Performance analysis of fractional order extremum seeking control.

Extremum-seeking scheme is a powerful adaptive technique to optimize steady-state system performance. In this paper, a novel extremum-seeking scheme for the optimization of nonlinear plants using fractional order calculus is proposed. The fractional order extremum-seeking algorithm only utilizes output measurements of the plant, however, it performs superior in many aspects such as convergence speed and robustness. A detailed stability analysis is given to not only guarantee a faster convergence of the system to an adjustable neighborhood of the optimum but also confirm a better robustness for proposed algorithm. Furthermore, simulation and experimental results demonstrate that the fractional order extremum-seeking scheme for nonlinear systems outperforms the traditional integer order one.

[1]  K.B. Ariyur,et al.  Control of formation flight via extremum seeking , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  Mohammad Ali Nekoui,et al.  Stability analysis of multiple time delayed fractional order systems , 2013, 2013 American Control Conference.

[3]  Wouter Caarls,et al.  Comparison of extremum seeking control algorithms for robotic applications , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[4]  Miroslav Krstic,et al.  Stability of extremum seeking feedback for general nonlinear dynamic systems , 2000, Autom..

[5]  Dragan Nesic,et al.  Extremum seeking control: Convergence analysis , 2009, ECC.

[6]  Zhicheng Ji,et al.  Maximum Power Point Tracking of Wind Energy Conversion Systems Based on Sliding Mode Extremum Seeking Control , 2008, 2008 IEEE Energy 2030 Conference.

[7]  Mary Ann Weitnauer,et al.  Distributed extremum seeking and formation control for nonholonomic mobile network , 2015, Syst. Control. Lett..

[8]  Miroslav Krstic,et al.  Extremum Seeking Control , 2019, Encyclopedia of Systems and Control.

[9]  Xiao Li,et al.  Maximum Power Point Tracking for Photovoltaic System Using Adaptive Extremum Seeking Control , 2013, IEEE Transactions on Control Systems Technology.

[10]  Nima Ghods,et al.  Extremum Seeking for Mobile Robots , 2011 .

[11]  Sergey V. Drakunov,et al.  ABS control using optimum search via sliding modes , 1995, IEEE Trans. Control. Syst. Technol..

[12]  I. Podlubny.  Fractional differential equations , 1998 .

[13]  K. Moore,et al.  Discretization schemes for fractional-order differentiators and integrators , 2002 .

[14]  Ying Luo,et al.  TUNING FRACTIONAL ORDER PROPORTIONAL INTEGRAL CONTROLLERS FOR TIME DELAYED SYSTEMS WITH A FRACTIONAL POLE , 2011 .

[15]  I. Queinnec,et al.  MPPT Based on Sinusoidal Extremum-Seeking Control in PV Generation , 2012 .

[16]  A. El Aroudi,et al.  Analysis and Comparison of Extremum Seeking Control Techniques , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[17]  S. Moura,et al.  Asymptotic convergence through Lyapunov-based switching in extremum seeking with application to photovoltaic systems , 2010, Proceedings of the 2010 American Control Conference.

[18]  Miroslav Krstic,et al.  Multivariable Newton-based extremum seeking , 2011, IEEE Conference on Decision and Control and European Control Conference.

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

[20]  Jing Li,et al.  A Novel Chaotic Annealing Recurrent Neural Network for Multi-parameters Extremum Seeking Algorithm , 2006, ICONIP.

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

[22]  Miroslav Krstic,et al.  HCCI Engine Combustion-Timing Control: Optimizing Gains and Fuel Consumption Via Extremum Seeking , 2009, IEEE Transactions on Control Systems Technology.

[23]  Miguel Romero,et al.  GPC Control of a Fractional–Order Plant: Improving Stability and Robustness , 2008 .

[24]  Erik Hellström,et al.  On-Board Calibration of Spark Timing by Extremum Seeking for Flex-Fuel Engines , 2013, IEEE Transactions on Control Systems Technology.

[25]  Chunlei Zhang,et al.  Extremum-Seeking Control and Applications: A Numerical Optimization-Based Approach , 2011 .

[26]  Denis Dochain,et al.  Extremum seeking control and its application to process and reaction systems: A survey , 2011, Math. Comput. Simul..

[27]  I. Petráš.  Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[28]  Ying Tan,et al.  On the Choice of Dither in Extremum Seeking Systems: a Case Study , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[29]  P. Olver.  Nonlinear Systems , 2013 .

[30]  Chris Manzie,et al.  Newton-Like Extremum-Seeking for the Control of Thermoacoustic Instability , 2010, IEEE Transactions on Automatic Control.

[32]  Bilin Aksun Güvenç,et al.  Extremum-Seeking Control of ABS Braking in Road Vehicles With Lateral Force Improvement , 2014, IEEE Transactions on Control Systems Technology.

[33]  Nicholas R. Gans,et al.  Extremum seeking control of a nonholonomic mobile robot with limited field of view , 2013, 2013 American Control Conference.

[34]  Her-Terng Yau,et al.  Design and Study on Sliding Mode Extremum Seeking Control of the Chaos Embedded Particle Swarm Optimization for Maximum Power Point Tracking in Wind Power Systems , 2014 .

[35]  Miroslav Krstic,et al.  Power Optimization for Photovoltaic Microconverters Using Multivariable Newton-Based Extremum Seeking , 2012, IEEE Transactions on Control Systems Technology.

[36]  Kartik B. Ariyur,et al.  Real-Time Optimization by Extremum-Seeking Control , 2003 .

[37]  S. Moura,et al.  Lyapunov-based switched extremum seeking for photovoltaic power maximization , 2013 .

[38]  Sara Dadras,et al.  Fractional order equivalent series resistance modelling of electrolytic capacitor and fractional order failure prediction with application to predictive maintenance , 2016 .

[39]  Mohammad Saleh Tavazoei,et al.  Chaotic attractors in incommensurate fractional order systems , 2008 .

[40]  Sara Dadras,et al.  Fractional Order Coulomb Friction Compensation: Convergence Analysis and Experimental Validation on a Fractional Horsepower Dynamometer , 2013 .

[41]  YangQuan Chen,et al.  UBIQUITOUS FRACTIONAL ORDER CONTROLS , 2006 .

[42]  Shouming Zhong,et al.  Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems , 2014, Autom..

[43]  Ivo Petras,et al.  Stability of Fractional-Order Systems , 2011 .

[44]  Tankut Acarman,et al.  Stability and performance improvement of extremum seeking control with sliding mode , 2003 .

[45]  Yangquan Chen,et al.  Application of fractional order current controller in three phase grid-connected PV systems , 2014, 2014 American Control Conference.

[46]  YangQuan Chen,et al.  Fractional Horsepower Dynamometer - A General Purpose Hardware-In-The-Loop Real-Time Simulation Platform for Nonlinear Control Research and Education , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[47]  Miroslav Krstic,et al.  Performance improvement and limitations in extremum seeking control , 2000 .

[48]  Yu Tian,et al.  Control of a Mobile Robot Subject to Wheel Slip , 2014, J. Intell. Robotic Syst..