Research Into The Reduction Algorithm For Linear Time Invariant Fractional Order Dynamic System

Fractional calculus is an old field of mathematics. The fractional integral and differential operators are built on the traditional sense of calculus by considering the real physical meaning established. And the fractional order control systems are based on fractional calculus and fractional differential operator theory. As fractional differential equations can describe some realities more accurately, such as flexibility or memory systems, it has been attracted increasing attention in recent years, which force it to be a new research area of Control Theory and Control Engineering. However, owing to the inherent complexities of fractional calculus, which make itself but some mathematicians’interest, it is still difficult to get precision solutions of many fractional control systems in theory even in today’s improvements of computer skills, not to mention the practical applications. This is mainly because most fractional order systems is essentially infinite dimensional systems, and there are not yet some equipments that can deal with infinite dimensional systems effectively. Thus, model reduction of the original complex and difficult fractional order systems to some simplicity finite-dimensional system by mathematical methods has become a very meaningful work. But the simplified models must satisfy some restrictions and approximate the original model outputs.This article aims to study one of the simplest classes of fractional order control system, i.e. the linear time-invariant control system. This thesis is based on the similar theory of the previous investigations foundation and is from the view point of actual engineering. The main contents of the paper include:Firstly, realize the S-function of fractional integral and differential operator under the powerful software MATLAB/SIMULINK. It can then provide a convenient way to finish dynamic simulation.Second, extend the existing model reduction method i.e. Pade order reduction to fractional order control systems. Third, study the method of model approximation method by the continued fraction approximation method and the traditional Oustaloup approximation method.Fourth, make use of the optimization theory to finish the system reduction in fractional order systems. This making fractional order reduction algorithm has certain evaluation methods and established a basis for the development of model approximations.This paper also provides some examples and verifies the conclusions with MATLAB/SIMULINK...