14,694 research outputs found
Optimized Quality Factor of Fractional Order Analog Filters with Band-Pass and Band-Stop Characteristics
Fractional order (FO) filters have been investigated in this paper, with
band-pass (BP) and band-stop (BS) characteristics, which can not be achieved
with conventional integer order filters with orders lesser then two. The
quality factors for symmetric and asymmetric magnitude response have been
optimized using real coded Genetic Algorithm (GA) for a user specified center
frequency. Parametric influence of the FO filters on the magnitude response is
also illustrated with credible numerical simulations.Comment: 6 pages, 13 figures; 2012 Third International Conference on
Computing, Communication and Networking Technologies (ICCCNT'12), July 2012,
Coimbator
Fractional robust control of ligthly damped systems
The article proposes a method to design a robust controller ensuring the damping ratio of a closed-loop control. The method uses a contour para-meterized by the damping ratio in the Nichols plane and the complex non-integer (or fractional)differentiation to compute a transfer function whose open-loop Nichols locus tangents this contour, thus ensuring dynamic performance. The proposed method is applied to a flexible structure (a clamped-free beam with piezoelectric ceramics). The aims of the control loop are to decrease the vibrations and to ensure the damping ratio of the controlled system
A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands
This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem
Radar matched filtering using the fractional fourier transform
Abstract-A matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive noise. Matched filters are commonly used in radar systems where the transmitted signal is known and may be used as a replica to be correlated with the received signal which can be carried out by multiplication in the frequency domain by applying Fourier Transform (FT). Fractional Fourier transform (FrFT) is the general case for the FT and is superior in chirp pulse compression using the optimum FrFT order. In this paper a matched filter is implemented for a chirp radar signal in the optimum FrFT domain. Mathematical formula for a received chirp signal in the frequency domain and a generalized formula in the fractional Fourier domain are presented in this paper using the Principle of Stationary Phase (PSP). These mathematical expressions are used to show the limitations of the matched filter in the fractional Fourier domain. The parameters that affect the chirp signal in the optimum fractional Fourier domain are described. The performance enhancement by using the matched filter in the fractional Fourier domain for special cases is presented
'Constant in gain Lead in phase' element - Application in precision motion control
This work presents a novel 'Constant in gain Lead in phase' (CgLp) element
using nonlinear reset technique. PID is the industrial workhorse even to this
day in high-tech precision positioning applications. However, Bode's gain phase
relationship and waterbed effect fundamentally limit performance of PID and
other linear controllers. This paper presents CgLp as a controlled nonlinear
element which can be introduced within the framework of PID allowing for wide
applicability and overcoming linear control limitations. Design of CgLp with
generalized first order reset element (GFORE) and generalized second order
reset element (GSORE) (introduced in this work) is presented using describing
function analysis. A more detailed analysis of reset elements in frequency
domain compared to existing literature is first carried out for this purpose.
Finally, CgLp is integrated with PID and tested on one of the DOFs of a planar
precision positioning stage. Performance improvement is shown in terms of
tracking, steady-state precision and bandwidth
The fractional orthogonal derivative
This paper builds on the notion of the so-called orthogonal derivative, where
an n-th order derivative is approximated by an integral involving an orthogonal
polynomial of degree n. This notion was reviewed in great detail in a paper in
J. Approx. Theory (2012) by the author and Koornwinder. Here an approximation
of the Weyl or Riemann-Liouville fractional derivative is considered by
replacing the n-th derivative by its approximation in the formula for the
fractional derivative. In the case of, for instance, Jacobi polynomials an
explicit formula for the kernel of this approximate fractional derivative can
be given. Next we consider the fractional derivative as a filter and compute
the transfer function in the continuous case for the Jacobi polynomials and in
the discrete case for the Hahn polynomials. The transfer function in the Jacobi
case is a confluent hypergeometric function. A different approach is discussed
which starts with this explicit transfer function and then obtains the
approximate fractional derivative by taking the inverse Fourier transform. The
theory is finally illustrated with an application of a fractional
differentiating filter. In particular, graphs are presented of the absolute
value of the modulus of the transfer function. These make clear that for a good
insight in the behavior of a fractional differentiating filter one has to look
for the modulus of its transfer function in a log-log plot, rather than for
plots in the time domain.Comment: 32 pages, 7 figures. The section between formula (4.15) and (4.20) is
correcte
Wavelets and Fast Numerical Algorithms
Wavelet based algorithms in numerical analysis are similar to other transform
methods in that vectors and operators are expanded into a basis and the
computations take place in this new system of coordinates. However, due to the
recursive definition of wavelets, their controllable localization in both space
and wave number (time and frequency) domains, and the vanishing moments
property, wavelet based algorithms exhibit new and important properties.
For example, the multiresolution structure of the wavelet expansions brings
about an efficient organization of transformations on a given scale and of
interactions between different neighbouring scales. Moreover, wide classes of
operators which naively would require a full (dense) matrix for their numerical
description, have sparse representations in wavelet bases. For these operators
sparse representations lead to fast numerical algorithms, and thus address a
critical numerical issue.
We note that wavelet based algorithms provide a systematic generalization of
the Fast Multipole Method (FMM) and its descendents.
These topics will be the subject of the lecture. Starting from the notion of
multiresolution analysis, we will consider the so-called non-standard form
(which achieves decoupling among the scales) and the associated fast numerical
algorithms. Examples of non-standard forms of several basic operators (e.g.
derivatives) will be computed explicitly.Comment: 32 pages, uuencoded tar-compressed LaTeX file. Uses epsf.sty (see
`macros'
Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset
In this paper a novel reset control synthesis method is proposed: CRONE reset
control, combining a robust fractional CRONE controller with non-linear reset
control to overcome waterbed effect. In CRONE control, robustness is achieved
by creation of constant phase behaviour around bandwidth with the use of
fractional operators, also allowing more freedom in shaping the open-loop
frequency response. However, being a linear controller it suffers from the
inevitable trade-off between robustness and performance as a result of the
waterbed effect. Here reset control is introduced in the CRONE design to
overcome the fundamental limitations. In the new controller design, reset phase
advantage is approximated using describing function analysis and used to
achieve better open-loop shape. Sufficient quadratic stability conditions are
shown for the designed CRONE reset controllers and the control design is
validated on a Lorentz-actuated nanometre precision stage. It is shown that for
similar phase margin, better performance in terms of reference-tracking and
noise attenuation can be achieved.Comment: American Control Conference 201
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