Analog Realization Of Fractional Order Circuits

Abstract

Calculus of integer orders was once the basic essential mathematical tool for analysis, synthesis response behavior, theorems, and many novel applications for any dynamical system from 1695 until 1960. However, these integer values are a very narrow subset of the real orders, and so during the last five decades, a dramatic shift has taken place and many scientific researchers have been concerned instead with fractional calculus. In particular, these scientists have attempted to broaden the scope of fundamentals and theorems from integer order systems into fractional ones, since many achievements are obtained as a result of employing the extra fractional-order variables, allowing for more flexibility, freedom, best fit, and optimization techniques. Furthermore, many new fundamentals have been investigated only in the fractional order sense.

In recent years it has turned out that many phenomena in engineering, physics, chemistry, and other sciences can be described very successfully by models using mathematical tools from fractional calculus. To obtain better performance, in last few decades, several applications based on fractional order modeling in wide spread fields of science and engineering have been proposed. This includes fluid flow, optics, geology, behavior of viscoelastic material, bioscience, medicine, non-linear control, signal processing, etc.

In this dissertation Studies on analysis and applications of fractance device and fractional order operator is the main objective. Time and frequency domain analysis, different ways of realization of fractance device is presented. Active realization of fractance device of order s0.5 using continues fraction expansion is carried out. Later, a general expression for sα is presented using CFE method and time domain response of sα for different input signal and for different values of α is carried out. Further, time and frequency domain analysis of fractance based circuits is considered. The rational approximation of fractional order operator using different methods (Newton, Mastuda, Oustaloup and CFE method) is presented and compared with the ideal response. Later , fractional order filter is studied and performance of the fractional order filter is checked for different input signals (sine wave, trapezoidal wave, sawtooth wave and chirp signal) with random noise and the resulted output is compared with the integer order filter output. All simulation for fractance device , fractional order operator and fractional order filter has done in MATLAB software.