Munmun Khanra

Realization of a carbon nanotube based electrochemical fractor

A fractor or a fractional order element should show a constant phase (CP), between ±90° (except 0°) at any frequency, theoretically. However, all the practical realization of single component fractor have limitation in their CP zone. Not many single-component-fractors have been reported having CP zone more than a decade. In this work, new electrochemical type fractors have been developed, by coating a polymer-carbon nanotube (CNT) composite over Cu clad epoxy block and putting the block in polarizing solution. By varying the percentage of CNT in polymer-CNT composite and the nature of polarizing solution, two different types of fractor have been realized. One is a wide-band fractor having CP zone of five decades (20 Hz to 2 MHz) with a ripple of ±2° only. The other one shows two distinct CP zones at two different phase angles. Each zone is about two decade long. These fractors will help to realize fractional order circuits which need to be operated in wide frequency band.

Rational approximation of fractional operator — A comparative study

A comparative study of some existing methods for rational approximation of fractional operator (fractional Laplace operator) is presented. The various methods along with their advantages and limitations are described in this paper. Simulation results are shown for different orders of the fractional operator.

Reduced Order Approximation of MIMO Fractional Order Systems

A new two-stage method for reduced integer order approximation of fractional multiple-input, multiple-output (MIMO) systems is proposed. In the first stage, the transfer function matrix (TFM) Gf(s) of the given fractional order MIMO system is obtained and an integer order approximate TFM R(s) is formed by applying an existing approximation method to each fractional order transfer function (FOTF) of Gf(s). In the second stage, a reduced order state space model is formed. The system matrix of the reduced order system is constructed by selecting the dominant poles from the intermediate high integer order model R(s). The input and output matrices are found by matching approximate time moments and Markov parameters of the final reduced order model and the original system. The proposed method has been illustrated by an example.

Rational Approximation and Analog Realization of Fractional Order Differentiator

An algorithm for rational approximation of all class of fractional order transfer function has been described briefly. The analog realization scheme for the approximated integer model has been shown. The analog equivalent circuit of fractional order differentiator has been realized in Matlab simulink and the results have been compared with the corresponding ideal values.

Equivalent circuit model of supercapacitor for self-discharge analysis — A comparative study

Self-discharge of supercapacitor is an important phenomenon that needs to be considered carefully, especially for the applications like wireless sensor networks, memory backup systems, etc. Different types of models have been proposed by the various researchers to capture the supercapacitor dynamics. In this paper, two electrical equivalent circuit models, variable leakage resistance (VLR) model and charge redistribution based model, have been considered for comparative study. Both the models have been analyzed based on the charge and long term self-discharge responses obtained through experimentation and simulation. The device under test is the Maxwell BCAP0100 P270 T07 supercapacitor. First, it has been charged at 2A constant current to its rated voltage; then, has been left for self-discharge. The terminal voltage has been collected for total charging time as well as self-discharge for 8000 seconds. The data have been acquired using National Instruments (NI) hardware and LabVIEW software. Based on the case study used in this paper, it is observed that the charge redistribution based model is better able to capture the self-discharge phenomenon. However, the error in the VLR model may not be insignificant always.

Circuit proposition for realization of approximated fractional order systems

This paper gives an effective alternative approach for circuit realization of a block containing a real zero and a pair of complex conjugate poles. The proposed approach is useful for analog realization of a class of integer order systems as well as fractional order systems (FOS) via integer order approximation. The proposed approach makes the system less sensitive to noise while the number of components used is a minimum. The method has been demonstrated by three examples of FOS via their integer approximation. Fractional order transfer functions have been approximated over a frequency range of (0.01-1000) rad/sec, and in all the three cases, the pair of complex conjugate poles and one of the real zeros of approximants have been realized through PSPICE simulation. For one example, the circuit has been implemented in hardware also. Experimental results are compared with PSPICE simulation results and theoretical results.

Design of FPGA based digital controller for 2nd and higher order systems

This paper describes a new method for designing digital controller and their FPGA based realization schemes. The design method is based on time domain response to meet three different time domain specifications settling time, peak overshoot/rise time and closed loop gain ensuring minimal ITAE. This design method follows Graham Lathrop optimal polynomials (GL Polynomials) with an introduction of Left Hand Side zero (LHS Zero). The same design method to be applicable for any system from 2nd to 6th order. Simulation results of tests for robustness and specifications change also featured in this paper.