Author

# Shantanu Das

Other affiliations: University of Chicago, Jadavpur University

Bio: Shantanu Das is an academic researcher from Bhabha Atomic Research Centre. The author has contributed to research in topic(s): Fractional calculus & PID controller. The author has an hindex of 24, co-authored 152 publication(s) receiving 2925 citation(s). Previous affiliations of Shantanu Das include University of Chicago & Jadavpur University.

##### Papers

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01 Jun 2011

TL;DR: In this article, a modern approach to solve the solvable system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving approximately exact series solutions.

Abstract: When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ordinary differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ordinary calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the solvable system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving approximately exact series solutions.Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.This XXI century has thus started to think-exactly for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.

597 citations

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TL;DR: A new fractional order template for reduced parameter modelling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is presented.

Abstract: In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modelling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The time domain optimal tuning of FOPID controllers have also been carried out to handle these higher order processes by performing optimization with various integral performance indices. The paper highlights on the practical control system implementation issues like flexibility of online autotuning, reduced control signal and actuator size, capability of measurement noise filtration, load disturbance suppression, robustness against parameter uncertainties etc. in light of the above tuning methodologies.

191 citations

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TL;DR: A novel fractional order fuzzy Proportional-Integral-Derivative (PID) controller is proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output.

Abstract: A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input-output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PI^@lD^@m controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.

189 citations

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TL;DR: Mutation analysis of LIS1, using highly sensitive techniques such as denaturing high-pressure liquid chromatography, should be considered for patients with posteriorly predominant subcortical band heterotopia and pachygyria.

Abstract: Background: Subcortical band heterotopia (SBH) is a neuronal migration disorder. DCX mutations are responsible for almost all familial cases, 80% of sporadic female cases, and 25% of sporadic male cases of SBH, and are associated with more severe gyral and migration abnormality over the anterior brain regions. Somatic mosaicism has previously been hypothesized in a patient with posteriorly predominant SBH and a mutation of the LIS1 gene, which is usually mutated in patients with severe lissencephaly. The authors identified mosaic mutations of LIS1 in two patients (Patients 1 and 2) with predominantly posterior SBH. Methods: After ruling out DCX mutations, the authors performed sequencing of the LIS1 gene in lymphocyte DNA. Because sequence peaks in both patients were suggestive of mosaic mutations, they followed up with denaturing high-pressure liquid chromatography analysis on blood and hair root DNA and compared the areas of heteroduplex and homoduplex peaks. A third patient showing the same mutation as Patient 2 but with no evidence of mosaicism was used for comparing the phenotype of mosaic vs full mutation. Results: The two patients with posterior SBH harbored a missense (Arg241Pro) and a nonsense (R8X) mosaic mutation of LIS1 . The rate of mosaicism in Patient 1 was 18% in the blood and 21% in the hair roots, whereas in Patient 2 it was 24% and 31% in the same tissues. The patient with a full R8X mutation of LIS1 had severe lissencephaly. Conclusions: Subcortical band heterotopia can occur with mosaic mutations of the LIS1 gene. Mutation analysis of LIS1 , using highly sensitive techniques such as denaturing high-pressure liquid chromatography, should be considered for patients with posteriorly predominant subcortical band heterotopia and pachygyria.

111 citations

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TL;DR: The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control.

Abstract: The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.

92 citations

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01 Jan 20152,819 citations

01 Nov 2000

TL;DR: In this paper, the authors compared the power density characteristics of ultracapacitors and batteries with respect to the same charge/discharge efficiency, and showed that the battery can achieve energy densities of 10 Wh/kg or higher with a power density of 1.2 kW/kg.

Abstract: The science and technology of ultracapacitors are reviewed for a number of electrode materials, including carbon, mixed metal oxides, and conducting polymers. More work has been done using microporous carbons than with the other materials and most of the commercially available devices use carbon electrodes and an organic electrolytes. The energy density of these devices is 3¯5 Wh/kg with a power density of 300¯500 W/kg for high efficiency (90¯95%) charge/discharges. Projections of future developments using carbon indicate that energy densities of 10 Wh/kg or higher are likely with power densities of 1¯2 kW/kg. A key problem in the fabrication of these advanced devices is the bonding of the thin electrodes to a current collector such the contact resistance is less than 0.1 cm2. Special attention is given in the paper to comparing the power density characteristics of ultracapacitors and batteries. The comparisons should be made at the same charge/discharge efficiency.

2,437 citations

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11 Dec 20121,459 citations

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01 Jan 2014TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24

Abstract: Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series
$$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$
(6.1.1)
Such a function with positive α 1 > 0, α 2 > 0 and real \(\beta _{1},\beta _{2} \in \mathbb{R}\) was introduced by Dzherbashian [Dzh60].

917 citations