On the Mixed H 2 / H ∞ Loop Shaping Trade-offs in Fractional Order Control of the AVR System

—This paper looks at frequency domain design of a fractional order (FO) PID controller for an Automatic Voltage Regulator (AVR) system. Various performance criteria of the AVR system are formulated as system norms and is then coupled with an evolutionary multi-objective optimization (MOO) algorithm to yield Pareto optimal design trade-offs. The conflicting performance measures consist of the mixed H 2 /H ∞ designs for objectives like set-point tracking, load disturbance and noise rejection, controller effort and as such are an exhaustive study of various conflicting design objectives. A fuzzy logic based mechanism is used to identify the best compromise solution on the Pareto fronts. The advantages and disadvantages of using a FOPID controller over the conventional PID controller, which are popular for industrial use, are enunciated from the presented simulations. The relevance and impact of FO controller design from the perspective of the dynamics of AVR control loop is also discussed.

[1]  Rachid Malti,et al.  A note on ℒpℒp-norms of fractional systems , 2013, Autom..

[2]  Kostas Tsakalis,et al.  PID controller tuning by frequency loop-shaping: application to diffusion furnace temperature control , 2000, IEEE Trans. Control. Syst. Technol..

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

[4]  Saptarshi Das,et al.  Intelligent Fractional Order Systems and Control - An Introduction , 2012, Studies in Computational Intelligence.

[5]  Ramon Vilanova,et al.  H∞ optimization‐based fractional‐order PID controllers design , 2014 .

[6]  Shantanu Das,et al.  Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power with a Robust PIλDμ Controller , 2012, ArXiv.

[7]  P.K.S. Tam,et al.  PID tuning based on loop-shaping H∞ control , 1998 .

[8]  Alberto Herreros,et al.  Design of PID-type controllers using multiobjective genetic algorithms. , 2002, ISA transactions.

[9]  Lixiang Li,et al.  Optimum design of fractional order PIλDμ controller for AVR system using chaotic ant swarm , 2012, Expert Syst. Appl..

[10]  R. Firoozian.  Feedback Control Theory , 2009 .

[11]  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.

[12]  Ivo Petráš,et al.  Fractional Order ControlA Tutorial , 2009 .

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

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

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

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

[17]  Saptarshi Das,et al.  Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization , 2013, ArXiv.

[18]  M. Abido.  Environmental/economic power dispatch using multiobjective evolutionary algorithms , 2003, 2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491).

[19]  Yangquan Chen,et al.  Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems , 2012, Autom..

[20]  Hassan Bevrani,et al.  An ILMI Based Solution for Robust Tuning of PI and PID Controllers , 2006 .

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

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

[23]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[24]  Nader Nariman-zadeh,et al.  Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties , 2012 .

[25]  V. Feliu-Batlle,et al.  Frequency specifications regions of fractional-order PI controllers for first order plus time delay processes , 2013 .

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

[27]  D. Valério,et al.  An Introduction to Fractional Control , 2012 .

[28]  Shiow-Fen Hwang,et al.  A Novel Intelligent Multiobjective Simulated Annealing Algorithm for Designing Robust PID Controllers , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[30]  Duarte Valério,et al.  Tuning of Fractional Controllers Minimising H 2 and H∞ Norms , 2006 .

[31]  Weng Khuen Ho,et al.  Self-tuning IMC-PID control with interval gain and phase margins assignment , 2001, IEEE Trans. Control. Syst. Technol..

[32]  YangQuan Chen,et al.  Fractional-order systems and control : fundamentals and applications , 2010 .