A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10In this paper a new least-squares (LS) approach is used to model the discrete-time fractional differintegrator. This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model. In minimizing the error power we obtain a set of suitable normal equations that allow us to obtain the ARMA parameters. This new LS is then applied to the same examples as in [R.S. Barbosa, J.A. Tenreiro Machado, I.M. Ferreira, Least-squares design of digital fractional-order operators, FDA’2004 First IFAC Workshop on Fractional Differentiation and Its Applications, Bordeaux, France, July 19–21, 2004, P. Ostalczyk, Fundamental properties of the fractional-order discrete-time integrator, Signal Processing 83 (2003) 2367–2376] so performance comparisons can be drawn. Simulation results show that both magnitude frequency responses are essentially identical. Concerning the modeling stability, both algorithms present similar limitations, although for different ARMA model orders

A novel ARX-based discretization method for linear non-rational systems

This paper presents a novel, simple, flexible and effective discretization method for linear non-rational systems including arbitrary linear fractional order systems (LFOS). The discretization algorithm relies on the direct integration in the complex domain and application of ARX (AutoRegressive eXogenous) model. Parameters of ARX-model are obtained by numerical inversion of Laplace transform from the set of input/output data from recorded step response to model of non-rational system. Numerical simulations of several representatives of LFOS (e.g. fractional order PID controller, fractional logarithmic filter, fractional oscillator etc.) are used to demonstrate the effectiveness of the proposed discretization method, both in the time and frequency domains. The obtained results indicate that the proposed ARX-based discretization method is adequate technique for obtaining digital approximation of LFOS

Furher results on PIalphaDbeta type control of expansion turbine in the air production cryogenic liquid

Here, it suggests and obtains a new algorithms of PID control based on fractional calculus (FC) in the producing of technical gases, i.e air production cryogenic liquid. Production liquid air low pressure was first introduced by P. L. Kapica and includes production liquor air pressure p2 = 6 - 7 bar and expansion in the gas turbine. For application in the synthesis of control input temperature and the flow of air expansion turbine, it is necessary to determine the appropriate differential equations linear’s part of the building guidance as well as the procedural object. The paper presents a new robust control algorithms of PIalpha Dbeta type which based on using fractional calculus. The objective of this work is to find out suitable settings for a fractional PIalpha Dbeta controller in order to fulfill different design specifications for the closed-loop system, taking advantage of the fractional orders, alpha and beta . Last, problem of discretization of proposed PIalpha Dbeta will be treated as a key step in digital implementatio