Simple Graphical Procedure Research Articles

STABILITY ROBUSTNESS OF CONTROL SYSTEMS OF MULTIROTOR UNMANNED AERIAL VEHICLES

Multirotor unmanned aerial vehicles (UAVs) are broadly used in various military and civilian areas and tasks. In real flights of the multirotor UAVs, certain unexpected situations may occur, which can lead to improper functionality and even failures of elements or devices of the UAV’s control system. In some cases, this can even lead to the complete collapse of the UAV. Therefore, the safety of UAV flights is nowadays of prime importance. A method of analysis of the stability robustness of the UAV’s control systems with respect to the parameters multiplicative uncertainties (or perturbations), including possible efficiency degradation of DC motors, is proposed in the paper. Stability robustness is determined by a simple graphical procedure on the complex plane of the Nyquist or Nichols hodographs of the control system’s separate channels. That procedure is quite similar to the well-known classical feedback control procedure of determining the peak gain of the single-input, single-output closed-loop control system by the Nyquist hodograph of the open-loop system. A numerical example illustrating the proposed method is given.

On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability.

ROBUSTNESS ANALYSIS OF UAVS’ CONTROL SYSTEMS IN CASE OF MOTORS’ PARTIAL EFFICIENCY DEGRADATION

Multirotor unmanned aerial vehicles (UAVs) are widely used in military tasks, as well as in various civilian areas such as agriculture, search and rescue operations, detection of fires in forests, traffic monitoring, etc. In real flights of the UAVs some unexpected situations may occur bringing to failures of various elements or devices of the UAV’s control system. This, in turn, can lead to the crush and complete collapse of the entire vehicle. First of all, it concerns the DC motors and propellers, which, as opposed to electronic devises and sensors, cannot be duplicated. A method of analysis of robustness of UAV’s control systems with respect to possible partial efficiency degradation of motors is proposed in the paper. The ultimately allowable efficiency degradation is determined by a simple graphical procedure on the complex plane of the Nyquist hodographs of the system’s separate channels. A numerical example illustrating the proposed method of analysis of the UAV’s control system robustness is given.

Robust stability testing function for a complex interval family of fractional-order polynomials

The robust stability of a family of interval fractional-order systems with complex coefficients is investigated in this study. The concept of “a family of interval fractional-order systems with complex coefficients” means that the characteristic function of a control system can be of both commensurate and non-commensurate orders, the coefficients of the characteristic function can be uncertain parameters, and may be complex numbers. At first, a simple graphical procedure is presented for robust stability analysis. The “robust stability testing function” is then extended to look at the robust conditions. To the best of the authors’ knowledge, no auxiliary function for analyzing the robust stability of the systems under investigation has been introduced until now. Moreover, lower and upper frequency bounds are provided which are useful to improve the computational efficiency of testing the robust stability conditions. Eventually, to verify the results, analytical examples and numerical simulations are provided.

Robust Stability Analysis of Interval Fractional-Order Plants With Interval Time Delay and General Form of Fractional-Order Controllers

This letter aims to investigate the robust stability of an interval fractional-order plant with an interval time delay by a general form of fractional-order controllers. Based on a simple graphical procedure, necessary and sufficient criteria are proposed to analyze the robust stability of an interval fractional-order plant. Then, the idea of “robust stability testing function” is extended to analyze the robust stability of the considered type of systems. Besides, an upper frequency bound is provided which is useful for the simulation purposes and it helps to reduce the computational cost. Finally, two examples are presented to verify the usefulness of the obtained results.

Dispersion in coiled tubular reactors: A CFD and experimental analysis on the effect of pitch

This work investigates axial dispersion in coiled tubes when the coil pitch is non-negligible compared to the other geometrical parameters. The axial dispersion model (ADM) is used for the description of residence time distributions (RTDs) and an analytical expression for the closed-closed (CC) ADM is presented and used for the analysis of coiled reactors. Correlations, based on validated computational fluid dynamics (CFD) results, are developed to take the coil pitch effect into account. The dispersion coefficient is evaluated numerically and experimentally for different coils, with a good agreement between predicted and observed values. Coiling not only reduces the dispersion significantly with respect to straight tubes, but also the ADM can be applied in a wider region of the common conditions used in practice. The results are summarized in a nomogram that displays applicability regions of the ADM and enables estimation of the dispersion coefficient with a simple graphical procedure.

Graphic Procedure for the Optimum Design of Elastomeric Isolators

A simple graphic procedure for the optimum design of elastomeric seismic isolation devices is proposed. Starting from the design requirements concerning a base-isolated building, such as the device’s stiffness, maximum displacement, and vertical load, as well as the code checks on the device, the procedure allows defining the optimum values of the mechanical and geometrical parameters, such as rubber shear modulus, diameter, and thickness, and the number of rubber and steel layers. In more detail, the procedure allows for first identifying the ranges of the geometrical characteristics through a graphic representation of code checks in terms of the rubber’s diameter and volume, and then their specific values that allow one to obtain the optimum solution according to the design requirements for any fixed values of the mechanical characteristics of the materials. The graphic representation represents a suitable tool to better understand the role and influence of the different checks. The procedure can be easily automated by means of a computer code.

Dynamic simulation of liquefied petroleum gas vaporisation for burners

This study numerically describes the transient behaviours of liquefied petroleum gas (LPG) natural vaporisation in a cylinder using an experimentally validated model. The model can be applied to easily predict transient compositions and thermophysical properties during the vaporisation process under various conditions. A simple graphical design procedure is presented to determine the Wobbe Index and the corresponding composition as design references for gas burners to avoid incomplete combustions. The effects of initial composition, surrounding temperature and discharge rate of LPG on both the LPG natural vaporisation and the residue amount in the cylinder are simulated and investigated. The results demonstrate that the present work may serve as a useful tool to evaluate the LPG behaviours throughout the vaporisation, design or retrofit gas burners, and predict the unburned residue.

The Fastest Known Globally Convergent First-Order Method for Minimizing Strongly Convex Functions

We design and analyze a novel gradient-based algorithm for unconstrained convex optimization. When the objective function is $m$ -strongly convex and its gradient is $L$ -Lipschitz continuous, the iterates and function values converge linearly to the optimum at rates $\rho $ and $\rho ^{2}$ , respectively, where $\rho = 1-\sqrt {m/L}$ . These are the fastest known guaranteed linear convergence rates for globally convergent first-order methods, and for high desired accuracies the corresponding iteration complexity is within a factor of two of the theoretical lower bound. We use a simple graphical design procedure based on integral quadratic constraints to derive closed-form expressions for the algorithm parameters. The new algorithm, which we call the triple momentum method, can be seen as an extension of methods such as gradient descent, Nesterov’s accelerated gradient descent, and the heavy-ball method.

A robust leaf area index algorithm accounting for the expected errors in gap fraction observations

The leaf area index, LAI, representing the physiological and structural functions of vegetation canopies, can be estimated from gap fraction measurements obtained at different zenith angles. Earlier works have provided practical and convenient theoretical solution to retrieve LAI based on the integration of contact numbers (a projected area of leaves on a plane perpendicular to the view or solar zenith angle) over zenith angles as obtained by a linear regression, i.e., LAI=2(A+B), where A and B are the coefficients of the regression of contact numbers against zenith angles. This graphical procedure is equivalent to the more accurate method of LAI retrieval by integrating gap fraction measurements from nadir through horizon angles. However, using an ordinary least-squares regression on inherently unsteady relationship between contact numbers and zenith angles limited the use of a simple graphical procedure for LAI estimation. In this study, we introduce the use of robust procedure to retrieve regression coefficients (i.e., A and B), and assess the performance of the new procedure using numerically derived hypothetical data, computer simulated and real measurements of hemispherical photographs. Our results indicated, the new procedure not only outperformed the ordinary least-squares solution for graphical procedure, but also outperformed all existing LAI methods We conclude from analyses using numerically derived hypothetical data, computer simulated and real measurements of hemispherical photographs that estimating A and B (where LAI=2(A+B)) using a robust procedure is a convenient and sufficiently accurate method for estimating LAI from field measurements of gap fractions at different zenith angles.

Development of the Barr & Stroud ZD Range of Topographical Stereoscopes for Mapping Applications

This paper presents an account of the development of the range of stereoscopes produced by Barr & Stroud (Glasgow, UK) during the period between the two World Wars of the 20th century. These instruments were critical to the adoption of simple graphical procedures (such as the Arundel method) for the rapid production of huge numbers of military topographic maps from aerial photography during the Second World War, since they allowed elevation and contour data to be incorporated into these maps without the need for complex and expensive photogrammetric instrumentation. The pivotal roles played in this development by Professor Barr and the young Lieutenant Hotine are highlighted.

Program realization of mathematical model of kinetostatical calculation of flat lever mechanisms

Global computerization determined the dominant position of the analytical methods for the study of mechanisms. As a result, kinetostatics analysis of mechanisms using software packages is an important part of scientific and practical activities of engineers and designers. Therefore, software implementation of mathematical models kinetostatical calculating mechanisms is of practical interest. The mathematical model obtained in [1]. In the language of Turbo Pascal developed a computer procedure that calculates the forces in kinematic pairs in groups Assur (GA) and a balancing force at the primary level. Before use appropriate computational procedures it is necessary to know all external forces and moments acting on the GA and to determine the inertial forces and moments of inertia forces. The process of calculations and constructions of the provisions of the mechanism can be summarized as follows. Organized cycle in which to calculate the position of an initial link of the mechanism. Calculate the position of the remaining links of the mechanism by referring to relevant procedures module DIADA in GA [2,3]. Using the graphics mode of the computer displaying on the display the position of the mechanism. The computed inertial forces and moments of inertia forces. Turning to the corresponding procedures of the module, calculated all the forces in kinematic pairs and the balancing force at the primary level. In each kinematic pair build forces and their direction with the help of simple graphical procedures. The magnitude of these forces and their direction are displayed in a special window with text mode. This work contains listings of the test programs MyTеst, is an example of using computing capabilities of the developed module. As a check on the calculation procedures of module in the program is reproduced an example of calculating the balancing forces according to the method of Zhukovsky (Zhukovsky lever).

A graphical procedure for sensor‐placement guidance for small utilities

Efforts to improve water security have led to the development of contamination warning systems aimed at providing early indication of accidental or intentional contamination in drinking water distribution systems. Sensors that detect changes in water quality are a critical component of a contamination warning system. Because the extent of any monitoring system is constrained by a limited budget, focus is placed on optimizing the placement of sensors to maximize contamination detection and protect human health. Robust models and algorithms have been developed to recommend sensor deployment, but many require hydraulic or water quality models. Small utilities typically do not possess the resources to develop these models; therefore, researchers for this study developed the Water Quality Sensor Placement Tool to recommend placement of one water quality sensor without a model or complicated algorithm. This simple graphical procedure allows utility managers to use basic information about the geometry of their network to determine near‐optimal sensor placement in limited time without complicated software.

Potku – New analysis software for heavy ion elastic recoil detection analysis

Time-of-flight elastic recoil detection (ToF-ERD) analysis software has been developed. The software combines a Python-language graphical front-end with a C code computing back-end in a user-friendly way. The software uses a list of coincident time-of-flight–energy (ToF–E) events as an input. The ToF calibration can be determined with a simple graphical procedure. The graphical interface allows the user to select different elements and isotopes from a ToF–E histogram and to convert the selections to individual elemental energy and depth profiles. The resulting sample composition can be presented as relative or absolute concentrations by integrating the depth profiles over user-defined ranges. Beam induced composition changes can be studied by displaying the event-based data in fractions relative to the substrate reference data. Optional angular input data allows for kinematic correction of the depth profiles. This open source software is distributed under the GPL license for Linux, Mac, and Windows environments.

Properties of a Natural Fracture and Its Skins From Reservoir Well Tests

Summary Two well tests are described that are aimed at the in-situ determination of the flow capacity (permeability-thickness product) of a natural fracture and the flow resistance of its skins at the boundaries with the reservoir matrix. Fracture skins tend to disperse flow, thus affecting the distribution of tracers in reservoir tests and contaminants and trace elements in aquifers. We are unaware of any other analytical procedure aimed at obtaining the properties of a natural fracture and its skins from subsurface measurements. Neither well test has been implemented. The well tests are modeled after previously reported analytical expressions for the transient pressure distributions in a three-region composite reservoir in a uniform-thickness reservoir in which (1) the natural fracture is represented by a thin middle region of relatively high permeability, (2) the pressure disturbance is caused by producing from a short interval in one of the outer regions, and (3) the response is measured relatively near the fracture. The source and sensor may be on the same side or on opposite sides of the fracture, distinguishing the two tests. Visualizing special completions in a horizontal well intersecting a natural fracture normally, pressure responses are given for both tests for a wide range of fracture/matrix permeability ratios and skin flow resistances for a source 190 ft from the fracture and 10 ft from the sensor and on either side of the fracture, both at the midplane of the reservoir. A simple graphical procedure, not intended to replace history matching or regression where field data are available, illustrates how the two unknowns—permeability-thickness product of a natural fracture and the flow resistance of its skins—may be estimated from two representative values of an assumed measured pressure response.

The Power to See: A New Graphical Test of Normality

Many statistical procedures assume that the underlying data-generating process involves Gaussian errors. Among the popular tests for normality, only the Kolmogorov–Smirnov test has a graphical representation. Alternative tests, such as the Shapiro–Wilk test, offer little insight as to how the observed data deviate from normality. In this article, we discuss a simple new graphical procedure which provides simultaneous confidence bands for a normal quantile–quantile plot. These bands define a test of normality and are narrower in the tails than those related to the Kolmogorov–Smirnov test. Correspondingly, the new procedure has greater power to detect deviations from normality in the tails. Supplementary materials for this article are available online.

Persistent long-term ( c. 24 Ma) exhumation in the Eastern Alaska Range constrained by stacked thermochronology

Abstract To address Miocene–present episodic v. persistent exhumation, we utilize a simple graphical procedure that vertically stacks spatially diverse K-feldspar 40 Ar/ 39 Ar multi-domain diffusion (MDD) models from the length of the approximately 100 km-long high-peak region of the Eastern Alaska Range. We supply additional constraints with 40 Ar/ 39 Ar mica dating because the higher closure-temperature-window places limits on the initiation of rapid Eastern Alaska Range exhumation. We also provide a broad 40 Ar/ 39 Ar K-feldspar minimum closure age data set to add more detail on spatial patterns in the regional exhumation history for the Eastern Alaska Range. We find that rapid and persistent exhumation has occurred in the Eastern Alaska Range since about 24 Ma at a long-term rate of approximately 0.9 km/Ma, but that this rapid exhumation is spatially variable through time. Onset of rapid Eastern Alaska Range exhumation is coincident with the initiation of rapid exhumation in SW Alaska, the Western Alaska Range and the Chugach–Saint Elias Range at around 25 Ma, implying a region-wide deformational response to a change in tectonic forcing. The initiation of highly coupled flat-slab subduction of the Yakutat microplate is probably responsible for this prolonged period of rapid exhumation in southern Alaska. Supplementary material: Sample locations from the Eastern Alaska Range, and 40 Ar/ 39 Ar data tables and age spectrum figures are available at www.geolsoc.org.uk/SUP18603 .

Suitable model for the calculation of the correlation between the real and the average specific heat capacity and possibilities of its application

Starting from the definition of the average specific heat capacity for chosen temperature range, the analytic dependence between the real and the mean specific heat capacities is obtained using differential and integral calculation. The obtained relation in differential form for the defined temperature range allows for the problem to be solved directly, without any special restrictions on its use. Using the obtained relation, a general model in the form of a polynomial of arbitrary degree in the function of temperature was derived, which has more suitable and faster practical application and is more general in character than the existing model. New graphical method for solving the problem is obtained based on differential geometry and using the derived equation. This may also have practical significance since many problems in thermodynamics are solved analytically and graphically. This result was used in order to obtain the amount of specific heat exchanged using an analytical model or a planimetric method. In addition, this graphical solution was used for the construction of the diagram showing the dependence between the specific heat exchanged and temperature. This diagram also gives a simple graphical procedure for the calculation of the real and the average specific heat capacity for arbitrary temperature or temperature interval. The confirmation for all graphic constructions is obtained using the differential properties between thermodynamic units. In order for the graphical solutions presented to be applicable in practice, suitable ratio coefficients have been determined for all cases. Verification of the model presented, as well as the possibilities of its application, were given using several characteristic examples of semi-ideal and real gas. Apart from linear and non-linear functions in the form of polynomials, the exponential function of the dependence between specific heat capacities and temperature was also analysed in this process.

Is non-loglinear allometry a statistical artifact?

The allometric equation, y = axb, is commonly fitted to data indirectly by transforming predictor (x) and response (y) variables to logarithms, fitting a straight line to the transformations, and then back-transforming (exponentiating) the resulting equation to the original arithmetic scale. Sometimes, however, transformation fails to linearize the observations, thereby giving rise to what has come to be known as non-loglinear allometry. A smooth curve for observations displayed on a log–log plot is usually interpreted to mean that the scaling exponent in the allometric equation is a continuously changing function of body size, whereas a breakpoint between two (or more) linear segments on a log–log plot is typically taken to mean that the exponent changes abruptly, coincident with some important milestone in development. I applied simple graphical and statistical procedures in re-analyses of three well-known examples of non-loglinear allometry, and showed in every instance that the relationship between predictor and response can be described in the original scale by simple functions with constant values for the exponent b. In no instance does the allometric exponent change during the course of development. Transformation of data to logarithms created new distributions that actually obscured the relationships between predictor and response variables in these investigations, and led to erroneous perceptions of growth. Such confounding effects of transformation are not limited to non-loglinear allometry but are common to all applications of the allometric method. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ••, ••–••.

PH‐metric Solubility. 1. Solubility‐pH Profiles from Bjerrum Plots. Gibbs Buffer and pKa in the Solid State

If measurements of solubility were not so laborious, slow, and consuming of sample, solubility-pH profiles would be used more often at the initial stages of drug discovery to screen out molecules with problematic pharmacokinetic profiles. An automated potentiometric titration method for solubility measurements, which addresses some of the shortcomings of the traditional methods, is described. A simple graphical procedure for estimating solubility constants, based on Bjerrum difference plots, is developed, and the relationships between titration data and solubility-pH profiles for mono- and diprotic ionizable substances are explored, drawing on generalized mass-balance based simulation methods. One useful derived equation (valid in a solution where part of the sample precipitates early in the titration) is: log So = log (C/2) - |ΔpKa| where C is the sample concentration, So is the intrinsic solubility of the unchanged substance, and ΔpKa = pKappa - pKa, the difference between the apparent pKa determined under conditions of precipitation and the true pKa, measured in the absence of the solid phase. The relationship holds in both aqueous and cosolvent solutions (e.g. dimethylsulphoxide-water). The properties of the state where an unchanged substance (e.g. HX) coprecipitates with its ionized form (e.g. X− salt) were explored. A super buffer, termed the Gibbs buffer, was formed and characterized by an ionization constant, pK(s)a, of the substance in the solid state. It was shown that pK(s)a - pKa = log SHX - log SX, where SHX and SX refer to the solubility constants of HX and X species. Flurbiprofen (acid), benzydamine (base), and buprenorphine (ampholye) were used to illustrate the experimental procedure. Our initial studies indicate that these new methods will meet many of the needs of not only discovery-stage researchers but also of preformulation and development scientists, traditionally concerned with solubility measurements.