Discrete Evolutionary Spectra of Discretized Beams and Plates Under Time-Frequency Modulated Random Excitations

1995 ◽  
Author(s):  
C. W. S. To ◽  
H. W. Hung
Keyword(s):  
White Noise ◽  
Linear Time ◽  
Response Analysis ◽  
Plate Structures ◽  
Time Frequency ◽  
Linear Time Invariant ◽  
Practical Engineering ◽  
Band Limited ◽  
Evolutionary Spectra ◽  
Time Invariant

Abstract Various methods that employed the theory of evolutionary spectral density of Priestley (1965) have been proposed for the non-stationary random response analysis of linear time-invariant multi-degree-of-freedom systems (Hammond, 1968, Fugimori and Lin, 1973, To, 1982, Shihab and Preumont, 1987, To and Hung, 1989). In this paper the method presented earlier by the authors (1989) is further applied to discrete or discretized systems under time-frequency moduated random excitations in which the white noise processes are replaced by band-limited white noise processes and Kanai-Tajimi models. Applications of the method to beam and plate structures discretized by the finite element method are made so as to illustrate its capability in dealing with practical engineering systems under intensive transient disturbances that may be modelled as such time-frequency modulated random excitations.

Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Mojtaba Soorki ◽  
Mohammad Tavazoei
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Response ◽  
Response Analysis ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Response Analysis ◽  
Necessary And Sufficient ◽  
Time Invariant

AbstractThis paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results.

Laplace wavelet transform theory and applications

2017 ◽  
Vol 24 (9) ◽  
pp. 1600-1620 ◽  
Author(s):  
Tariq Abuhamdia ◽  
Saied Taheri ◽  
John Burns
Keyword(s):  
Wavelet Transform ◽  
Differential Equations ◽  
Laplace Transform ◽  
Linear Time ◽  
Time Frequency ◽  
Linear Time Invariant ◽  
The Laplace Transform ◽  
Invariant Differential ◽  
Short Time ◽  
Time Invariant

This study introduces the theory of the Laplace wavelet transform (LWT). The Laplace wavelets are a generalization of the second-order under damped linear time-invariant (SOULTI) wavelets to the complex domain. This generalization produces the mother wavelet function that has been used as the Laplace pseudo wavelet or the Laplace wavelet dictionary. The study shows that the Laplace wavelet can be used to transform signals to the time-scale or time-frequency domain and can be retrieved back. The properties of the new generalization are outlined, and the characteristics of the companion wavelet transform are defined. Moreover, some similarities between the Laplace wavelet transform and the Laplace transform arise, where a relation between the Laplace wavelet transform and the Laplace transform is derived. This relation can be beneficial in evaluating the wavelet transform. The new wavelet transform has phase and magnitude, and can also be evaluated for most elementary signals. The Laplace wavelets inherit many properties from the SOULTI wavelets, and the Laplace wavelet transform inherits many properties from both the SOULTI wavelet transform and the Laplace transform. In addition, the investigation shows that both the LWT and the SOULTI wavelet transform give the particular solutions of specific related differential equations, and the particular solution of these linear time-invariant differential equations can in general be written in terms of a wavelet transform. Finally, the properties of the Laplace wavelet are verified by applications to frequency varying signals and to vibrations of mechanical systems for modes decoupling, and the results are compared with the generalized Morse and Morlet wavelets in addition to the short time Fourier transform’s results.

scholarly journals TDARMA Model Estimation Using the MLS and the TF Distribution

10.29007/64fl ◽  
2019 ◽  
Author(s):  
Abdullah Al-Shoshan
Keyword(s):  
Linear Time ◽  
Moving Average ◽  
Least Square ◽  
Time Dependent ◽  
Simple Relationship ◽  
Time Frequency ◽  
Linear Time Invariant ◽  
Stationary Signals ◽  
Generalized Transfer Function ◽  
Time Invariant

An approach for modeling linear time-dependent auto-regressive moving-average (TDARMA) systems using the time-frequency (TF) distribution is presented. The proposed method leads to an extension of several well-known techniques of linear time- invariant (LTI) systems to process the linear, time-varying (LTV) case. It can also be applied in the modeling of non-stationary signals. In this paper, the well-known modified least square (MLS) and the Durbin's approximation methods are adapted to this non- stationary context. A simple relationship between the generalized transfer function and the time-dependent parameters of the LTV system is derived and computer simulation illustrating the effectiveness of our method is presented, considering that the output of the LTV system is corrupted by additive noise.

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

Design and implementation of decoupled periodic control scheme for a laboratory-based quadruple-tank process

2021 ◽  
pp. 095965182110228
Author(s):  
Jatin K Pradhan ◽  
Arun Ghosh
Keyword(s):  
Real Time ◽  
High Frequency ◽  
Linear Time ◽  
Disturbance Attenuation ◽  
Minimum Phase ◽  
Periodic Control ◽  
Linear Time Invariant ◽  
Control Scheme ◽  
Gain Margin ◽  
Time Invariant

It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with [Formula: see text]-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.

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