Field Programmable Analog Array Implementation of Noninteger Order PIλDμ Controller

Recently, a renewed interest has been devoted to noninteger, or fractional, order systems. This is due to the fact that they well model a lot of physical systems and can be usefully applied in the area of automatic control. On drawback, mainly faced in the area of control systems, is related to their practical realization, essentially due to their infinite dimension nature. In this paper, an analog implementation of a noninteger order PIλDμ controller by using field programmable analog array is proposed. The frequency analysis of the reported examples shows the feasibility and reliability of the proposed approach.

[1]  Vasily E. Tarasov,et al.  Coupled oscillators with power-law interaction and their fractional dynamics analogues , 2007 .

[2]  J. C. Wang.  Realizations of Generalized Warburg Impedance with RC Ladder Networks and Transmission Lines , 1987 .

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

[4]  B. Ross,et al.  Fractional Calculus and Its Applications , 1975 .

[5]  Benoit B. Mandelbrot,et al.  Some noises with I/f spectrum, a bridge between direct current and white noise , 1967, IEEE Trans. Inf. Theory.

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

[7]  Gary W. Bohannan.  Analog fractional order controller in a temperature control application , 2006 .

[8]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

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

[10]  Maria da Graça Marcos,et al.  Fractional dynamics in the trajectory control of redundant manipulators , 2008 .

[11]  Alain Oustaloup,et al.  Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation , 1981 .

[12]  M. S. Keshner.  1/f noise , 1982, Proceedings of the IEEE.

[13]  Vasily E. Tarasov,et al.  Conservation laws and Hamilton’s equations for systems with long-range interaction and memory , 2008 .

[14]  B. Onaral,et al.  Linear and nonlinear properties of platinum electrode polarisation. Part 1: frequency dependence at very low frequencies , 1982, Medical and Biological Engineering and Computing.

[15]  G. Zaslavsky,et al.  Fractional dynamics of systems with long-range interaction , 2006, 1107.5436.