Search results for: Fourier integral

Authors: Adel Salem Bahakeem, Ahmad Jamal, Mir Md. Maruf Morshed, Elwaleed Awad Khidir

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Direct Current (DC) servo motors, or simply DC motors, play an important role in many industrial applications such as manufacturing of plastics, precise positioning of the equipment, and operating computer-controlled systems where speed of feed control, maintaining the position, and ensuring to have a constantly desired output is very critical. These parameters can be controlled with the help of control systems such as the Proportional Integral Derivative (PID) controller. The aim of the current work is to investigate the effects of Proportional (P) and Integral (I) controllers on the steady state and transient response of the DC motor. The controller gains are varied to observe their effects on the error, damping, and stability of the steady and transient motor response. The current investigation is conducted experimentally on a servo trainer CE 110 using analog PI controller CE 120 and theoretically using Simulink in MATLAB. Both experimental and theoretical work involves varying integral controller gain to obtain the response to a steady-state input, varying, individually, the proportional and integral controller gains to obtain the response to a step input function at a certain frequency, and theoretically obtaining the proportional and integral controller gains for desired values of damping ratio and response frequency. Results reveal that a proportional controller helps reduce the steady-state and transient error between the input signal and output response and makes the system more stable. In addition, it also speeds up the response of the system. On the other hand, the integral controller eliminates the error but tends to make the system unstable with induced oscillations and slow response to eliminate the error. From the current work, it is desired to achieve a stable response of the servo motor in terms of its angular velocity subjected to steady-state and transient input signals by utilizing the strengths of both P and I controllers.

Keywords: DC servo motor, proportional controller, integral controller, controller gain optimization, Simulink

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Sunil Dehipawala, Aregama Sirisumana, stephan Smith, P. Schneider, G. Tremberger Jr, D. Lieberman, Todd Holden, T. Cheung

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The arsenic and iron environments in different growth stages have been studied with EXAFS and XANES using Brookhaven Synchrotron Light Source. Collard Greens plants were grown and tissue samples were harvested. The project studied the EXAFS and XANES of tissue samples using As and Fe K-edges. The Fe absorption and the Fourier transform bond length information were used as a control comparison. The Fourier transform of the XAFS data revealed the coexistence of As (III) and As (V) in the As bonding environment inside the studied plant tissue samples, although the soil only had As (III). The data suggests that Collard Greens has a novel pathway to handle arsenic absorption in soil.

Keywords: EXAFS, fourier transform, metalloproteins, XANES

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Nasser Mohamed Ramli, Nurul Izzati Zulkifli

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Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. The current conventional controllers would not be able to solve problems with large time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proportional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32 s for step input and 5 s for pulse generator, by producing small Integral Absolute Error (IAE) values that are 0.66 and 0.36 respectively.

Keywords: fuzzy, sump, level, controller

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Authors: Kankeyanathan Kannan

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On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

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Authors: Karthik K. R, Viswanath V, Asraff A. K

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The first stage of a new-generation launch vehicle of ISRO makes use of large pressure vessels made of Aluminium alloy AA2219 to store fuel and oxidizer. These vessels have many weld joints that may contain cracks or crack-like defects during their fabrication. These defects may propagate across the vessel during pressure testing or while in service under the influence of tensile stresses leading to catastrophe. Though ductile materials exhibit significant stable crack growth prior to failure, it is not generally acceptable for an aerospace component. There is a need to predict the initiation of stable crack growth. The structural integrity of the vessel from fracture considerations can be studied by constructing the Failure Assessment Diagram (FAD) that accounts for both brittle fracture and plastic collapse. Critical crack sizes of the pressure vessel may be highly conservative if it is predicted from FAD alone. If the J-R curve for material under consideration is available apriori, the critical crack sizes can be predicted to a certain degree of accuracy. In this paper, a novel approach is proposed to predict the integrity of a weld in a pressure vessel made of AA2219 material. Fracture parameter ‘J-integral’ at the crack front, evaluated through finite element analyses, is used in the new procedure. Based on the simulation of tension tests carried out on SCT specimens by NASA, a cut-off value of J-integral value (J?ᵤₜ_ₒ??) is finalised. For the pressure vessel, J-integral at the crack front is evaluated through FE simulations incorporating different surface cracks at long seam weld in a cylinder and in dome petal welds. The obtained J-integral, at vessel level, is compared with a value of J?ᵤₜ_ₒ??, and the integrity of vessel weld in the presence of the surface crack is firmed up. The advantage of this methodology is that if SCT test data of any metal is available, the critical crack size in hardware fabricated using that material can be predicted to a better level of accuracy.

Keywords: FAD, j-integral, fracture, surface crack

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Rufus Temidayo Akinnubi, M. O. Adeniyi

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Existing diurnal air temperature models simulate night time air temperature over Nigeria with high biases. An improved parameterization is presented for modeling the diurnal pattern of air temperature (Ta) which is applicable in the calculation of turbulent heat fluxes in Global climate models, based on Nigeria Micrometeorological Experimental site (NIMEX) surface layer observations. Five diurnal Ta models for estimating hourly Ta from daily maximum, daily minimum, and daily mean air temperature were validated using root-mean-square error (RMSE), Mean Error Bias (MBE) and scatter graphs. The original Fourier series model showed better performance for unstable air temperature parameterizations while the stable Ta was strongly overestimated with a large error. The model was improved with the inclusion of the atmospheric cooling rate that accounts for the temperature inversion that occurs during the nocturnal boundary layer condition. The MBE and RMSE estimated by the modified Fourier series model reduced by 4.45 oC and 3.12 oC during the transitional period from dry to wet stable atmospheric conditions. The modified Fourier series model gave good estimation of the diurnal weather patterns of Ta when compared with other existing models for a tropical environment.

Keywords: air temperature, mean bias error, Fourier series analysis, surface energy balance,

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

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In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

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Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

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In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: non-minimum phase system, optimal linear quadratic tracker, proportional plus integral observer, state and disturbance estimator

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Authors: Marwa A. A. Ragab, Hadir M. Maher, Eman I. El-Kimary

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Co-administration of methotrexate (MTX) and aspirin (ASP) can cause a pharmacokinetic interaction and a subsequent increase in blood MTX concentrations which may increase the risk of MTX toxicity. Therefore, it is important to develop a sensitive, selective, accurate and precise method for their simultaneous determination in urine. A new hybrid chemometric method has been applied to the emission response data of the two drugs. Spectrofluorimetric method for determination of MTX through measurement of its acid-degradation product, 4-amino-4-deoxy-10-methylpteroic acid (4-AMP), was developed. Moreover, the acid-catalyzed degradation reaction enables the spectrofluorimetric determination of ASP through the formation of its active metabolite salicylic acid (SA). The proposed chemometric method deals with convolution of emission data using 8-points sin xi polynomials (discrete Fourier functions) after the derivative treatment of these emission data. The first and second derivative curves (D1 & D2) were obtained first then convolution of these curves was done to obtain first and second derivative under Fourier functions curves (D1/FF) and (D2/FF). This new application was used for the resolution of the overlapped emission bands of the degradation products of both drugs to allow their simultaneous indirect determination in human urine. Not only this chemometric approach was applied to the emission data but also the obtained data were subjected to non-parametric linear regression analysis (Theil’s method). The proposed method was fully validated according to the ICH guidelines and it yielded linearity ranges as follows: 0.05-0.75 and 0.5-2.5 µg mL-1 for MTX and ASP respectively. It was found that the non-parametric method was superior over the parametric one in the simultaneous determination of MTX and ASP after the chemometric treatment of the emission spectra of their degradation products. The work combines the advantages of derivative and convolution using discrete Fourier function together with the reliability and efficacy of the non-parametric analysis of data. The achieved sensitivity along with the low values of LOD (0.01 and 0.06 µg mL-1) and LOQ (0.04 and 0.2 µg mL-1) for MTX and ASP respectively, by the second derivative under Fourier functions (D2/FF) were promising and guarantee its application for monitoring the two drugs in patients’ urine samples.

Keywords: chemometrics, emission curves, derivative, convolution, Fourier transform, human urine, non-parametric regression, Theil’s method

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Authors: Jinghui Peng, Shanyu Tang, Jia Li

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Steganalysis seeks to detect the presence of secret data embedded in cover objects, and there is an imminent demand to detect hidden messages in streaming media. This paper shows how a steganalysis algorithm based on Fast Fourier Transform (FFT) can be used to detect the existence of secret data embedded in streaming media. The proposed algorithm uses machine parameter characteristics and a network sniffer to determine whether the Internet traffic contains streaming channels. The detected streaming data is then transferred from the time domain to the frequency domain through FFT. The distributions of power spectra in the frequency domain between original VoIP streams and stego VoIP streams are compared in turn using t-test, achieving the p-value of 7.5686E-176 which is below the threshold. The results indicate that the proposed FFT-based steganalysis algorithm is effective in detecting the secret data embedded in VoIP streaming media.

Keywords: steganalysis, security, Fast Fourier Transform, streaming media

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Authors: Dong Sang Yoo

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We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: J. M. de Luis Ruiz, P. M. Sierra García, R. P. García, R. P. Álvarez, F. P. García, E. C. López

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Given the evolution of viaducts, structural health monitoring requires more complex techniques to define their state. two alternatives can be distinguished: experimental and operational modal analysis. Although accelerometers or Global Positioning System (GPS) have been applied for the monitoring of structures under exploitation, the dynamic monitoring during the stage of construction is not common. This research analyzes whether GPS data can be applied to certain dynamic geometric controls of evolving structures. The fundamentals of this work were applied to the New Bridge of Cádiz (Spain), a worldwide milestone in bridge building. GPS data were recorded with an interval of 1 second during the erection of segments and turned to the frequency domain with Fourier transform. The vibration period and amplitude were contrasted with those provided by the finite element model, with differences of less than 10%, which is admissible. This process provides a vibration record of the structure with GPS, avoiding specific equipment.

Keywords: Fourier transform, global position system, operational modal analysis, structural health monitoring

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Authors: Bojan Radisic, Katarina Stavlic

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The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples.

Keywords: consumer surplus, producer surplus, definite integral, integration

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Jafar Razmi

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Integral abutment bridges are bridges that do not have joints. If these bridges are subject to large seasonal and daily temperature variations, the expansion and contraction of the bridge slab is transferred to the piles. Since the piles are deep into the soil, displacement induced by slab can cause bending and stresses in piles. These stresses cause fatigue and failure of piles. A complex mechanical interaction exists between the slab, pile, soil and abutment. This complex interaction needs to be understood in order to calculate the stresses in piles. This paper uses a mechanical approach in developing analytical equations for the complex structure to determine the stresses in piles. The solution to these analytical solutions is developed and compared with finite element analysis results and experimental data. Our comparison shows that using analytical approach can accurately predict the displacement in piles. This approach offers a simplified technique that can be utilized without the need for computationally extensive finite element model.

Keywords: integral abutment bridges, piles, thermo-mechanical stress, stress and strains

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Authors: N. Chayaopas, W. Assawinchaichote

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In order to maximize energy capturing from wind energy, controlling the doubly fed induction generator to have optimal power from the wind, generator speed and output electrical power control in wind energy system have a great importance due to the nonlinear behavior of wind velocities. In this paper purposes the design of a control scheme is developed for power control of wind energy system via H∞ fuzzy integral controller. Firstly, the nonlinear system is represented in term of a TS fuzzy control design via linear matrix inequality approach to find the optimal controller to have an H∞ performance are derived. The proposed control method extract the maximum energy from the wind and overcome the nonlinearity and disturbances problems of wind energy system which give good tracking performance and high efficiency power output of the DFIG.

Keywords: doubly fed induction generator, H-infinity fuzzy integral control, linear matrix inequality, wind energy system

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Authors: H. Al-Qassem, L. Cheng, Y. Pan

Abstract:

In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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Authors: Mohammed S. Al-Rawi, J. Bastos, J. Rodriguez

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Object detection and object recognition are essential components of every computer vision system. Despite the high computational complexity and other problems related to numerical stability and accuracy, Zernike moments of 2D images (ZMs) have shown resilience when used in object recognition and have been used in various image analysis applications. In this work, we propose a novel method for computing ZMs via Fast Fourier Transform (FFT). Notably, this is the first algorithm that can generate ZMs up to extremely high orders accurately, e.g., it can be used to generate ZMs for orders up to 1000 or even higher. Furthermore, the proposed method is also simpler and faster than the other methods due to the availability of FFT software and/or hardware. The accuracies and numerical stability of ZMs computed via FFT have been confirmed using the orthogonality property. We also introduce normalizing ZMs with Neumann factor when the image is embedded in a larger grid, and color image reconstruction based on RGB normalization of the reconstructed images. Astonishingly, higher-order image reconstruction experiments show that the proposed methods are superior, both quantitatively and subjectively, compared to the q-recursive method.

Keywords: Chebyshev polynomial, fourier transform, fast algorithms, image recognition, pseudo Zernike moments, Zernike moments

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Payel Das, Gnaneshwar Nelakanti

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In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.

Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence

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Authors: Hamdy M. Youssef

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In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of Lord-Shulman thermoelastic theorem, which contains non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations, and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.

Keywords: nanobeam, vibration, constant magnetic field, ramp-type thermal loading, non-Fourier heat conduction law

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Authors: Sanjay Kumar, Lillie Dewan

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The study of complex dynamic systems has advanced through various scientific approaches with the help of computer modeling. The common design trends in aerospace system design can be applied to quadcopter design. A quadcopter is a nonlinear, under-actuated system with complex aerodynamics parameters and creates challenges that demand new, robust, and effective control approaches. The flight control stability can be improved by planning and tracking the trajectory and reducing the effect of sensors and the operational environment. This paper presents a modern design Simmechanics visual modeling approach for a mechanical model of a quadcopter with three degrees of freedom. The Simmechanics model, considering inertia, mass, and geometric properties of a dynamic system, produces multiple translation and rotation maneuvers. The proportional, integral, and derivative (PID) controller is integrated with the Simmechanics model to follow a predefined quadcopter rotational trajectory for a fixed time interval. The results presented are satisfying. The simulation of the quadcopter control performed operations successfully.

Keywords: nonlinear system, quadcopter model, simscape modelling, proportional-integral-derivative controller

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Authors: Cui Fu, Yi-Zhou Zhuang, Sheng-Zhi Wang

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Full scale tests of six micropiles with different predrilled-hole parameters under low frequency cyclic lateral loading in-sand were carried out using the MTS hydraulic loading system to analyze the seismic performance of micropiles. Hysteresis curves, skeleton curves, energy dissipation capacity and ductility of micropiles were investigated. The experimental results show the hysteresis curves appear like plump bows in the elastic–plastic stage and failure stage which exhibit good hysteretic characteristics without pinching phenomena and good energy dissipating capacities. The ductility coefficient varies from 2.51 to 3.54 and the depth and loose backfill of oversized holes can improve ductility, but the diameter of predrilled-hole has a limited effect on enhancing its ductility. These findings and conclusions could make contribution to the practical application of the semi-integral abutment bridges and provide a reference for the predrilled oversized hole technology in integral abutment bridges.

Keywords: ductility, energy dissipation capacity, micropile with predrilled oversized hole, seismic performance, semi-integral abutment bridge

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Authors: Jatinderdeep Kaur

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In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results.

Keywords: conjugate dirichlet kernel, conjugate fejer kernel, fourier series, semi-convexity

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