An Efficient Recursive Approach for Analysis of Rational and Irrational Control Systems

For reducing mathematical complexity in the solution of real-life systems, additional assumptions like zero initial condition, integer order system, etc. result in inaccurate modeling of systems, leading to erroneous estimation. This paper presents a complete recursive method for solving irrational systems considering nonzero initial values. Generalized operational integration matrices based on orthogonal HF have been utilized to solve the differential equations describing a fractional order system. The orthogonal HF set is effective in producing piecewise linear solutions of various sorts of control systems when it is used with function samples. A few illustrative instances are provided to confirm the effectiveness of the technique.

I. Introduction

For over three centuries, factional calculus [1], [2] was seen as an interesting field of study, because of its wide applications in several scientific and technical domains, like as chemical processes [3], electromagnetism [4], thermal engineering [5], macro-economic [6], solid mechanics [7], continuum and statistical mechanics [8], electrical and electronic engineering [9], biomedical engineering [10] and in many more domain. Dynamics of the real-life physical systems can accurately be described with the help of fractional calculus, which is the most generalized form of traditional calculus. So, we need one efficient mathematical tool that can convert those describing equations into a simpler form (say, algebraic equation), and will help to build an easier and quick responding algorithm.