Pole Placement and Reduced-Order Modelling for Time-Delayed Systems Using Galerkin Approximations

The dynamics of time-delayed systems (TDS) are governed by delay differential equa- tions (DDEs), which are infinite dimensional and pose computational challenges. The Galerkin approximation method is one of several techniques to obtain the spectrum of DDEs for stability and stabilization studies. In the literature, Galerkin approximations for DDEs have primarily dealt with second-order TDS (second-order Galerkin method), and the for- mulations have resulted in spurious roots, i.e., roots that are not among the characteristic roots of the DDE. Although these spurious roots do not affect stability studies, they never- theless add to the complexity and computation time for control and reduced-order modelling studies of DDEs. A refined mathematical model, called the first-order Galerkin method, is proposed to avoid spurious roots, and the subtle differences between the two formulations (second-order and first-order Galerkin methods) are highlighted with examples. For embedding the boundary conditions in the first-order Galerkin method, a new pseudoinverse-based technique is developed. This method not only gives the exact location of the rightmost root but also, on average, has a higher number of converged roots when compared to the existing pseudospectral differencing method. The proposed method is combined with an optimization framework to develop a pole-placement technique for DDEs to design closed-loop feedback gains that stabilize TDS. A rotary inverted pendulum system apparatus with inherent sensing delays as well as deliberately introduced time delays is used to experimentally validate the Galerkin approximation-based optimization framework for the pole placement of DDEs. Optimization-based techniques cannot always place the rightmost root at the desired location; also, one has no control over the placement of the next set of rightmost roots. However, one has the precise location of the rightmost root. To overcome this, a pole- placement technique for second-order TDS is proposed, which combines the strengths of the method of receptances and an optimization-based strategy. When the method of receptances provides an unsatisfactory solution, particle swarm optimization is used to improve the location of the rightmost pole. The proposed approach is demonstrated with numerical studies and is validated experimentally using a 3D hovercraft apparatus. The Galerkin approximation method contains both converged and unconverged roots of the DDE. By using only the information about the converged roots and applying the eigenvalue decomposition, one obtains an r-dimensional reduced-order model (ROM) of the DDE. To analyze the dynamics of DDEs, we first choose an appropriate value for r; we then select the minimum value of the order of the Galerkin approximation method system at which at least r roots converge. By judiciously selecting r, solutions of the ROM and the original DDE are found to match closely. Finally, an r-dimensional ROM of a 3D hovercraft apparatus in the presence of delay is validated experimentally

Scaled Particle Theory for Hard Sphere Pairs. I. Mathematical Structure

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6 percent lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the sequel (following paper

Analytical Modeling of Metal Gate Granularity based Threshold Voltage Variability in NWFET

Estimation of threshold voltage V T variability for NWFETs has been compu- tationally expensive due to lack of analytical models. Variability estimation of NWFET is essential to design the next generation logic circuits. Compared to any other process induced variabilities, Metal Gate Granularity (MGG) is of paramount importance due to its large impact on V T variability. Here, an analytical model is proposed to estimate V T variability caused by MGG. We extend our earlier FinFET based MGG model to a cylindrical NWFET by sat- isfying three additional requirements. First, the gate dielectric layer is replaced by Silicon of electro-statically equivalent thickness using long cylinder approxi- mation; Second, metal grains in NWFETs satisfy periodic boundary condition in azimuthal direction; Third, electrostatics is analytically solved in cylindri- cal polar coordinates with gate boundary condition defined by MGG. We show that quantum effects only shift the mean of the V T distribution without sig- nificant impact on the variability estimated by our electrostatics-based model. The V T distribution estimated by our model matches TCAD simulations. The model quantitatively captures grain size dependence with {\sigma}(V T ) with excellent accuracy (6%error) compared to stochastic 3D TCAD simulations, which is a significant improvement over the state-of- the-art model with fails to produce even a qualitative agreement. The proposed model is 63 times faster compared to commercial TCAD simulations

SMART INDOOR VERTICAL FARMING MONITORING USING IoT

 The population of the world is expected to reach around 9.7 billion by the end of the year 2050. Currently, around 56% of the world‟s population lives in the urban areas, putting a lot of pressure on the maintenance of the air quality and the greenery in these areas. But the issue is that there is lack of space for cultivation in urban areas where urban gardening comes into picture. Human labour is involved in traditional methods of monitoring and farming and is it is time consuming. Vertical farming is the practice of growing plants in the vertically inclined surfaces or in vertically stacked layers. Here, plants are grown in a controlled environment. The proposed system uses the concepts of artificial photosynthesis, vertical and zone-wise crops production and the Internet of Things. This increases the productivity. By using the various sensor networks, the environmental parameters can be noted. The retrieved data is stored and displayed on a customized webpage which can be accessed through mobile app. Thus, the indoor vertical farm can be monitored and controlled even without direct presence of the cultivator at the plant environment. The variations in the individual sensor‟s data with respect to time can be graphically plotted for the improved analysis and monitoring of the system. Increasing population demands increase in food production by the next decade. Internet of things is implemented in vertical and indoor farming to establish a smart way of cultivation. Basic functions like monitoring the soil moisture, temperature, humidity are performed. Artificial photosynthesis for the plants using grow-lamps and drip irrigation is implemented to maintain the urban gardens. Using GSM technology systematic alerts regarding the status of garden to the user at regular intervals of time is delivered. An android app interface is also implemented in the proposed system to remotely control the garden functioning hence enhancing the smart way of agriculture

Quantum direct communication protocol using recurrence in k-cycle quantum walk

The ability of quantum walks to evolve in a superposition of distinct quantum states has been used as a resource in quantum communication protocols. Under certain settings, the $k$-cycle discrete-time quantum walks\,(DTQW) are known to recur to its initial state after every $t_r$ steps. We first present a scheme to optically realize any $k$-cycle DTQW using $J$-plate, orbital angular momentum\,(OAM) sorters, optical switch, and optical delay line. This entangles the polarization and OAM degrees of freedom\,(DoF) of a single photon. Making use of this recurrence phenomena of $k$-cycle DTQW and the entanglement generated during the evolution, we present a new quantum direct communication protocol. The recurrence and entanglement in $k$-cycle walk are effectively used to retrieve and secure the information, respectively, in the proposed protocol. We investigate the security of the protocol against intercept and resend attack. We also quantify the effect of amplitude damping and depolarizing noises on recurrence and mutual information between polarization and OAM DoF of a single photon.Comment: 9 pages, 6 figure

Avoiding Fire in the Operating Suite: An Intersection of Prevention and Common Sense

The operating room (OR) is a complex environment that involves large teams and multiple competing priorities, dynamically interacting throughout the entire course of a surgical procedure. The simultaneous presence of flammable substances, volatile gases, and the frequent use of electrical current results in a potentially dangerous combination. Operating room fire (ORF) is a rare but potentially devastating occurrence. To prevent this “never event”, it is critical for institutions to establish and follow proper fire safety protocols. Adherence to proven prevention strategies and awareness of associated risk factors will help reduce the incidence of this dreaded safety event. When ORF does occur despite strict adherence to established safety protocols, the entire OR team should know the steps required to contain and extinguish the fire as well as essential measures to minimize or avoid thermal injury. If injury does occur, it is important to recognize and treat it promptly. Appropriate and honest disclosure to all injured persons and their families should be made without delay. As with all serious patient safety events, regulatory reporting and root cause determinations must take place in accordance with applicable laws and regulations. The goal of patient safety champions at each institution should be the attainment of zero incidence of ORF

A prospective study on clinical profile and incidence of acute kidney injury due to hair dye poisoning

Background: Globally suicides are mounting at an alarming rate over the last few decades thus claiming the most productive age group of the society. Developing country like India is no exception to this needless increasing toll.Methods: This study was a prospective observational study with 31 patients recruited at Osmania General Hospital between November 2011 – October 2013. Patients of alleged hair dye ingestion admitted in MICU were taken up for study after the exclusion criteria were ruled out. Informed consent was obtained from every patient or patient’s relatives. All routine laboratory investigations were done basing on standard clinical procedures and protocols and patient related clinical information were recorded on the prepared proforma from the time of hospital admission till discharge or death. The presence of AKI was defined and graded as per the RIFLE criteria.Results: The present work examines 31 cases of suicidal ingestion of hair dye, out of which males were 6 (19.35%) and females were 25 (80.64%). It was observed that the tendency to commit suicide was more in the age group 21 -30 years with males (30%) and females (70%). 19% of total patients who ingested more than 50 ml of dye had developed Acute Kidney injury requiring hemodialysis. Upon treatment about 58% of patients were discharged from hospital in good general health condition, Four patients expired due to respiratory complications with pneumonia, ARDS, sepsis and ARF.Conclusions: So in current scenario of emerging hair dye poisoning, it is imperative for a timely intervention by reducing the time of admission in hospital and also early management by clinicians is the need of an hour

Comparative efficacious study between preoperative pregabalin and gabapentin on postoperative pain in abdominal hysterectomy: an institutional experience

Background: Pain is a consistent and predominant complaint following surgical intervention including abdominal open hysterectomy. A multimodal approach has been suggested to improve postoperative analgesia and to reduce opioid related side effects. In this context we conducted a comparative study on efficacy between gabapentin and pregabalin on postoperative pain relief.Methods: In this prospective randomised study, 60 patients were divided in to two arms group G and group P. 900 mg of gabapentin and 300 mg of pregabalin were administered orally one hour before spinal anaesthesia to respective groups. Hemodynamic parameters such as heart rate, mean arterial pressure, respiratory rate was monitored pre, per and postoperatively. Also, the need for first analgesic dose and visual analog pain score were documented in all subjects of both groups. Statistical analysis with SPSS 16.0 performed.Results: There was significant fall in mean arterial pressure in group G than group P patients. Further the fall in mean pulse rate was more in group G compared to group P throughout pre, per and post-operative phases. In terms of mean postoperative time required for first dose of analgesic drug, pregabalin and gabapentin was required after 7 and 5 hours respectively. There was a statistically significant change in Visual Analogue Scale, showing pregabalin as better drug than gabapentin in post operative pain control with score 5 and 7 respectively.Conclusions: Pre-emptive analgesia with pregabalin appears to be superior to gabapentin as a part of multimodal perioperative pain management in abdominal hysterectomy

Fact versus Conjecture: Exploring Levels of Evidence in the Context of Patient Safety and Care Quality

Evidence-based medicine (EBM) can be defined as the integration of optimized clinical judgment, patient values, and available evidence. It is a philosophical approach to making the best possible clinical decisions for individual patients. Based on objective evaluation and categorization of methodological design and data quality, all existing literature can be organized according to a hierarchy of “evidence quality” that helps determine the applicability and value of scientific findings in terms of clinical implementation and the potential to change existing patterns of practice. In terms of general categorization of scientific impact, randomized controlled trials (RCTs) are placed on top of the hierarchy, followed by systematic reviews of randomized controlled trials (RCTs), quasi-randomized designs, observational studies including retrospective case series, and finally case reports and expert opinion. Each study design is susceptible to certain limitations and biases, highlighting the importance of both clinical and scientific acumen of the interpreting provider. Such approach is critical to determining the value and the applicability of study recommendations in everyday practice. Evidence-based practice (EBP) has become one of the fundamental components of modern medicine and plays an indispensible role in the development (and improvement) of patient care and safety worldwide. Furthermore, organizations that create guidelines and policies for the management of specific conditions, often base the content and strength of their recommendations on the quality of evidence available to expert decision-makers. Therefore, understanding the “state of the science” upon which those recommendations are based will help guide the medical practitioner on “if, when and how” to apply evidence-based guidelines in his or her everyday medical or surgical practice. This chapter focuses on clinically relevant application of levels of scientific evidence (LSE) and the corresponding levels of clinical recommendation (LCR) in the context of care quality and safety