Showing papers by "Shantanu Das published in 2018"

Design and implementation of digital fractional order PID controller using optimal pole-zero approximation method for magnetic levitation system

Abstract: The aim of this paper is to employ fractional order proportional integral derivative ( FO-PID ) controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system ( MLS ), which is inherently nonlinear and unstable system. The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller. An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored. The controller parameters are tuned using dynamic particle swarm optimization ( dPSO ) technique. Effectiveness of the proposed control scheme is verified by simulation and experimental results. The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers. It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

An insight into Newton's cooling law using fractional calculus

Abstract: For small temperature differences between a heated body and its environment, Newton's law of cooling predicts that the instantaneous rate of change of temperature of any heated body with respect to time is proportional to the difference in temperature of the body with the ambient, time being measured in integer units Our experiments on the cooling of different liquids (water, mustard oil, and mercury) did not fit the theoretical predictions of Newton's law of cooling in this form The solution was done using both Caputo and Riemann-Liouville type fractional derivatives to check if natural phenomena showed any preference in mathematics In both cases, we find that cooling of liquids has an identical value of the fractional derivative of time that increases with the viscosity of the liquid On the other hand, the cooling studies on metal alloys could be fitted exactly by integer order time derivative equations The proportionality constant between heat flux and temperature difference was examined with resp

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

Abstract: In this paper, we obtain approximate bound state solutions of an N-dimensional fractional time independent Schrodinger equation for a generalised Mie-type potential, namely, V(rα)=Ar2α+Brα+C. Here α(0 < α < 1) acts like a fractional parameter for the space variable r. When α = 1 the potential converts into the original form of Mie-type of potential that is generally studied in molecular and chemical physics. The entire study is composed with a Jumarie-type fractional derivative approach. The solution is expressed via the Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous studies for different potential parameter configurations, specially for α = 1. At the end, few numerical calculations for energy eigenvalue and bound state eigenfunctions are furnished for a typical diatomic molecule.

A Simple Adaptive Fractional Order Model of Supercapacitor for Pulse Power Applications

Abstract: The porous nature of the electrodes results in complex dynamics of the supercapacitors. Consequently, the value of the capacitance varies with the voltage level, frequency and magnitude of the charging/discharging current. Conventional RC models or ladder RC network models are not apt for accurate representation of such dynamics. This paper investigates the suitability of a simple fractional order model for accurately representing such characteristics of the supercapacitors for pulse power applications. The identification of the fractional order model parameters from constant resistance charge/discharge test, constant current charge/discharge test and impedance spectroscopy is discussed. Based on the test results, the shortcomings of the simple fractional order model in representing the pulse power applications, owing to the variation of the fractional order model parameters are examined. An adaptive fractional order model considering the nonlinear voltage and frequency dependence on the parameters is then deduced. A procedure for identifying the model parameters is presented and the validity of the model is verified using various test profiles.

Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

Abstract: Klein–Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein–Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein–Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein–Gordon equation, we can overcome the problem. The fractional Klein–Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

Energy/Fuel Efficient and Enhanced Robust Systems Demonstrated with Developed Fractional Order PID Controller

Abstract: In this brief article, the design and implementation of Fractional Order Proportional-Integral-Derivative (FOPID) controller is presented in analog and digital domains. Here we show the measured results for energy/fuel efficiency and enhanced robustness, as compared to classical PID controls. The FOPID controller is tested with DC-Motor, Magnetic Levitation System, and Brushless DC Motor, that we report in this article.

State of Charge Estimation of Supercapacitors with Fractional Order Modelling

Abstract: Supercapacitors are widely employed for substituting/assisting batteries for various applications like electric vehicles, traction, micro grids and so on. Design of efficient and cost effective energy management schemes for these applications demands accurate estimation of the State of Charge (SOC) of the supercapacitors. If the behavior of supercapacitors can be modelled using a simple RC circuit, then SOC can be directly calculated from the open circuit voltage. However, because of the porous nature of their electrodes, supercapacitors are subjected to charge redistribution during/following every charge/discharge cycle. Consequently, the value of the capacitance exhibits a nonlinear relation with the voltage, frequency, magnitude of the charge/discharge current and temperature. This paper presents some interesting observations regarding the charge and discharge mechanisms of the supercapacitors. The SOC of key commercial supercapacitors is calculated based on a fractional order model and the results are verified using Ampere counting method. Further the effect of the charge redistribution on defining the utilizable capacity limits is analyzed and an empirical method for calculating the utilizable SOC is presented.

Application of fractional calculus to distinguish left ventricular hypertrophy with normal ECG

Abstract: ECG graphs are the rough type of graphs which are continuous everywhere but non-differentiable at some points of PQRST complexes of each leads of ECG. These non-differentiable points cannot be interpreted by usual classical calculus but it can be characterized by fractional calculus. In this paper we have applied fractional calculus to distinguish Left Ventricular Hypertrophic ECG from Normal ECG. To interpret the non-differentiable points we have calculated modified left and right Riemann-Liouville fractional derivatives, corresponding Phase Transition(P.T.) values (i.e. difference between left and right modified R-L fractional derivative), mean and standard deviation of the P.T. values at the non-differentiable points of the considerable ECG leads. From the study we observe that the P.T. values are higher for Left Ventricular Hypertrophy cases compared to the normal ones. In addition for LVH patients mean and standard deviation of the P.T. values of considerable ECG leads are higher than those for normal ECGs. This may be a new approach to study any ECG via fractional calculus.

Formulation and Solution of Three Dimensional Space-Time Fractional KdV-Zakharov-Kuznetsov and Modified KdV-Zakharov-Kuznetsov Equation

Abstract: In the present paper, we have constructed two fractional non-linear evolution equations: Those are the space-time fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation and space-time modified fractional mKdV-Zakharov-Kuznetsov (mKdV-ZK) equation and obtained their exact analytical solutions using the modified fractional Sub-Equation method. Here the modified fractional derivative is used to establish the fractional order KdV-ZK and mKdV-ZK equation using the fractional variational principle. Finally, numerical simulation is done to represent the results graphically.

A Comparative Study of Different Negative Permeability Metamaterial Structures at X band : Useful for Microwave Applications

Abstract: This paper presents a comparative study of eight frequently used negative permeability metamaterial structures at X band (8GHz -- 12.4GHz). The structures have been simulated using commercial 3D FEM (Finite Element Method) solver. A standard scattering-parameter based retrieval method is applied to extract permeability of these structures and compared for size, insertion loss and negative permeability characteristics. Finally, one of the structures have been fabricated and tested using free space focused beam metamaterial characterization setup at X band for validation.