Gautam Sarkar

Bio: Gautam Sarkar is an academic researcher from University of Calcutta. The author has contributed to research in topics: Orthogonal functions & Piecewise. The author has an hindex of 12, co-authored 86 publications receiving 545 citations.

A new set of orthogonal functions and its application to the analysis of dynamic systems

Abstract: The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.

Block pulse functions, the most fundamental of all piecewise constant basis functions

Abstract: It is established that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983). The superiority is mainly due to the most elemental nature of BPFs in comparison to any other PCBF function. It is also proved that the operational matrix for integration in the BPF domain is connected to the integration operational matrix in the DUSF domain by simple linear transformation involving invertible Toeplitz matrices. The transformation appears to be transparent because the integration operational matrices are found to match exactly. The reason for such transparency is explained mathematically. Finally, Hwang claimed superiority of DUSFs compared to Walsh functions in obtaining the solution of functional differential equations using a stretch matrix in the DUSF domain. It is shown that the stretch matrices of Walsh and DUSF domains are also related by linear transformation and use of any of these two matrices leads to exactly the same result. This is supported by a...

PSO based PID controller design for twin rotor MIMO system

Abstract: This paper presents particle swarm optimization (PSO) based design of proportional-integral-derivative (PID) controller for a twin rotor MIMO (multi-input multi-output) system (TRMS). The objective of the paper is to tune the gains of the PID controller automatically, by means of a global search method like PSO, so that the transient tracking error will be minimum. The modeling of TRMS exploiting the nonlinear characteristics and cross-coupling phenomena and proper designing of PID control law for it, is being realized in simulation environment. The proposed design methodology is utilized to explore different mode of operations of TRMS under different reference trajectories. The results demonstrate that the proposed design of PID controller is capable of tracking different reference trajectories in satisfactory manner.

Geochemistry and Rb-Sr geochronology of acid tuffs from the northern fringe of the Singhbhum craton and their significance in the precambrian evolution

Abstract: Acid volcanic rocks of tuffaceous nature occur interlayered with metasediments and basic - ultrabasic rocks between the Dalma volcanic belt to the south and the Chotanagpur Gneissic Complex to the north. Inspite of the low-grade metamorphism suffered by the rocks, certain textural - mineralogical attributes, abundance of high field strength and rare-earth elements and primary isotopic signature have remained unaffected. All the samples represent evolved composition but samples from Chandil and Ankro are interpreted to have crystallised from primary melts generated from variable source compositions. On the basis of the nature of isochron, the age of 1484 {+-} 44 Ma is inferred to be the age of eruption of the acid volcanics. This constrains the age of the metasediments and the basic - ultrabasic rocks occurring conformably interlayered with the acid volcanics and reports for the first time the presence of a mid-Proterozoic sequence in eastern Indian craton. The initial Sr ratio of 0.708545 for the Chandil samples is not very high. It is inferred to be largely dominated by Sr from mantle-derived components and the acid volcanics may be products of differentiation from some mantle-derived basic magma. (author)

Numerical solution of fractional differential equations using the generalized block pulse operational matrix

Abstract: The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples.

A survey on consumers empowerment, communication technologies, and renewable generation penetration within Smart Grid

Abstract: The Smart Grid (SG) is a technological transformation from conventional electric grid, electro-mechanically controlled system, to smart, intelligent, and electronically controlled system called the “Smart Grid” (SG). There are about 20–30% losses present in the conventional electric grid due to substandard operations at generation, transmission and distribution side. The major players in the transformation are: (a) increased electricity cost, (b) aging infrastructure, (c) carbon footprint, (d) Green House Gas emissions, (e) climate change, and (f) less efficient electrical network. The promising features of the Smart Grid are: (a) intelligent de-centralized control, (b) resilience, (c) flexibility, (d) sustainability, (e) digitalization, (f) intelligence, (g) consumer empowerment, (h) green energy, and (i) smart infrastructure. The fundamental issues and open challenges in the SG are lack of awareness, consumer acceptance, cyber terrorism, data collection management, energy metering, dynamic optimization and energy control. Considering above, in this paper, a comprehensive review exploring information of development, technologies, and techniques in the SG. The main goal is to investigate and reveal the key enabling technologies, to obtain better picture about the current status of SG development. The focus areas of this review study are Architectural Model focusing Consumer Empowerment (CE), Demand Response Program (DRP), and Demand Side Management (DSM). Our survey discusses in detail the Communication Technologies, such as Wireless Advance Metering Infrastructure (AMI), Phasor Measurement Unit (PMU), Supervisory Control and Data Acquisition (SCADA), and Machine to Machine Communication (M2M). The power systems such as Micro Grid, Nano Grid, Pico Grid, Inter Grid, Virtual Power Plants, and Distributed Generation are also elaborated in this review study. Renewable Energy Resources (RERs) Integration with the SG and Integration issues related to Distributed generation (DG) are presented in this survey. This survey also analyzes Architectural Model of the Smart Grid focusing consumer empowerment and prosumers interaction. The aim of this study is to provide deep understanding of technologies and their applications in the SG.