytical Rule Extraction with Genetic Programming , 2012, ISA transactions.

[101]  Inés Tejado,et al.  Auto-tuning of fractional order PI·D· controllers using a PLC , 2009, 2009 IEEE Conference on Emerging Technologies & Factory Automation.

[102]  Robain De Keyser,et al.  Fractional order control of unstable processes: the magnetic levitation study case , 2015 .

[103]  Saptarshi Das,et al.  Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization , 2015, Appl. Soft Comput..

[104]  P. Lino,et al.  New tuning rules for fractional PIα controllers , 2007 .

[105]  Reyad El-Khazali,et al.  Fractional-order PIλDμ controller design , 2013, Comput. Math. Appl..