Determination of the Maximum Error for Pole Placement for a Nonlinear Third-Order Process

2017 ◽  
pp. 249-256
Keyword(s):  
Maximum Error ◽  
Pole Placement ◽  
Order Process ◽  
Third Order

Graphical Determination of Optimum Trajectories for Third-Order Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 271-278
Author(s):  
Yousri M. Abd-El-Fattah
Keyword(s):  
Control Function ◽  
Maximum Error ◽  
Control Signal ◽  
Graphical Solution ◽  
Third Order ◽  
Two Phase ◽  
State Trajectory ◽  
Optimum Trajectories ◽  
Initial States

The present paper explains the use of two phase planes in the graphical determination of optimum trajectories for third-order systems, depending on the sign of a single control function. The control function is defined on these planes by means of different contours. Accordingly, the control signal is known at the different points on these planes. Once the control signal is found, the state trajectory is determined. Most of the arbitrary initial states are treated and, in particular, the cases of separate steps in each of the error and its first as well as second time derivatives. This work also explains the use of the graphical solution in obtaining the maximum error and switching times.

The two-dimensional laminar jet in parallel streaming flow

1967 ◽  
Vol 27 (3) ◽  
pp. 431-443 ◽  
Author(s):  
I. Wygnanski
Keyword(s):  
Order Term ◽  
Asymptotic Series ◽  
Maximum Error ◽  
Approximate Determination ◽  
Two Dimensional ◽  
Direct Expansion ◽  
Third Order ◽  
Laminar Jet ◽  
External Stream

Solutions to the problem of a two-dimensional, laminar jet of incompressible fluid issuing into a uniform stream in the direction of the main flow are considered. Two co-ordinate-type expansions are developed. A direct expansion, when suitably transformed, predicts approximately the velocity along the plane of symmetry of the jet for all values of the abscissa, with a maximum error of 7·6% far downstream from the origin. This error is established by comparison with a second, asymptotic expansion valid only at large values of the abscissa. The two expansions are subsequently joined, permitting an approximate determination of a constant which multiplies a third-order term in the asymptotic series and which initially remained unknown even after satisfying all boundary conditions imposed on these series.The decay of velocity excess along the plane of symmetry of the jet is accelerated by the presence of the external stream.

A multitechnique investigation of the second order NLO response of a 10,20-diphenylporphyrinato nickel(II) complex carrying a phenylethynyl based push-pull system in the 5- and 15-positions

2004 ◽  
Vol 08 (11) ◽  
pp. 1311-1324 ◽  
Author(s):  
Maddalena Pizzotti ◽  
Elisabetta Annoni ◽  
Renato Ugo ◽  
Silvia Bruni ◽  
Silvio Quici ◽  
...  
Keyword(s):  
Ab Initio ◽  
Planar Structure ◽  
Third Order ◽  
Incident Wavelength ◽  
Pull System ◽  
Nlo Response ◽  
Self Consistent ◽  
Order Of Magnitude ◽  
Zero Frequency

A multitechnique investigation of the determination of the order of magnitude of the second and third order NLO response of [5-[(4-dimethylaminophenyl)ethynyl]-15-[(4-nitrophenyl)ethynyl]-10,20-diphenylporphyrinato]nickel(II) (1) is reported with the aim to produce self consistent evidence for a significant NLO response of this kind of push-pull porphyrin chromophore. The experimental multitechnique approach is based on the EFISH technique, working with a non-resonant incident wavelength of 1.907 μm, on the solvatochromic method and finally on a vibrational method, avoiding any fluorescence or resonance interference. A theoretical MNDO-TDHF evaluation of the zero-frequency quadratic and cubic hyperpolarizabilities of an ab initio optimized planar structure is also reported. The order of magnitude of the quadratic hyperpolarizability of (1) at zero frequency (β0), was found to be significantly lower than that reported for the corresponding Cu (II) or Zn (II) complexes with the same push-pull porphyrin chromophore.

scholarly journals DETERMINATION OF THE ENERGY GAP OF C60 MOLECULE USING THIRD-ORDER DERIVATIVE ABSORPTION SPECTROSCOPY

1998 ◽  
Vol 47 (2) ◽  
pp. 208
Author(s):  
ZHAO MING-SHAN ◽  
DAI ZUO-XIAO ◽  
LI YI ◽  
LI GUO-HUA ◽  
BU YU-XIANG ◽  
...  
Keyword(s):  
Absorption Spectroscopy ◽  
Energy Gap ◽  
Order Derivative ◽  
Third Order

scholarly journals A NEW VALIDATED THIRD ORDER DERIVATIVE SPECTROSCOPIC METHOD FOR SIMULTANEOUS ESTIMATION OF METOPROLOL SUCCINATE AND RAMIPRIL IN TABLET DOSAGE FORM

2020 ◽  
pp. 54-59
Author(s):  
ALEKHYA B. ◽  
M. SINDHUSHA ◽  
SORAJ K. RAUL ◽  
GOPAL K. PADHY
Keyword(s):  
Quantitative Analysis ◽  
Dosage Form ◽  
Spectroscopic Method ◽  
Simultaneous Estimation ◽  
Third Order ◽  
Metoprolol Succinate ◽  
Zero Crossing ◽  
Ich Guidelines ◽  
Tablet Dosage

Objective: The objective of the present work is to develop and validate a new UV derivative spectrophotometric method for simultaneous estimation of metoprolol succinate and ramipril in methanol: water (50:50v/v). Methods: “Zero crossing technique” was chosen for quantitative determination. The zero-crossing points (ZCP’s) were found to be 209 nm where metoprolol succinate was quantified and 211 nm where ramipril was quantified. This method was then subjected to accuracy, linearity, sensitivity and reproducibility according to ICH guidelines to ensure and confirm its validity. Results: The method was found to be obeying Beer’s law in the range of 10-50 µg/ml and 5-25 µg/ml for metoprolol succinate and ramipril, respectively. The % recoveries were observed between the range of 99.2-100.2 for metoprolol succinate and 99.57-99.86 for ramipril. The intra-day and inter-day results showed reproducibility. Conclusion: It can be concluded that the developed third-order UV derivative spectroscopic method for the simultaneous determination of metoprolol succinate and ramiprilcan be recommended for routine quantitative analysis.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

scholarly journals Derivative Spectrophotometric Analysis of 4-Quinolone Antibacterials in Formulations and Spiked Biological Fluids by Their Cu(II) Complexes

2001 ◽  
Vol 84 (2) ◽  
pp. 368-375 ◽  
Author(s):  
Mohammed Rizk ◽  
Fathalla Belal ◽  
Fawiza Ibrahim ◽  
Soad Ahmed ◽  
Zeinab A Sheribah
Keyword(s):  
Aqueous Medium ◽  
Linear Correlation ◽  
Analytical Procedure ◽  
Biological Fluids ◽  
Reference Method ◽  
Spectrophotometric Analysis ◽  
Third Order ◽  
Selective Determination ◽  
Average Percentage

Abstract A derivative UV-spectrophotometric analytical procedure was developed for determination of three 4-quinolone antibacterials: norfloxacin (NFX), ciprofloxacin (CFX), and sparfloxacin (SFX). The method depends on the complexation of Cu(II) with the studied compounds in aqueous medium. A third order, measurement was applied for their quantification. A linear correlation was established between the amplitude of the peak and concentration for all the studied drugs in the range of 15–80, 35–120, and 200–700 ng/mL, with minimum detectability (S/N = 2) of 1.0, 1.3, and 5.1 ng/mL for NFX, CFX, and SFX, respectively. The method was successfully applied for accurate, sensitive, and selective determination of the studied drugs in bulk and tablets formulation with average percentage recoveries of 99.22 ± 0.55 to 100.33 ± 1.60. The results obtained were favorably compared with those of the reference method. The method was also used to determine sparfloxacin in spiked human plasma and urine. The results obtained were satisfactory, accurate, and precise.

Measurement and modelling of homogeneous axisymmetric turbulence

1998 ◽  
Vol 374 ◽  
pp. 59-90 ◽  
Author(s):  
TORBJÖRN SJÖGREN ◽  
ARNE V. JOHANSSON
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Theoretical Description ◽  
Wind Tunnel Experiments ◽  
Third Order ◽  
Point Velocity ◽  
First Time ◽  
Rapid Pressure

A new method for determining the slow and rapid pressure-strain rate terms directly from wind-tunnel experiments has been developed with the aid of a newly developed theoretical description of the kinematics of homogeneous axisymmetric turbulence. Both the straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. Direct experimental determination of the different terms in the transport equation for the Reynolds stress tensor plays a major role in the validation and development of turbulence models. For the first time it is shown that the pressure{strain correlation can be determined with good accuracy without balancing it out from the Reynolds stress transport equation (and without measuring the pressure). Instead it is determined through evaluation of integrals containing second- and third-order two-point velocity correlations. All the terms in the Reynolds stress equations are measured directly and balance is achieved.

A New Criterion to Determine the Start of Combustion in Diesel Engine

2004 ◽  
Author(s):  
Tomazˇ Katrasˇnik ◽  
Samuel Rodman Opresˇnik ◽  
Ferdinand Trenc ◽  
Nedjeljko Sˇkific´
Keyword(s):  
Experimental Data ◽  
Diesel Engine ◽  
Cylinder Pressure ◽  
Third Order ◽  
First Law Of Thermodynamics ◽  
The Third ◽  
Crank Angle ◽  
New Criterion ◽  
Start Of Combustion

A new criterion for the determination of the start of combustion (SOC) from the diesel engine in-cylinder pressure diagram was developed. It is defined as the maximum of the third order derivative of the cylinder pressure with respect the crank angle. This criterion declares SOC more precisely than other previously published criterions based on pressure diagnostics. This fact was proven analytically and was discernable from the analysis of the experimental data. Beside its accuracy it is also robust enough to allow automatic evaluation of the SOC during processing of the pressure data for a large number of cycles. Analysis of the first law of thermodynamics applied to the engine cylinder showed that the third order derivative of the cylinder pressure with respect to the crank angle is the most suitable criterion for determination of the SOC from the cylinder pressure diagram. Subsequently the criterion was validated through experimental data analysis of the cylinder pressure diagrams for various engine speeds and loads. Cylinder pressure diagrams were processed with a computer code based on the first law of thermodynamics to evaluate the rate of heat release (ROHR), which formed the base for experimental validation. The cylinder pressure was measured with an advanced piezoelectric sensor at the resolution 0.1 deg. CA. Top dead center was determined with the capacitive top dead center sensor. Due to the analytic foundation of the developed method and its validation through highly accurate experimental data it can be concluded that new criterion is credible for the determination of the SOC.

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