1,721,087 research outputs found
On the Laguerre Rational Approximation to Fractional Discrete Derivative and Integral Operators
No full textThis note ties the Laguerre continued fraction expansion of the Tustin fractional discrete-time operator to irreducible Jacobi tri-diagonal matrices. The aim is to prove that the Laguerre approximation to the Tustin fractional operator s(-v) (or s(v)) is stable and minimum-phase for any value 0 < v < 1 of the fractional order v. It is also shown that zeros and poles of the approximation are interlaced and lie in the unit circle of the complex z-plane, keeping a special symmetry on the real axis. The quality of the approximation is analyzed both in the frequency and time domain. Truncation error bounds of the approximants are given
Erratum: Correction to “Closed-Form Rational Approximations of Fractional, Analog and Digital Differentiators/Integrators”
No full textThiele’s continued fractions in digital implementation of noninteger differintegrators
No full textA rational approximation is the preliminary step of all the indirect methods for implementing digital fractional differintegrators s^nu, with nu in R, 0 < |nu| < 1, and where s in C. This paper employs the convergents of two Thiele’s continued fractions as rational approximations of s^nu. In a second step, it uses known s-to-z transformation rules to obtain a rational, stable, and minimum-phase z-transfer function,with zeros interlacing poles. The paper concludes with a comparative analysis of the quality of the proposed approximations in dependence of the used s-to-z transformations and of the sampling period
A Digital, Noninteger Order, Differentiator using Laguerre Orthogonal Sequences
No full textThis paper presents a novel procedure to design a digital, noninteger order, differentiator. The method is based on the Laguerre series expansion. Firstly, a discrete equivalent of the noninteger derivative Euler backward operator is given in the z-domain. Secondly, this operator is expanded into a Taylor series, which provides the data for the approximation of the Laguerre noninteger order digital derivative operator. Simulation results show the accuracy of the approximation, by measuring the frequency response for different values of the derivative noninteger order
Laguerre Approximation of Fractional Systems
No full textSystems characterised by fractional power poles can be called fractional systems. Here, Laguerre orthogonal polynomials are employed to approximate fractional systems by minimum phase, reduced order, rational transfer functions. Both the time and the frequency-domain analysis exhibit the accuracy of the approximation
Analog Realizations of Fractional-Order Integrators/Differentiators: A Comparison
No full textNon-integer differential or integral operators can be used to realize fractional-order controllers, which provide better performance than conventional PID controllers, especially if controlled plants are of non-integer-order. In many cases, fractional-order controllers are more flexible than PID and ensure robustness for high gain variations. This paper compares three different approaches to approximate fractional-order differentiators or integrators. Each approximation realizes a rational transfer function characterized by a sequence of interlaced minimum-phase zeros and stable poles. The frequency-domain comparison shows that best approximations have nearly the same zero-pole locations, even if they are obtained starting from different points of view
Concerning Continued Fractions Representation of Noninteger Order Digital Differentiators
No full textThe discretization of a fractional-order differentiator s^nu, where nu is a real number 0<nu<1, is an important issue in digital signal processing. This letter gives the analytical expression of the convergents of a continued fraction expansion of the binomial (1+s)^nu to get a rapidly convergent, stable, minimum-phase approximation of digital differentiators
Discrete-Event Simulation of a Complex Intermodal Container Terminal - A Case-Study of Standard Unloading/Loading Processes of Vessel Ships
No full textThis paper analyzes the performance of a complex maritime intermodal container terminal. The aim is to propose changes in the system resources or in handling procedures that guarantee better performance in perturbed conditions. A discrete-event system simulation study shows that, in future conditions of increased traffic volumes and reduced available stacking space, more internal transport vehicles, or appropriate scheduling and routing policies, or an increased degree of automation would improve the performance
Closed-form rational approximations of fractional, analog and digital differentiators/integrators
No full textThis paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating , with , and . The expressions of the coefficients are given in terms of and of the degree of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition
High-Speed Digital Realizations of Fractional Operators in the Delta Domain
No full textThe realization of fractional-order controllers is based on the approximation of the irrational operators by continuous or discrete transfer functions. However, at high sampling frequencies, discrete z-transfer functions approximations can be very sensitive even to small changes in coefficient values. This technical note proposes a realization of s^nu, in terms of transfer functions in the complex delta-domain, which improves considerably the robustness of the approximation to parameter changes and then to truncation in transfer function coefficients applied for implementation with finite word length
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