Integer order approximation of fractional order systems

2010 ◽  
Author(s):  
M Mine Ozyetkin ◽  
Nusret Tan
Keyword(s):  
Fractional Order ◽  
Order Approximation ◽  
Fractional Order Systems ◽  
Integer Order

The multi-model approach for fractional-order systems modelling

2016 ◽  
Vol 40 (1) ◽  
pp. 331-340 ◽  
Author(s):  
Samia Talmoudi ◽  
Moufida Lahmari
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Global Model ◽  
Fractional Order Systems ◽  
New Approach ◽  
Physical Systems ◽  
Integer Order ◽  
Systems Modelling ◽  
Model Approach

Currently, fractional-order systems are attracting the attention of many researchers because they present a better representation of many physical systems in several areas, compared with integer-order models. This article contains two main contributions. In the first one, we suggest a new approach to fractional-order systems modelling. This model is represented by an explicit transfer function based on the multi-model approach. In the second contribution, a new method of computation of the validity of library models, according to the frequency [Formula: see text], is exposed. Finally, a global model is obtained by fusion of library models weighted by their respective validities. Illustrative examples are presented to show the advantages and the quality of the proposed strategy.

Model Predictive Control of General Fractional Order Systems Using a General Purpose Optimal Control Problem Solver: RIOTS

2019 ◽  
Author(s):  
Sina Dehghan ◽  
Tiebiao Zhao ◽  
YangQuan Chen ◽  
Taymaz Homayouni
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Fractional Order ◽  
Predictive Control ◽  
Order System ◽  
Problem Solver ◽  
Fractional Order Systems ◽  
Application Process ◽  
Order Model ◽  
Integer Order

Abstract RIOTS is a Matlab toolbox capable of solving a very general form of integer order optimal control problems. In this paper, we present an approach for implementing Model Predictive Control (MPC) to control a general form of fractional order systems using RIOTS toolbox. This approach is based on time-response-invariant approximation of fractional order system with an integer order model to be used as the internal model in MPC. The implementation of this approach is demonstrated to control a coupled MIMO commensurate fractional order model. Moreover, the performance and its application process is compared to examples reported in the literature.

scholarly journals Fractional Dynamics of Computer Virus Propagation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Carla M. A. Pinto ◽  
J. A. Tenreiro Machado
Keyword(s):  
Steady State ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Initial Conditions ◽  
Computer Virus ◽  
Fractional Dynamics ◽  
Fractional Order Systems ◽  
Virus Propagation ◽  
Integer Order ◽  
Fast Transients

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Global Stabilization for a class of nonlinear fractional-order systems

2019 ◽  
Vol 10 (01) ◽  
pp. 1941009 ◽  
Author(s):  
Taide Liu ◽  
Feng Wang ◽  
Wanchun Lu ◽  
Xuhuan Wang
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Global Stabilization ◽  
Fractional Order Systems ◽  
Closed Loop System ◽  
Integer Order ◽  
Backstepping Algorithm

The problem of Mittag–Leffler stabilization (MLS) is studied for a class of nonlinear non-integer order systems. The stabilizer is constructed by using the Lyapunov function and backstepping algorithm. The continuous controller is designed to ensure that the state of the nonlinear fractional-order closed-loop system converges to the equilibrium. Two simulation examples are given to illustrate the effectiveness of the method.

An Integer-Order Transfer Function Estimation Algorithm for Fractional-Order PID Controllers

2020 ◽  
Vol 11 (3) ◽  
pp. 133-150
Author(s):  
Kishore Bingi ◽  
Rosdiazli Ibrahim ◽  
Mohd Noh Karsiti ◽  
Sabo Miya Hassan ◽  
Vivekananda Rajah Harindran
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Curve Fitting ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
Fractional Order Systems ◽  
Function Estimation ◽  
Frequency Range ◽  
Integer Order ◽  
Fractional Order Differentiator

Fractional-order systems and controllers have been extensively used in many control applications to achieve robust modeling and controlling performance. To implement these systems, curve fitting based integer-order transfer function estimation techniques namely Oustaloup and Matsuda are most widely used. However, these methods are failed to achieve the best approximation due to the limitation of the desired frequency range. Thus, this article presents a simple curve fitting based integer-order transfer function estimation method for fractional-order differentiator/integrator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Using the approach, an approximation table for fractional-order differentiator has also been obtained which can be used directly to obtain the approximation of fractional-order systems. A simulation study on fractional systems shows that the proposed approach produced better parameter approximation for the desired frequency as compared to Oustaloup, refined Oustaloup and Matsuda techniques.

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