Cheng Equation: A Revisit Through Symmetry Analysis

The symmetry analysis of the Cheng Equation is performed. The Cheng Equation is reduced to a first-order equation of either Abel's Equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati Equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng Equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae journa

Missile Attitude Control via a Hybrid LQG-LTR-LQI Control Scheme with Optimum Weight Selection

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.This paper proposes a new strategy for missile attitude control using a hybridization of Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques. The LQG control design is carried out in two steps i.e. firstly applying Kalman filter for state estimation in noisy environment and then using the estimated states for an optimal state feedback control via Linear Quadratic Regulator (LQR). As further steps of performance improvement of the missile attitude control system, the LTR and LQI schemes are applied to increase the stability margins and guarantee set-point tracking performance respectively, while also preserving the optimality of the LQG. The weighting matrix (Q) and weighting factor (R) of LQG and the LTR fictitious noise coefficient (q) are tuned using Nelder-Mead Simplex optimization technique to make the closed-loop system act faster. Simulations are given to illustrate the validity of the proposed technique

Magnetocaloric effect and critical behavior near the paramagnetic to ferrimagnetic phase transition temperature in TbCo2-xFex

Magnetocaloric effect (MCE) in TbCo2-xFex has been studied by dc magnetization measurements.On substituting Fe in TbCo2, not only the magnetic transition temperature is tuned to room temperature, but also the operating temperature range for MCE is increased from 50 K for TbCo2 to 95 K for TbCo1.9Fe0.1. The maximum magnetic entropy change (-{\Delta}SM) for TbCo1.9Fe0.1 is found to be 3.7 J kg-1 K-1 for a 5 T field change, making it a promising candidate for magnetic refrigeration near room temperature. The temperature dependent neutron diffraction study shows a structural phase transition (from cubic to rhombohedral phase with lowering of temperature) which is associated with the magnetic phase transition and these transitions broaden on Fe substitution. To investigate the nature of the paramagnetic to ferrimagnetic phase transition, we performed a critical exponent study. From the derived values of critical exponents, we conclude that TbCo2 belongs to the 3D Heisenberg class with short-range interaction, while on Fe substitution it tends towards mean-field with long-range interaction. The derived values of critical exponents represent the phenomenological universal curve for the field dependence of {\Delta}SM, indicating that TbCo2 and TbCo1.9Fe0.1 belong to two different universality classes.Comment: 12 figure

Child Mortality Inequalities and Linkage with Sanitation Facilities in Bangladesh

Principal component analysis (PCA) was applied to assets and other household data, collected as part of the Bangladesh Demographic and Health Survey (BDHS) in 2004, to rank individuals according to a household socioeconomic index and to investigate whether this predicts access to the sanitation system or outcomes. PCA was used for determining wealth indices for 11,440 women in 10,500 households in Bangladesh. The index was based on the presence or absence of items from a list of 13 specific household assets and three housing characteristics. PCA revealed 35 components, of which the first component accounted for 18% of the total variance. Ownership of assets and housing features contributed almost equally to the variance in the first component. In this study, ownership of latrines was examined as an example of sanitation-intervention access, and rates of mortality of neonates, infant, and children aged less than five years (under-five mortality) as examples of health outcomes. The analysis demonstrated significant gradients in both access and outcome measures across the wealth quintiles. The findings call for more attention to approaches for reducing health inequalities. These could include reforms in the health sector to provide more equitable allocation of resources, improvement in the quality of health services offered to the poor, and redesigning interventions and their delivery to ensure that they are more pro-poor

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