On fuzzy semi δ – V continuity in fuzzy δ – V topological space

New concepts of fuzzy semi δ – V and fuzzy semi δ – Λ sets were introduced in the work „On fuzzy semi δ – Λ sets and fuzzy semi δ – V sets V – 6” by the authors (J. Trip. Math. Soc., 6, 81 – 88 (2004)). It was shown that the family of all fuzzy semi δ – V sets forms a fuzzy supra topological space on X denoted by ( X, FS δV ). The aim of this paper is to introduce the concept of fuzzy semi δ – V continuity in a fuzzy δ – V topological space. Finally, some properties, preservation theorems, etc., are studied.Нові поняття нечітких напів δ - V та нечітких напів δ - Λ множин введено у роботі авторів „On fuzzy semi δ - Λ sets and fuzzy semi δ - V sets V - 6" (J. Trip. Math. Soc. - 2004. - 6. - C. 81 - 88). Було показано, що сім'я усіх нечітких напів δ - V множин формує нечіткий супра-топологічний простір в X, що позначається як ( X, FS δ V ). Метою даної статті є введення поняття нестійкої напів δ - V неперервності у нестійкому δ - V топологічному просторі. Також досліджено деякі її властивості, наведено теорему про збереження та інші питання

Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

Integrated optical source of polarization entangled photons at 1310 nm

We report the realization of a new polarization entangled photon-pair source based on a titanium-indiffused waveguide integrated on periodically poled lithium niobate pumped by a CW laser at $655 nm$. The paired photons are emitted at the telecom wavelength of $1310 nm$ within a bandwidth of $0.7 nm$. The quantum properties of the pairs are measured using a two-photon coalescence experiment showing a visibility of 85%. The evaluated source brightness, on the order of $10^5$ pairs $s^{-1} GHz^{-1} mW^{-1}$, associated with its compactness and reliability, demonstrates the source's high potential for long-distance quantum communication.Comment: There is a typing mistake in the previous version in the visibility equation. This mistake doesn't change the result

Photon-bunching measurement after 2x25km of standard optical fibers

To show the feasibility of a long distance partial Bell-State measurement, a Hong-Ou-Mandel experiment with coherent photons is reported. Pairs of degenerate photons at telecom wavelength are created by parametric down conversion in a periodically poled lithium niobate waveguide. The photon pairs are separated in a beam-splitter and transmitted via two fibers of 25km. The wave-packets are relatively delayed and recombined on a second beam-splitter, forming a large Mach-Zehnder interferometer. Coincidence counts between the photons at the two output modes are registered. The main challenge consists in the trade-off between low count rates due to narrow filtering and length fluctuations of the 25km long arms during the measurement. For balanced paths a Hong-Ou-Mandel dip with a visibility of 47.3% is observed, which is close to the maximal theoretical value of 50% developed here. This proves the practicability of a long distance Bell state measurement with two independent sources, as e.g. required in an entanglement swapping configuration in the scale of tens of km.Comment: 6 pages, 5 figure