Integral Derivative Research Articles

Active Vibration Control of Landing Gear System

The vibration of the aircraft when taxing, landing, and taking off is a great problem. Vibration induced due to the dynamic interaction of aircraft with the ground causes serious problems. Therefore, the vibration should be reduced or completely absorbed if possible by some external means. So, in this study active vibration control of an aircraft LG is investigated. The equation of motion of the aircraft LG system is obtained by Newton’s second law and simulated in MATLAB/Simulink environment. Two different controllers are fitted to the landing gear system. Proportional, integral derivative (PID) and Linear Quadratic Regulator (LQR) controllers are used in controlling active suspension structure. In the study, vertical displacement and acceleration of the fuselage are set as objective since it has harmful effects on the performance of the pilot’s capability. Simulation is run under B grade road and bump road for passive and active systems simultaneously. The performance of controllers is compared to one another and also with that of a passive system. From the results, it was obtained that under bump road excitation, LQR and PID controllers make 57.32% and 53.34% improvement in fuselage displacement, respectively. Similarly, under B Grade road, compared to passive systems LQR and PID controllers improve the vertical acceleration of the fuselage by 92.86% and 53.55% respectively.

Socio-psychological factors and conditions for the formation of responsible parenthood

The proposed article highlights the conditions for the formation of parenthood as a psychological phenomenon, which acts as an integral psychological development of the personality. Parenthood includes the value orientations of parents, parental attitudes and expectations, parental positions, parental attitudes, parental feelings, parental responsibility, and the style of family upbringing in its developed form. It was determined that the purpose of this article is to deepen the conceptual foundations of the study of responsible parenthood and to present it as an integral derivation that must be considered from the standpoint of a systemic approach. The task consists in researching social and psychological factors that determine the formation of the parenting system and clarifying the conditions for the formation of responsible parenting. It was analyzed in the article that the phenomenon of parenthood is systemically determined. It represents a relatively independent system, simultaneously acting as a subsystem in relation to the family. The authors characterized the features of the phenomenon of parenthood, which simultaneously appears in several angles from different sides and reveal the complex structure of its organization. Attention is focused on the fact that young people's perception of parenthood most often depends on their image in the parental family and sociocultural stereotypes. In conclusion, the fact that the combined influence of the factors that characterize the considered levels leads to the formation of a certain model of parenting is highlighted as an argument of significance

Analytical solution of the fractional neutron point kinetic equations using the Mittag-Leffler function

A new analytical solution of the fractional point kinetic equations is developed in the present work, which considers one group of delayed neutrons as well as a constant reactivity. One of the main novelties and theoretical contributions of the developed solution is that it does not require approximating the Inverse Laplace transform by numerical means, as other solutions do, and instead it is obtained analytically using the Green and the Mittag-Leffler functions. A set of algorithms and MATLAB codes are developed with the purpose to implement and compute the developed solution in an adequate way, which represents the major computational contribution. Numerical experiments show that the developed solution is very accurate solving short-time dynamics phenomena, being able to reproduce, in a precise way, data that is reported in literature. The development of the proposed analytic solution represents an important contribution to validate numerical methods that are currently used to solve the neutron fractional point kinetic equations. Program SummaryProgram Title: Mittag-Leffler FNPKECPC Library link to program files:https://doi.org/10.17632/v4kfhzw7sf.1Developer's repository link:https://github.com/Cruz-Lopez-Carlos-Antonio/Mittag-Leffler-FNPKE/tree/mainLicensing provisions: Creative Commons by 4.0Programming language: MATLAB (2021a) / Python 3Nature of problem:Fractional Neutron Point Kinetic Equations describe the neutron population in a nuclear reactor, considering the changes on transport and thermohydraulic properties of the system. For such task, a mass balance approach based on fractional and integral derivatives is used, which improves and generalizes the integer case that uses the classical definitions of these mathematical operators. From a physical point of view, this new approach takes into account memory and non-local effects that are omitted in the standard neutron diffusion theory and which are relevant in scenarios where the current neutron density undergoes strongly variations on time. From a mathematical point of view, using fractional derivatives leads to a new and more general type of differential equations of arbitrary order that requires different methods of solution and approximation, and which must include the integer approach as particular case. In such context, the development of analytical solutions is a fundamental problem because it provides a framework to carry out verifications of numerical methods, as well as an insight to perform theoretical comparisons with the classical model. The developed Mittag-Leffler FNPK codes analytically solve the Fractional Neutron Point Kinetic Equations defined in terms of the Caputo's derivatives and subject to classical initial conditions.Solution method:The developed codes are written in MATLAB and Python programming languages, and solve the mentioned fractional differential equation system using a power series expansion as well as the Laplace transform. Such solution considers a single group of precursors of delayed neutrons and it is expressed in terms of the 2-parameter Mittag-Leffler function, being accurately computed considering a small number of terms of the infinite sum. Unlike other approaches, in the present case it is not necessary to use a numerical procedure to find the inverse Laplace transform, because it is analytically found using the Green function. Even when the developed solution is found for a constant reactivity case, the Mittag-Leffler FNPKE codes can extended it to more general scenarios where the reactivity is a function of time or where it depends on the neutron density itself. In these cases, it is necessary to apply a subinterval methodology where the time is divided in small steps, assuming a constant reactivity in each of them. The smaller of the intervals, the more accurate the approximation. With the purpose to overcome the numerical issues related to the computation of the 2-parameter Mittag-Leffler function, the developed codes integrate the most advanced algorithm reported in literature, which is useful also to estimate the high-order derivatives of such function.Additional comments including restrictions and unusual features:The developed codes do not face issues related to arithmetical precision digits, as other solutions do, because it is not expressed in terms of high order polynomials and instead it is written as a linear combination of the Green function. Additionally, several steps can be precomputed without regard the neutron parameters and initial conditions, which represents an important advantage in terms of the computational time.

Efficient analytical gradients of property-based diabatic states: Geometry optimizations for localized holes.

We present efficient analytical gradients of property-based diabatic states and couplings using a Lagrangian formalism. Unlike previous formulations, the method achieves a computational scaling that is independent of the number of adiabatic states used to construct the diabats. The approach is generalizable to other property-based diabatization schemes and electronic structure methods as long as analytical energy gradients are available and integral derivatives with the property operator can be formed. We also introduce a scheme to phase and reorder diabats to ensure their continuity between molecular configurations. We demonstrate this for the specific case of Boys diabatic states obtained from state-averaged complete active space self-consistent field electronic structure calculations with GPU acceleration in the TeraChem package. The method is used to test the Condon approximation for the hole transfer in an explicitly solvated model DNA oligomer.

Ant colony optimization technique optimized controller for frequency stabilization of an isolated power system with non-linearity

The load frequency control of a thermal power producing system, the ant colony optimization (ACO) approach adjusted proportional integral derivative (PID) controller is proposed. This work examines the single area thermal power system with /without generation rate constraint. For emergency situations, a PID controller is developed and used to regulate power system characteristics. This study uses the ACO method with the integral time absolute error objective function optimize controller gain values. In addition, the performance of the suggested approach is evaluated by introducing non-linearity components to the power-generating systems under study. Conventional, particle swarm optimization (PSO), and genetic algorithms (GA) approach tuned controller responses are compared with ACO. Fast settling with minimal peak and undershoots in the producing power supply of the system under emergency loading situations demonstrates the superiority of the proposed controller over competing controllers.

Modeling and Controller Design for Temperature Control of Heat Exchangers in Power Plants

A heat exchanger is a device that transfers heat from one place to another. Because it can withstand a wide range of temperature and pressure, the power plant heat exchanger is widely employed in chemical and petroleum facilities. A heat exchanger is a device that transfers heat from one place to another. Plant with strong nonlinearity and low dynamics; as a result it is tough to model and manage its dynamics. There are two types of heat exchanger models in this study. For selecting an appropriate model, controllers are used. Controller. (Physical model) is the first model. Generated from genuine heat exchanger plant parameters Second, there's Dead Time plus a Second Order (SOPDT model)This is obtained from the heat exchanger's response. While The controllers are made up of fuzzy proportional controllers. Proportional integral (FPD) controller and derivative (FPD) controller applied to the model as a derivative (PID) controller Their comments are compared to those of the others. Keywords Power Plant Heat Exchanger, Modelling, Fuzzy Control.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C5Me5)2Y(μ-S)2Mo(μ-S)2Y(C5Me5)2]-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C6Cl5)4]- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

EFFECT OF RISK-SENSITIVE STOCHASTIC OPTIMAL CONTROL WITH TRACKING IN AN EVAPORATOR

This work presents an application of the Risk-Sensitive (R-S) control with tracking applied to a stochastic nonlinear system which models the operation of an electronic expansion valve (EEV) in a conventional evaporator. A novel dynamical stochastic equation represents the mathematical model of the evaporator system. The R-S stochastic optimal problem consists of the design of an optimal control u(t) such that the state reaches setpoint values (SP) and minimizes the exponential quadratic cost function. The presence of disturbances and errors in the sensor measurements is represented by Gauss white noise in the state equation, with the coefficient v(e/(2?^2 )) . One novel characteristic in this proposal is that the coefficient of the control into the state equation contains the state term. The error and exponential quadratic cost function show that the R-S control has a better performance versus the classical PID (Proportional, Integral Derivative) control. Key Words: Optimal Risk-Sensitive control with tracking, modelling of the evaporator.

Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method

<abstract><p>In this research work, we consider a class of nonlinear fractional integro-differential equations containing Caputo fractional derivative and integral derivative. We discuss the stabilities of Ulam-Hyers, Ulam-Hyers-Rassias, semi-Ulam-Hyers-Rassias for the nonlinear fractional integro-differential equations in terms of weighted space method and Banach fixed-point theorem. After the demonstration of our results, an example is given to illustrate the results we obtained.</p></abstract>

Speed control in DC and AC drives

<div><span lang="EN-US">Three speed-control strategies for DC and AC drives are presented in this study: a proportional<strong> </strong>integral derivative (PID) control strategy; an internal model control (IMC); and a state-space control by pole assignment with full state observer (ESSO). The three strategies are applied to a case study, demonstrating the potential of each one. Experimental identification was used to obtain the drive models used for the synthesis of the controllers. The three strategies showed satisfactory results when compared with the requirements imposed on the system, in addition to the good rejection of disturbances. However, the IMC strategy showed itself to be a little softer and with no maximum overshoot, which in some cases and some applications is usually a restriction.</span></div>

Multidimensional Free Energy and Accelerated Quantum Library Methods Provide a Gateway to Glycoenzyme Conformational, Electronic, and Reaction Mechanisms.

Enzyme reactions are complex to simulate accurately, and none more so than glycoenzymes (glycosyltransferase and glycosidases). A rigorous sampling of the protein frame and the conformationally plural carbohydrate substrate coupled with an unbiased treatment of the electron dynamics is needed to discover the true reaction landscapes. Here, we demonstrate the effectiveness of two computational methods ported in libraries that we have developed. The first is a flat histogram free energy method called FEARCF capable of multidimensional sampling and rapidly converging to a complete coverage of phase space. The second, the Quantum Supercharger Library (QSL), is a method that accelerates the computation of the ab initio electronic wave function as well as the integral derivatives on graphical processing units (GPUs). These QSL accelerated computations form the core components needed for direct quantum dynamics and QM/MM dynamics when coupled with legacy codes such as GAMESS and NWCHEM, making state of the art hyper-parallel electronic computations in chemistry and chemical biology possible. The combination of QSL (acceleration of ab initio QM computation) and FEARCF (multidimensional hyper-parallel reaction dynamics) makes the simulation of ab initio QM/MM reaction dynamics of enzyme catalysis feasible. Enzymes that process carbohydrates pose an added challenge as their pyranose ring substrates span multidimensional conformational space whose sampling is an intimate function of the catalytic mechanism. Here, we use the pairing of FEARCF and QSL to simulate the catalytic effect of the glycoenzyme β-N-acetylglucosamine transferase (OGT). The reaction mechanism is discovered from a variable three bond reaction surface using SCCDFTB. The role of the OGT in distorting the pyranose ring of β-N-acetylglucosamine (GlcNAc) away from the equilibrium 4C1 chair conformation toward the E3 envelope needed for the transition state is discovered from its pucker free energy hypersurfaces (or free energy volume, FEV). A complete GlcNAc ring pucker HF 6-31g FEV is constructed from ab initio QM dynamics in vacuum and ab initio QM/MM dynamics in the OGT catalytic domain. The OGT is shown to clearly lower the pathway toward the transition state E3 ring conformer as well as stabilize it by 1.63 kcal/mol. Illustrated here is the use of QSL accelerated ab initio QM/MM dynamics that thoroughly explores carbohydrate catalyzed reactions through a FEARCF multidimensional sampling of the interdependence between reaction and conformational space. This demonstrates how experimentally inaccessible molecular and electronic mechanisms that underpin enzyme catalysis can be discovered by directly modeling the dynamics of these complex reactions.

FURTHER DISCUSSION ABOUT FRACTIONAL DIFFERENTIABILITY OF CERTAIN CONTINUOUS FUNCTIONS

This paper concentrates on discussing the properties of Riemann–Liouvile fractional (RLF) calculus of two special continuous functions. The first type proves the non-differentiability of a special continuous function that does not satisfy Hölder condition, and the second type uses fractal iteration to construct a fractal function defined on [Formula: see text] with unbounded variation. Then we calculate RLF integral and RLF derivative of this special function, and give the corresponding numerical calculation results and the corresponding function image.

Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function

This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving fundamental constants. The goal of this paper is to expand upon current tables of definite integrals with the aim of assisting researchers in need of new integral formulae.

Comparison of Various Load Frequency Control Schemes in Restructured Power System Environment

This paper presents comparison of performances of secondary controllers like Integral (I), Proportional-Integral (PI), Integral-Derivative (ID), Proportional-Integral-Derivative (PID) and Integral-Double Derivative (IDD) as load frequency control scheme. The controllers have been tested on two equal areas thermal power system with non-reheat turbines in the presence of nonlinearity i.e. generation rate constraint (GRC) of 3% per minute. The disco participation matrix (DPM) is considered for various power transactions between Genco and Discos in both areas. A well-known optimization algorithm i.e. genetic algorithm (GA) is used to determine the optimal parameters of different controllers. Three cases i.e. load perturbation in one area only, load perturbation in both areas and more demand asked by Disco than the contract have been considered to check the response of controllers. Comparative analysis of the results obtained for all three cases show that Proportional-Integral-Derivative (PID) controller provides better performance than other controllers in terms of settling time..

An anti-periodic singular fractional differential problem of Lane-Emden type

In this paper, we use both Riemann-Liouville integral and Caputo derivative to investigate a new nonlinear singular differential problem of Lane and Emden type. We note that for the studied singular problem, we will be concerned with some anti periodic conditions. So, we prove a first uniqueness result by application of Banach principle of contraction. Then, we prove a “second” existence result by application of Schaefer theorem. Two illustrative examples are discussed in details to show the applicability of the obtained results.

Some analytical merits of Kummer-Type function associated with Mittag-Leffler parameters

As of late, the study of Fractional Calculus (FC) and Special Functions (SFs) has been interestingly prompted in various realms of mathematics, engineering and sciences. This is due to the considerable demonstrated potential of their applications. Among these SFs, Gamma function and Mittag-Leffler functions are the most renowned and distinguished. Numerous authors continue to study this line. The current analysis attempts to introduce and further examine new modifications of Gamma and Kummer function in terms of Mittag-Leffler functions, respectively. Several attributes and formulations of this new Kummer-type function that include integral representations, Beta transform, Laplace transform, derivative formulas, and recurrence relation are investigated. Furthermore, outcomes of Riemann-Liouville fractional integral and fractional derivative in relation to this newly established Kummer function are also investigated.

H ∞ control for a hyperchaotic finance system with external disturbance based on the quadratic system theory

This paper considers the control problem for a hyperchaotic system with energy-bounded disturbance under the delayed feedback controller. Using the quadratic system theory, an augmented Lyapunov functional, some integral inequalities and rigorous mathematical derivations, a sufficient condition is first established by using linear matrix inequalities under which the closed-loop system can achieve some desirable performances including the boundedness, the performance and the asymptotic stability. Subsequently, several convex optimization problems are formulated to obtain the optimal performance indices. Finally, numerical simulations are presented to illustrate the effectiveness of the obtained results.

Hermitian Characteristic Scheme for a Linear Inhomogeneous Transfer Equation

In this paper, we design an interpolation-characteristic scheme for the numerical solution of the inhomogeneous transfer equation. The scheme is based on the Hermitian interpolation to reconstruct the value of an unknown function at the point of intersection of the backward characteristic with the cell faces. The Hermitian interpolation to reconstruct the function values ​​uses both the nodal values ​​of the desired function and its derivative. Unlike previous studies also based on the Hermitian interpolation, not only the differential continuation of the transfer equation but also the relationship between the integral averaged values, nodal values, ​​and derivatives according to the Euler-Maclaurin formula is used to transfer information about the derivatives to the next layer. The third-order difference scheme is shown to converge for smooth solutions. The dissipative and dispersive properties of the scheme are considered using numerical examples of solutions with decreasing smoothness.

Some Existence Results for High Order Fractional Impulsive Differential Equation on Infinite Interval

In this paper, we consider the high order impulsive differential equation on infinite interval D 0 + α u t + f t , u t , J 0 + β u t , D 0 + α − 1 u t = 0 , t ∈ 0 , ∞ ∖ t k k = 1 m △ u t k = I k u t k , t = t k , k = 1 , … , m u 0 = u ′ 0 = ⋯ = u n − 2 0 = 0 , D 0 + α − 1 u ∞ = u 0 By applying Schauder fixed points and Altman fixed points, we obtain some new results on the existence of solutions. The nonlinear term of the equation contains fractional integral operator J β u t and lower order derivative operator D 0 + α − 1 u t . An example is presented to illustrate our results.

Automatic generation controller for multi area multisource regulated power system using grasshopper optimization algorithm with fuzzy predictive PID controller

AbstractThis paper presents a fuzzy predictive‐proportional integral derivative (FP‐PID) controller approach for automatic generation controller (AGC). This new AGC approach aims to balance the total generating system without any power losses and load changes in keeping constant system frequency per tie‐lie power flow. But, a sudden load variation in multi‐area Interconnected power system (MIPS) creates nonlinearities (frequency deviation & tie‐line) in all control areas. Because, penetrating of renewable sources to the power system, the sluggish control action may cause inefficiency in migrating frequency and tie‐line power flow. Hence, an accurate and fast‐acting controller is required to maintain the nominal value also the quality and stability of power system, because traditional AGC is not feasible for further process. Here, we propose an FP‐PID controller in MIPS for controlling large parametric uncertainties. Modeling error is taken into account to reduce the maximum deviation and time of oscillation. The main purpose of FP‐PID based AGC is to ensure stable and reliable power system operation. A grasshopper optimization algorithm (GOA) is used to tune the parameters of FP‐PID controller with Integral of time multiplied squared error (ITSE) as the objective function. The proposed method is compared with conventional two‐area and three‐area system, the result are built‐in Simulink/MATLAB show that the proposed method has a good dynamic response, fast operation reduced magnitude error and minimized frequency transients for three power areas. The robustness of the controller is, it need not be retuned for wide variations in system parameters and random step load power.