Unique fractional calculus engineering laboratory for learning and research

Abstract

In this paper, a novel prototype laboratory is presented for engineering education, in which experiments are based on the fractional calculus. The prototypes of analog and digital fractional-order proportional-integral-derivative (PID) controllers are built in the laboratory. These fractional-order PID controllers are applied to linear and nonlinear plants to demonstrate the effectiveness of fractional-order calculus in real time. These experiments are designed, developed, and implemented on the analog and digital platforms. These controllers are integrated to control the DC motor, brushless DC motor, and magnetic levitation modules through hardware-in-loop as well as stand-alone systems. The analog type of fractional-order PID implementation is carried out by using passive components (i.e. resistances and capacitances) with an operational amplifier. However, real-time digital implementation is carried out using field-programmable gate array and digital signal processor. This paper describes how the experiments on fractional calculus can be tailored for graduate, undergraduate students’ education and extended for research in this emerging area.

RETRACTED: Intelligent grading system based on deep learning

“…Higher education is a very important form of education. [1][2][3] One of the popular method for off-line grading in higher education is to grade the scanned copies of the examination paper. The main technique of this method is image recognition.…”

DSP-HIL Comparison between IM Drive Control Strategies

“…An interesting effort to bring FO to the engineering classrooms was reported by Khubalkar et al [41], who reported the FO implementation of analog fractional integrator, a digital fractional integrator, a FO-PID controller for a DC motor, a FO-PID controller for hardware in the loop MagLev system, a FO-PID controller for a brushless direct current motor and a digital FO-PID controller for a direct current motor. A five-level space vector pulse width modulated multipoint clamped (MPC) inverter fed direct torque-controlled IM drive with FO PI controllers was reported by Chandra Sekhar and Lakhimsetty [42].…”

Adjustable Multiphase Sinusoidal Oscillator with Fractional–Order Elements

“…The relations for calculation of values of the transconductances g m1 and g m2 are obtained by rearranging the equations (5) and (6) to:…”

“…The fractional-order systems can be used in many diverse scientific fields. For example in cryptography for generating random numbers [2], in biology for modelling of biological phenomena [3], in agriculture for analysis of the fruits or vegetable properties [4], in electrical engineering for design of the precise controllers [5], frequency filters [6] and oscillators [7]- [11].…”