Intelligent Fractional Order Systems and Control

2013 ◽  
Author(s):  
Indranil Pan ◽  
Saptarshi Das
Keyword(s):  
Fractional Order ◽  
Fractional Order Systems ◽  
Systems And Control ◽  
And Control

scholarly journals Stability of Fractional Order Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Margarita Rivero ◽  
Sergei V. Rogosin ◽  
José A. Tenreiro Machado ◽  
Juan J. Trujillo
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
State Of The Art ◽  
Point Of View ◽  
Fractional Order Systems ◽  
Short Period ◽  
Systems And Control ◽  
Different Types ◽  
The Stability ◽  
And Control

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Quantitative Analysis of Singularities for Fractional Order Systems

2015 ◽  
Author(s):  
Yan Li ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Intrinsic Property ◽  
Time Domain Analysis ◽  
Order System ◽  
Fractional Order Systems ◽  
Stability And Control ◽  
Practical Strategy ◽  
The Time Domain ◽  
And Control

The singularity is an intrinsic property for various fractional order systems. This paper focuses on the time domain analysis of typical “non-proper” fractional order transfer functions, which plays the crucial role in the implementation, stability and control of fractional order systems. To this end, the fractional order system is converted into a weak singularity integro-differential equation, where the non-proper property can be clearly presented. A practical strategy is shown to find out the poles in the first Riemann plane, which is especially applicable to small commensurate order problems. The distributed order and order sensitivity problems are discussed as well. A number of examples are illustrated by using some reliable fractional order numerical methods.

scholarly journals Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function

2007 ◽  
Vol 17 (4) ◽  
pp. 455-462 ◽  
Author(s):  
Abdelbaki Djouambi ◽  
Abdelfatah Charef ◽  
Alina Besançon
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Analog Circuit ◽  
Phase Error ◽  
Optimal Approximation ◽  
Fractional Systems ◽  
Systems And Control ◽  
And Control ◽  
Simple Analog ◽  
Irrational Transfer Function

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer FunctionThis paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.

scholarly journals Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems

2018 ◽  
Vol 21 (5) ◽  
pp. 1238-1261 ◽  
Author(s):  
Mikhail I. Gomoyunov
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Fractional Derivatives ◽  
Original System ◽  
Control Problems ◽  
Fractional Order Systems ◽  
Control Procedures ◽  
Fractional Differential ◽  
And Control ◽  
Derivatives Of

Abstract The paper is devoted to the development of control procedures with a guide for fractional order dynamical systems controlled under conditions of disturbances, uncertainties or counteractions. We consider a dynamical system which motion is described by ordinary fractional differential equations with the Caputo derivative of an order α ∈ (0, 1). For the case when the guide is, in a certain sense, a copy of the system, we propose a mutual aiming procedure between the original system and guide. The proof of proximity between motions of the systems is based on the estimate of the fractional derivative of the superposition of a convex Lyapunov function and a function represented by the fractional integral of an essentially bounded measurable function. This estimate can be considered as a generalization of the known estimates of such type. We give an example that illustrates the workability of the proposed control procedures with a guide.

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