Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

A simple technique for computing theH ∞-norm of polynomials

In this note, computation of theH -norm of polynomials is considered. It is shown that direct computation of theH -norm of polynomials, based on the definition of the norm, results in a simple and inexpensive technique for computing the norm.     

Extended Cauchy Model for Tunable Refractive Index of Titania Nanoparticles at Visible Region

The extended Cauchy model is derived based on the experimental data for describing the mass fraction-, crystallite size-, and calcination-dependent refractive index of anatase and rutile TiO₂ nanoparticles. This model fits the experimental data of TiO₂ nanoparticles well in the visible spectral region. There is a tunable correlation between the refractive index of TiO₂ nanoparticle and the anatase nanoparticle size at visible region. Moreover, there is a near correlation between experimental and calculated Abbe number at 588 nm.     

Ultrasensitive aflatoxin B1 assay based on FRET from aptamer labelled fluorescent polymer dots to silver nanoparticles labeled with complementary DNA

The authors describe a new method for the selective detection of aflatoxin B1 (AFB1) by an off-on signaling procedure in a fluorescence resonance energy transfer (FRET)-based nanobioprobe. An amino-modified aptamer against AFB1 was conjugated to fluorescent polymer dots, containing poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-thiadiazole)] as the fluorophore. Complementary DNA (cDNA) was conjugated to silver nanoparticles (cDNA-AgNPs) which act as FRET acceptors. Mixed in solution, in the absence of AFB1, the aptamer and its cDNA hybridize to form (aptamer-cDNA). This brings the polymer dots into close proximity of the AgNPs and result in FRET from the donor to the acceptor due to spectral overlap between the emission of the polymer dots and the absorption of the AgNPs. The fluorescence of the polymer dots probe is thereby switched off. However, in the presence of AFB1, the aptamer with high affinity for AFB1 will be released from the cDNA-AgNP aggregate, which results in recovery of fluorescence (“switch on” state). The yellow fluorescence of the polymer dots, best measured at 538 nm, increases linearly in the 5 pg·mL^?1 to 1.0 ng·mL^?1 AFB1 concentration range, with a 0.3 pg·mL-1 detection limit. The assay was successfully applied to the detection of AFB1 in (spiked) wheat flour, and the results were found to be in satisfactory agreement with those obtained by an enzyme-linked immunosorbent assay.

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Graphical abstract An efficient FRET-based nano-bio-probe was developed for the selective detection of Aflatoxin B1 (AFB1). In the absence of AFB1, the hybridization occurred between anti-aptamer AFB1 linked to polymer dots and its cDNA conjugated to AgNPs that led to FRET from the polymer dots to the AgNPs. By adding AFB1, the AgNP-cDNA was released resulting in linear recovery of the fluorescence of polymer dots in an appropriate AFB1 concentration range.

     

Self-equalization of energies of solitons in transmission systems by guiding filters

In this paper, the regulating effect of guiding filters on the energies of solitons in wave-length division multiplexing (WDM) transmission systems is rigorously studied. More precisely, it is shown that guiding filters prevent the energies of solitons from decaying to zero in long distances. This goal is achieved by studying a mathematical model of the evolution of energies of solitons in transmission systems. The approach is mathematical and does not use numerical or experimental results available in the literature; nevertheless, it reaffirms such results.     

Optimal damping ratio for linear second-order systems

In this paper, it is shown that the optimal damping ratio for linear second-order systems that results in minimum-time no-overshoot response to step inputs is of bang-bang type. The optimal damping ratio is zero at the outset and is switched to some maximum value at an appropriate instant of time. The switching time is shown to be a function of the maximum damping ratio and the system natural frequency. Furthermore, it is shown that the larger the maximum damping ratio is, the shorter it takes for the system to reach the desired set point. Finally, it is shown that, if the optimal damping ratio is switched as a function of the system state, then the minimum-time no-overshoot criterion is satisfied, irrespective of the magnitude of the uncertainty in the value of the system natural frequency.     

Boundedness of outputs of a class of lasers

In this note, a large class of lasers, represented by planar nonlinear ordinary differential equations known as the rate equations, is considered. It is shown that the outputs of the lasers are bounded when bounded inputs (currents) are applied to them.