Robust second-order PD α type iterative learning control for a class of uncertain fractional order singular systems

This paper presents a robust second-order feedback PD α type iterative learning control (ILC) for a class of uncertain fractional-order singular systems. Sufficient conditions for the robust convergence of the proposed PD α type of learning control algorithm, with respect to the bounded external disturbance and uncertainity, have been established and specified for time domain. Finally, simulation examples are presented to illustrate the performance of the proposed fractional order ILC.

[1]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[2]  Jian-Xin Xu,et al.  Analysis of continuous iterative learning control systems using current cycle feedback , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[3]  Peter C. Müller,et al.  Modelling and control of mechatronic systems by the descriptor approach , 2005 .

[4]  Jian-Xin Xu,et al.  Iterative Learning Control , 1998 .

[5]  H. Rosenbrock.  Structural properties of linear dynamical systems , 1974 .

[6]  Salim Ibrir.  LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case , 2009 .

[7]  I. Ozkol,et al.  Classical and Fractional-Order Analysis of the Free and Forced Double Pendulum , 2010 .

[8]  Yangquan Chen,et al.  A Survey on Fractional-Order Iterative Learning Control , 2013, J. Optim. Theory Appl..

[9]  Hyo-Sung Ahn,et al.  Fractional‐order iterative learning control for fractional‐order linear systems , 2011 .

[10]  Mihailo P. Lazarević,et al.  Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula , 2014 .

[11]  Peter J. Torvik,et al.  Fractional calculus in the transient analysis of viscoelastically damped structures , 1983 .

[12]  Tadeusz Kaczorek.  SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS , 2013 .

[13]  Kevin L. Moore,et al.  On D"-type Iterative Learning Control , 2001 .

[14]  Y. Chen,et al.  Fractional order iterative learning control , 2009, 2009 ICCAS-SICE.

[15]  Peter C. Müller,et al.  Stability of Linear Mechanical Systems With Holonomic Constraints , 1993 .

[16]  Zhou Lun,et al.  Iterative Learning Control for the Singular Systems with Delay , 2006, 2007 Chinese Control Conference.

[17]  Piao Feng,et al.  Iterative Learning Control for a Class of Singular Systems , 2007 .

[18]  Yong-Hong Lan,et al.  Dα‐Type Iterative Learning Control for Fractional‐Order Linear Time‐Delay Systems , 2013 .

[19]  Yisheng Zhong,et al.  Sufficient and Necessary Condition of Admissibility for Fractional-order Singular System , 2011, ArXiv.

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

[21]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[22]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[23]  A.G. Alleyne,et al.  A survey of iterative learning control , 2006, IEEE Control Systems.

[24]  Yangquan Chen,et al.  Analysis of a high-order iterative learning control algorithm for uncertain nonlinear systems with state delays , 1998, Autom..

[25]  Dumitru Baleanu,et al.  A Central Difference Numerical Scheme for Fractional Optimal Control Problems , 2008, 0811.4368.

[26]  Zhen Wang,et al.  Stabilization of singular fractional-order systems: A linear matrix inequality approach , 2012, 2012 IEEE International Conference on Automation and Logistics.

[27]  Zeungnam Bien,et al.  Higher-order iterative learning control algorithm , 1989 .

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

[29]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

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

[31]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[32]  Hak-Sung Lee,et al.  Study on robustness of iterative learning control with non-zero initial error , 1996 .

[33]  Shengda Liu,et al.  Iterative learning control based on a noninstantaneous impulsive fractional-order system , 2016 .

[34]  Ivan Buzurovic.  DYNAMIC MODEL OF MEDICAL ROBOT REPRESENTED AS DESCRIPTOR SYSTEM , 2007 .

[35]  M. Ortigueira,et al.  THE INITIAL CONDITIONS OF RIEMANN-LIOUVILLE AND CAPUTO DERIVATIVES , 2011 .

[36]  Zeungnam Bien,et al.  Iterative learning control: analysis, design, integration and applications , 1998 .

[37]  Wojciech Mitkowski,et al.  Fractional-Order Models of the Ultracapacitors , 2013, RRNR.

[38]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[39]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[40]  Tadeusz Kaczorek,et al.  Singular fractional linear systems and electrical circuits , 2011, Int. J. Appl. Math. Comput. Sci..

[41]  Emre Kural,et al.  96 A Survey of Iterative Learning Control Al earning-based method for high-performance tracking control , 2006 .

[42]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[43]  K. Moore,et al.  Iterative Learning Control: Robustness and Monotonic Convergence for Interval Systems , 2010 .

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

[45]  T. R.. Harris Tephly.  Singular systems of differential equations as dynamic models for constrained robot systems , 1986 .

[46]  Christophe Farges,et al.  Fractional systems state space description: some wrong ideas and proposed solutions , 2014 .

[47]  F. Mainardi.  Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena , 1996 .

[48]  Michael J. Grimble,et al.  Iterative Learning Control for Deterministic Systems , 1992 .

[49]  C. Fang,et al.  Analysis of stability robustness for generalized state-space systems with structured perturbations , 1993 .

[50]  Chong-Ho Choi,et al.  Iterative learning control in feedback systems , 1995, Autom..

[51]  Masaru Uchiyama,et al.  Formation of High-Speed Motion Pattern of a Mechanical Arm by Trial , 1978 .

[52]  P. Tzekis,et al.  A descriptor package for Mathematica , 2003 .

[53]  Qingling Zhang,et al.  Iterative Learning Control for Uncertain Singular System , 2006, 2006 IEEE International Conference on Information Acquisition.