Maximum Decay Rate Research Articles

Design of Maximum Decay Rate for SISO Systems with Delayed Output Feedback Using Elimination Theory

In this paper we study the delayed output feedback control of a class of LTI systems. We present an analytical methodology based on discriminant operations by which the maximum decay rate of the closed-loop is designed as an explicit function of the system parameters. More precisely, this approach uses elimination theory for the tuning of the controller in an optimal fashion such that the system is not only stable but also responds to control commands as fast as possible. A case study is presented to demonstrate the utility of the approach.

Design of a Class of Sliding Mode Observer with Time‐Varying Delay

AbstractThis paper is concerned with the design of observers for a linear system with time‐varying delay in the field of structural control. A class of sliding mode observers with state and input time‐varying delays is developed on the basis of the coordinate transformation and free‐weighting matrix methods. The exponential dynamic properties of the observers are introduced to improve the performance of the observer. The delay and delay‐rate dependent conditions formulated by linear matrix inequalities (LMIs) are proposed to obtain the gains of the observers. Then, the bisection method is proposed to obtain the maximum exponential decay rate and allowable time delay. Finally, a numerical example of a fourth‐order system is used to show the feasibility and efficiency of the proposed observer.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection.

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

Effect of Coil Design on the Temperature and Velocity Fields during Solidification in Electromagnetic Stirring Processes

This paper examines the role of induction coil design on stirring of molten metal in electromagnetic (EM) solidification processes. A model is presented to describe the EM, heat transfer, and fluid flow phenomena in these processes. It is based on a dual-zone description of the mushy region, and accounts for damping of turbulence by the solidified crystallites. The electromagnetic field equations were solved using the mutual inductance technique, while the temperature and turbulent flow fields were calculated using the control volume method. Calculations were performed for solidification of an Al–Cu alloy placed in a stationary magnetic field generated by an induction coil. The effect of coil design on the flow structure was investigated for three different coil positions. It was found that changing the coil position significantly alters the flow pattern from four recirculating loops when the coil is above the midsection of the melt to two loops, typical of a travelling magnetic field, when the coil is at the base of the melt. This significantly modifies the rate of solidification across the ingot, as well as the temperature gradient, in the mushy region. The decay of the velocity and turbulent fields in the mushy region was found to be exponential, with the maximum rate of decay at the solidification front. These results indicate that through changes in coil design, it is possible to control the flow characteristics and solidification behavior in the molten metal.

Robust Exponential Stability Analysis of Uncertain Discrete Time‐Varying Linear Systems

AbstractThis paper studies the robust exponential stability of uncertain discrete linear time‐varying (UDLTV) systems. The key tool is the recently proposed generating functions. It can be found that a class of improved generating functions (IGFS) can fully characterize the robust exponential stability of UDLTV systems, and the maximum exponential decay rate of system trajectories can be computed by the radius of convergence of the IGFS. Moreover, the application of convex optimization technique and dynamic programming method provides an effective algorithm for the computation of the IGFS. Finally, the numerical example illustrates the efficacy and advantage of the proposed approach.

Studying on the stability of fractional-order nonlinear system

In this paper, we study the properties of the Mittag–Leffler function and propose an approach for calculating the maximum norm of eigenvalue of Jacobian matrix of nonlinear system. Then a simple approach is proposed for judging the stability of fractional nonlinear system. Based on the approach, the maximum decay rate of fractional nonlinear system can be calculated. Finally, some examples are provided to illustrate the approach.

The effects of moderately high temperature on zeaxanthin accumulation and decay

Moderately high temperature reduces photosynthetic capacities of leaves with large effects on thylakoid reactions of photosynthesis, including xanthophyll conversion in the lipid phase of the thylakoid membrane. In previous studies, we have found that leaf temperature of 40°C increased zeaxanthin accumulation in dark-adapted, intact tobacco leaves following a brief illumination, but did not change the amount of zeaxanthin in light-adatped leaves. To investigate heat effects on zeaxanthin accumulation and decay, zeaxanthin level was monitored optically in dark-adapted, intact tobacco and Arabidopsis thaliana leaves at either 23 or 40°C under 45-min illumination. Heated leaves had more zeaxanthin following 3-min light but had less or comparable amounts of zeaxanthin by the end of 45min of illumination. Zeaxanthin accumulated faster at light initiation and decayed faster upon darkening in leaves at 40°C than leaves at 23°C, indicating that heat increased the activities of both violaxanthin de-epoxidase (VDE) and zeaxanthin epoxidase (ZE). In addition, our optical measurement demonstrated in vivo that weak light enhances zeaxanthin decay relative to darkness in intact leaves of tobacco and Arabidopsis, confirming previous observations in isolated spinach chloroplasts. However, the maximum rate of decay is similar for weak light and darkness, and we used the maximum rate of decay following darkness as a measure of the rate of ZE during steady-state light. A simulation indicated that high temperature should cause a large shift in the pH dependence of the amount of zeaxanthin in leaves because of differential effects on VDE and ZE. This allows for the reduction in ΔpH caused by heat to be offset by increased VDE activity relative to ZE.

Evaluation and Improvement of Asphalt Mixture’s Performance at Low Temperature

In order to evaluate and improve the performance of asphalt mixture at low temperature, low-temperature bending test of asphalt mixture was done at first. It was shown that flexural-tensile strength and flexural-tensile strain of different oil-stone ratios reduced under freeze-thaw condition compared to no freeze-thaw condition. The maximum decay rate of flexural-tensile strength is about 18.97% and the maximum decay rate of flexural-tensile strain is about 6.59%. Then six types of polyester fiber were added to asphalt mixture and bending test at low temperature was done. Through the experiment results comparison of fiber asphalt mixtures, it is found that ultimate flexural strain of Good Road II fiber asphalt mixture increases the largest which is up to 12.95%. Ultimate flexural strain of Dolanit AS fiber asphalt mixture increases 8.67% and other fiber asphalt mixtures increase from 3% to 6%. Fiber bridging and fiber micro-reinforced role in the mixture improves the performance of asphalt mixture at low temperature.

The dynamics analysis and controller design for the PEM fuel cell under gas flowrate constraints

This paper is on the dynamics analysis and controller design for the PEM fuel cell under the flowrate constraints of the supplied hydrogen and oxygen. By linearization around the equilibrium trajectories defined by the quantities of hydrogen and oxygen input flowrate, the nonlinear dynamics of the PEM fuel cell can be expressed as a linear parameter varying system with the output current and temperature as the system parameters. The state-feedback controller design is performed based on the linear time-invariant model obtained from the derived linear parameter varying system evaluated at the half load operation condition. The control objective is to achieve a maximized relative stability or equivalently the maximum decay rate under the specified magnitude constraints on the input flowrate of hydrogen and oxygen. The convex linear matrix inequality algorithm is utilized for numerical construction of the state-feedback control law. Under the fixed load resistance corresponding to the half load condition, the time response simulations are conducted for both the cases of initial condition regulation and external command tracking. For the simulation of regulation, the initial deviation of state variables diminishes quickly that agrees with the obtained large delay rate during controller design. In the case of command tracking for the same amount of state variables, the controlled system can follow the issued command in the right direction but leave large tracking error, which is due to the weak controllability of the gas flowrates on the activation overvoltage for the PEM fuel cell system dynamics.

Exponential Convergence Rate Estimation for a Class of BAM Neural Networks with Time-Delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory (BAM) neural networks with parameter uncertainties and mixed time-delays where the parameter uncertainties are norm-bounded and the mixed time-delays involve discrete, distributed and neutral time-delays. By utilizing free-weighting matrix method and an appropriately constructed Lyapunov-Krasovskii Functional, some nove delay-dependent and decay-rate dependent exponential stability criteria are derived in the terms of linear matrix inequalities (LMIs). Meanwhile, the maximum allowable decay rate can be estimated based on the obtained results. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.

Equilibrium evolution in oscillating-field current-drive experiments

Oscillating-field current drive (OFCD) is a proposed method of steady-state toroidal plasma sustainment in which ac poloidal and toroidal loop voltages are applied to produce a dc plasma current. OFCD is added to standard, inductively sustained reversed-field pinch plasmas in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. Equilibrium profiles and fluctuations during a single cycle are measured and analyzed for different relative phases between the two OFCD voltages and for OFCD off. For OFCD phases leading to the most added plasma current, the measured energy confinement is slightly better than that for OFCD off. By contrast, the phase of the maximum OFCD helicity-injection rate also has the maximum decay rate, which is ascribed to transport losses during discrete magnetic-fluctuation events induced by OFCD. Resistive-magnetohydrodynamic simulations of the experiments reproduce the observed phase dependence of the added current.

Exponential convergence rate estimation for neutral BAM neural networks with mixed time-delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory neural networks with mixed time-delays, where discrete, distributed and neutral delays are involved. By utilizing the delay decomposition approach and an appropriately constructed Lyapunov–Krasovskii functional, some novel delay-dependent and decay rate-dependent criteria for the exponential stability of the considered neural networks are derived and presented in terms of linear matrix inequalities. Furthermore, the maximum allowable decay rate can be estimated based on the obtained results. Three numerical examples are given to demonstrate the effectiveness of the proposed method.

Observations on the decay of glycated hemoglobin HbA1c in diabetic patients.

In 44 diabetic patients, who within 7 days lowered their average glycemia by 140 to 220 mg % and kept it at this level over a mean of 36 days, HbA1c was measured repeatedly by HPLC (normal range 4.2-5.6% of total hemoglobin). Thereby, the maximum decay rate of HbA1c could be observed in vivo as being 0.1% per day which is consistent with previous theoretical considerations by other authors. Some clinical implications that this finding may have for diabetic patients are being discussed.

Drag Measurement on an Oscillating Sphere in Helium II

Here we report measurement of the drag on a 3 mm oscillating sphere in superfluid 4He in the temperature range 1.6 K to 2.1 K. A Nb-Ti superconducting solenoid is used to suspend a niobium sphere; meanwhile a similar superconducting quadrupole magnet centers and helps to stabilize the ball at one location in the flow channel. The niobium sphere is levitated by the superconducting magnetic suspension system; then the oscillation is obtained by dropping the ball from one equilibrium point to a lower equilibrium point via reducing the levitating magnetic field. The sphere’s oscillation is then recorded with a high-speed CCD camera. The velocity of the sphere is obtained by comparing the images captured and the distance the sphere has moved with time. Drag force is calculated through its relation to the maximum velocity decay rate. The sphere is contained within a closed end channel that allows measurements in liquid or gaseous helium and vacuum.

A robust method for the joint estimation of yield coefficients and kinetic parameters in bioprocess models

Bioprocess model structures that require nonlinear parameter estimation, thus initialization values, are often subject to poor identification performances because of the uncertainty on those initialization values. Under some conditions on the model structure, it is possible to partially circumvent this problem by an appropriate decoupling of the linear part of the model from the nonlinear part of it. This article provides a procedure to be followed when these structural conditions are not satisfied. An original method for decoupling two sets of parameters, namely, kinetic parameters from maximum growth, production, decay rates, and yield coefficients, is presented. It exhibits the advantage of requiring only initialization of the first subset of parameters. In comparison with a classical nonlinear estimation procedure, in which all the parameters are freed, results show enhanced robustness of model identification with regard to parameter initialization errors. This is illustrated by means of three simulation case studies: a fed-batch Human Embryo Kidney cell cultivation process using a macroscopic reaction scheme description, a process of cyclodextrin-glucanotransferase production by Bacillus circulans, and a process of simultaneous starch saccharification and glucose fermentation to lactic acid by Lactobacillus delbrückii, both based on a Luedeking-Piret model structure. Additionally, perspectives of the presented procedure in the context of systematic bioprocess modeling are promising.

Differential effects of phospholamban and Ca2+/calmodulin-dependent kinase II on [Ca2+]itransients in cardiac myocytes at physiological stimulation frequencies

In cardiac myocytes, the activity of the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) is hypothesized to regulate Ca(2+) release from and Ca(2+) uptake into the sarcoplasmic reticulum via the phosphorylation of the ryanodine receptor 2 and phospholamban (PLN), respectively. We tested the role of CaMKII and PLN on the frequency adaptation of cytosolic Ca(2+) concentration ([Ca(2+)](i)) transients in nearly 500 isolated cardiac myocytes from transgenic mice chronically expressing a specific CaMKII inhibitor, interbred into wild-type or PLN null backgrounds under physiologically relevant pacing conditions (frequencies from 0.2 to 10 Hz and at 37 degrees C). When compared with that of mice lacking PLN only, the combined chronic CaMKII inhibition and PLN ablation decreased the maximum Ca(2+) release rate by more than 50% at 10 Hz. Although PLN ablation increased the rate of Ca(2+) uptake at all frequencies, its combination with CaMKII inhibition did not prevent a frequency-dependent reduction of the amplitude and the duration of the [Ca(2+)](i) transient. High stimulation frequencies in the physiological range diminished the effects of PLN ablation on the decay time constant and on the maximum decay rate of the [Ca(2+)](i) transient, indicating that the PLN-mediated feedback on [Ca(2+)](i) removal is limited by high stimulation frequencies. Taken together, our results suggest that in isolated mouse ventricular cardiac myocytes, the combined chronic CaMKII inhibition and PLN ablation slowed Ca(2+) release at physiological frequencies: the frequency-dependent decay of the amplitude and shortening of the [Ca(2+)](i) transient occurs independent of chronic CaMKII inhibition and PLN ablation, and the PLN-mediated regulation of Ca(2+) uptake is diminished at higher stimulation frequencies within the physiological range.

A continuous damped vibration absorber to reduce broad-band wave propagation in beams

In order to attenuate structural waves in beams, a damped mass–spring absorber system is considered that is attached continuously along the beam length. Compared with other measures, such as impedance changes or tuned neutralisers applied at a single point, it is effective for excitation at any location along the beam. Although it is a tuned system, it can also be designed to be effective over a broad frequency range by the use of a high damping loss factor and multiple tuning frequencies. It has the advantage over constrained layer damping treatments that it can be effective even when the structural wavelength is long. The parameters controlling its behaviour are investigated and simple formulae developed, allowing optimisation of its performance. The effective frequency bandwidth increases as the mass ratio of the absorber and the beam is increased and, for moderate-to-high damping, it also increases as the damping loss factor is increased. The maximum decay rate is independent of mass and damping for light damping, but for higher damping it reduces as loss factor increases and increases as the mass ratio increase. A particular application is the reduction of noise from a railway track, which requires the attenuation of structural waves along the rail to be increased over a frequency band of two or more octaves.

Biodegradation rate of diesel range n-alkanes by bacterial cultures Exiguobacterium aurantiacum and Burkholderia cepacia

The biodegradation rate of hydrocarbons is an important consideration determining the time scale for bioremediation in oil-contaminated environments. Two naturally occurring bacterial cultures, Exiguobacterium aurantiacum and Burkholderia cepacia, were capable of utilizing diesel oil as the sole source of carbon and energy by induction of hydrophobic cell surfaces with water contact angle greater than 70°. The cultures demonstrated good degradation characteristics for diesel range n-alkanes (C9–C26) and were also capable of degrading pristane. A significant correlation was observed between maximum decay rate (MTR) of individual n-alkane peak area and initial abundance of n-alkanes in diesel ( r 2=0.79 and 0.97 for E. aurantiacum and B. cepacia, respectively). Thus, MTR (day −1) was essentially constant, in the range of 0.07–0.20, for n-alkanes with a wide range of carbon numbers from C12 to C26. Biodegradation altered the relative abundance of n-alkanes in diesel and resulted in a loss of symmetry in n-alkane distribution. C9, C17–C19, and C26 were completely degraded by both the cultures. In B. cepacia, the residual diesel was enriched in the higher carbon number n-alkanes C20–C25. The MTR of n-C16 present as a component of diesel was comparable to that for n-C16 when present as sole substrate for B. cepacia but not for E. aurantiacum. Scientific relevance Two cultures E. aurantiacum and B. cepacia were capable of utilizing diesel oil as sole substrate and exhibited uniform decay rates for a wide range of n-alkanes from C12 to C26. In contrast, most researchers have reported decreasing degradation rate with increasing carbon number.

Model evaluation of temperature dependency for carbon and nitrogen removal in a full-scale activated sludge plant treating leather-tanning wastewater

Organic carbon and nitrogen removal performance of a full-scale activated sludge plant treating pre-settled leather tanning wastewater was evaluated under dynamic process temperatures. Emphasis was placed upon observed nitrogen removal depicting a highly variable magnitude with changing process temperatures. As the plant was not specifically designed for this purpose, observed nitrogen removal could be largely attributed to simultaneous nitrification and denitrification presumably occurring at increased process temperatures (T > 25°C) and resulting low dissolved oxygen levels (DO < 0.5 mgO2/L). Model evaluation using long-term data revealed that the yearly performance of activated sludge reactor could be successfully calibrated by means of temperature dependent parameters associated with nitrification, hydrolysis, ammonification and endogenous decay parameters. In this context, the Arrhenius coefficients of (i) for the maximum autotrophic growth rate, A, (ii) maximum hydrolysis rate, khs and (iii) endogenous heterotrophic decay rate, bH were found to be 1.045, 1.070 and 1.035, respectively. The ammonification rate (ka) defining the degradation of soluble organic nitrogen could not be characterized however via an Arrhenius-type equation.

Characterization of Hydrophobic Flavor Release Profile in Oil‐in‐Water Emulsions

An instrumental approach to better understand the release and persistence of flavor in oil-in-water emulsions has been developed. Emulsions were prepared with various whey protein (0.1% to 3.16%), sunflower oil (1% to 8%), and ethyl hexanoate (0% to 0.04%) concentrations. Flavor release profile in real time was measured at 37 degrees C using a specially designed glass cell connected directly to a gas chromatograph equipped with a flame ionization detector. The intensity of flavor released from the emulsion stirred at a shear rate of 100 s(-1) was monitored as a function of time and data were fitted to a 1st-order kinetic equation. Maximum intensity and decay rate constant were both determined from the model and the persistence index (inversely associated to decay rate constant) was calculated. For constant aroma concentration in the emulsion, maximum intensity significantly decreased as whey protein and oil concentrations increased. For increasing aroma concentration, maximum intensity was directly proportional to the ethyl hexanoate concentration when the oil content was kept constant but leveled off when oil content was increased. Persistence of flavor significantly increased with increasing protein and oil concentrations while aroma concentrations had no effect when oil content was constant. The results showed that oil concentration had a greater influence on flavor release characteristics than protein concentration. Aroma concentration in the oil phase, rather than in the emulsion, determines the kinetics of hydrophobic flavor release. The method provides a useful tool for the rapid and reproducible measurement of flavor release profile.