Realization of Fractional Order Inductive Transducer

In this paper, a new fractional order reluctance inductive transducer is realized by combining a basic reluctance inductive transducer with a general impedance converter circuit and a fractional order element. The fractional order element is realized using an RC ladder network attained by the integer-order rational approximation of the fractional term. A prototype of the fractional order reluctance inductive sensor was developed using the ferrite E-core-shaped variable reluctance inductive sensor and used for analyzing its characteristics. The impedance of the prototype device attained theoretically is validated with the experimental results. Hay’s bridge-based conditioning circuit is used with the fractional order inductive transducer to get the voltage output for the given input displacement; the output measured depends on the order of the fractional element. A suitable fractional order for which the output is both higher and linear is identified and presented. Through simulation and the experimental results obtained from the prototype transducer, it is demonstrated that the fractional-order inductive transducer is more effective in reducing the nonlinearity inherent in the real system with a considerable improvement in the sensitivity.

[1]  Donglin Peng,et al.  An Inductive Angular Displacement Sensor Based on Planar Coil and Contrate Rotor , 2015, IEEE Sensors Journal.

[2]  José António Tenreiro Machado,et al.  Fractional order electromagnetics , 2006, Signal Process..

[3]  Chu-Sun Yen,et al.  Time-domain skin-effect model for transient analysis of lossy transmission lines , 1982, Proceedings of the IEEE.

[4]  Roberto Kawakami Harrop Galvão,et al.  Identification of Fractional-Order Transfer Functions Using a Step Excitation , 2015, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Karabi Biswas,et al.  Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Karabi Biswas,et al.  Limit of Detection for Five Common Adulterants in Milk: A Study With Different Fat Percent , 2018, IEEE Sensors Journal.

[7]  Ahmed S. Elwakil,et al.  Fractional-order sinusoidal oscillators: Design procedure and practical examples , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Debasmita Mondal,et al.  Design and performance study of phase‐locked loop using fractional‐order loop filter , 2015, Int. J. Circuit Theory Appl..

[9]  Arjuna Madanayake,et al.  Approximate Realization of Fractional-Order 2-D IIR Frequency-Planar Filters , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[10]  Dongli Zhang,et al.  Fractional order sliding mode controller design for antilock braking systems , 2013, Neurocomputing.

[11]  K. Salama,et al.  Theory of Fractional Order Elements Based Impedance Matching Networks , 2011, IEEE Microwave and Wireless Components Letters.

[12]  Ahmed S. Elwakil,et al.  Capacitive behavior and stored energy in supercapacitors at power line frequencies , 2018 .

[13]  Jianjun Hu,et al.  Adaptive Synchronization of the Fractional-Order Chaotic Arch Micro-Electro-Mechanical System via Chebyshev Neural Network , 2018, IEEE Sensors Journal.

[14]  Victor Farm-Guoo Tseng,et al.  Resonant Inductive Coupling-Based Piston Position Sensing Mechanism for Large Vertical Displacement Micromirrors , 2016, Journal of Microelectromechanical Systems.

[15]  Pranab K. Dutta,et al.  Modeling of a capacitive probe in a polarizable medium , 2005 .

[16]  A. Charef,et al.  Fractional Euler analog-to-digital transform , 2015 .

[17]  Dumitru Baleanu,et al.  Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution , 2017, Commun. Nonlinear Sci. Numer. Simul..

[18]  I. Schäfer.  Beschreibung der Dämpfung in Stäben mittels fraktionaler Zeitableitungen , 2000 .

[19]  D. Mondal,et al.  Packaging of Single-Component Fractional Order Element , 2013, IEEE Transactions on Device and Materials Reliability.

[20]  Yves Perriard,et al.  Electromagnetic Analysis and Validation of an Ironless Inductive Position Sensor , 2013, IEEE Transactions on Instrumentation and Measurement.

[21]  Satish Chandra Bera,et al.  A modified technique of displacement measurement of a piston made of magnetic material inside a cylinder. , 2013, ISA transactions.

[22]  I. Schäfer,et al.  Modelling of lossy coils using fractional derivatives , 2008 .

[23]  Karabi Biswas,et al.  Realization of Fractional Order Elements , 2017 .

[24]  Parthasarathi Veeraian,et al.  Fractional Order Linear Variable Differential Transformer: Design and analysis , 2017 .

[25]  Boby George,et al.  Design and Development of a New Non-Contact Inductive Displacement Sensor , 2018, IEEE Sensors Journal.

[26]  S. Djuric,et al.  A Novel Approach to Extending the Linearity Range of Displacement Inductive Sensor , 2008, IEEE Transactions on Magnetics.

[27]  YangQuan Chen,et al.  ANALOGUE FRACTIONAL-ORDER GENERALIZED MEMRISTIVE DEVICES , 2009 .

[28]  A. Masi,et al.  Real-time high-precision reading algorithm for the ironless inductive position sensor , 2012, 2012 18th IEEE-NPSS Real Time Conference.

[29]  Karabi Biswas,et al.  A constant phase element sensor for monitoring microbial growth , 2006 .

[30]  Siddhartha Sen,et al.  Optimal Design for Realizing a Grounded Fractional Order Inductor Using GIC , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  I. Schäfer,et al.  Modelling of coils using fractional derivatives , 2006 .

[32]  Parthasarathi Veeraian,et al.  Design and analysis of fractional order seismic transducer for displacement and acceleration measurements , 2018 .

[33]  Ahmad Taher Azar,et al.  Modeling and analysis of fractional order DC-DC converter. , 2017, ISA transactions.

[34]  M. Jagiella,et al.  Progress and Recent Realizations of Miniaturized Inductive Proximity Sensors for Automation , 2006, IEEE Sensors Journal.