Response of a Helix Made of a Fractional Viscoelastic Material

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
M. Ostoja-Starzewski ◽  
H. Shahsavari
Keyword(s):  
Fractional Order ◽  
Viscoelastic Material ◽  
Order Model ◽  
Effective Response ◽  
Integer Order ◽  
Torsional Response ◽  
Fractional Order Model ◽  
Higher Derivatives ◽  
Better Than ◽  
Helical Strand

Under investigation is the effective response of a helical strand (helix) made of a viscoelastic material governed by a constitutive relation with fractional-order (i.e., not integer-order) derivatives. The relation involves a 5-parameter model, which is well known to represent a real response much better than the conventional, integer-order models with the same number of parameters. We employ the correspondence principle of viscoelasticity to pass from the level of the strand’s material to that of an effective, coupled axial-torsional response of the helix. The resulting fractional-order differential equation is more complex (i.e., it involves higher derivatives) than the constitutive equation governing the material per se. Also, the use of a fractional-order model results in more complexity of the helix’ effective viscoelastic response than does an integer-order model with the same number of parameters. It is shown that shear deformations are more important than dilatational deformations. Lastly, a standard relaxation test is studied and an analytic solution is derived.

Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation

2019 ◽  
Vol 22 (2) ◽  
pp. 424-443 ◽  
Author(s):  
Wojciech Przemysław Hunek
Keyword(s):  
Fractional Order ◽  
Control Algorithm ◽  
Mimo System ◽  
Practical Implementation ◽  
Space Systems ◽  
Order Model ◽  
Integer Order ◽  
Fractional Order Model ◽  
State Space Systems ◽  
Systems Simulation

Abstract A new perfect control algorithm dedicated to fractional-order right-invertible systems, i.e. plants with a greater number of input than output variables, is presented in this paper. It is shown that such a control strategy can be particularly applied with regard to practical tasks. Henceforth, the Grünwald-Letnikov difference operator Δα of an assumed order α can be truncated without loss of generality. For that reason, the so-called pole-free perfect control formula can be used to minimize the essential drawback of the Grünwald-Letnikov approach engaged, so as to define the intriguing issue regarding the robust perfect control for non-integer-order right-invertible LTI discrete-time state-space systems. Simulation examples show that the presented method can compete with a classical stable-pole one, for which the actual systems described by a fractional-order model often correspond with an inconvenient asymptotic perfect control solution given by the unlimited original operator Δα. In the end, the possibility of employing of author’s nonunique right inverses dedicated to nonsquare MIMO system matrices is demonstrated, thus giving rise to the introduction of a new powerful tool for robustification of non-integer-order closed-loop perfect control plants as well.

Consensus of compound-order multi-agent systems with communication delays

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Hong-yong Yang ◽  
Lei Guo ◽  
Xun-lin Zhu ◽  
Ke-cai Cao ◽  
Hai-lin Zou
Keyword(s):  
Fractional Order ◽  
Networked Systems ◽  
Multi Agent Systems ◽  
Complex Environments ◽  
Order Model ◽  
Agent Systems ◽  
Integer Order ◽  
Fractional Order Model ◽  
Multi Agent ◽  
Special Case

AbstractIn complex environments, many distributed networked systems can only be illustrated with fractional-order dynamics. When multi-agent systems show individual diversity with difference agents, heterogeneous (integer-order and fractional-order) dynamics are used to illustrate the agent systems and compose integerfractional compounded-order systems. Applying Laplace transform and frequency domain theory of the fractional-order operator, the consensus of delayed multi-agent systems with directed weighted topologies is studied. Since an integer-order model is the special case of a fractional-order model, the results in this paper can be extended to systems with integer-order models. Finally, numerical examples are used to verify our results.

scholarly journals Fractional-order mathematical model of an irrigation main canal pool

2015 ◽  
Vol 13 (3) ◽  
pp. e0212 ◽  
Author(s):  
Shlomi N. Calderon-Valdez ◽  
Vicente Feliu-Batlle ◽  
Raul Rivas-Perez
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fractional Order ◽  
Order Model ◽  
Integer Order ◽  
Direct System ◽  
Fractional Order Model ◽  
Main Canal ◽  
Laboratory Prototype ◽  
Hydraulic Processes

<p>In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (<em>ISE</em>) performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.</p>

Fractional Order Model Identification for a Billet Unloading Robotic Arm

2016 ◽  
Vol 841 ◽  
pp. 234-239 ◽  
Author(s):  
Iulia Clitan ◽  
Vlad Mureşan ◽  
Andrei Florin Clitan ◽  
Mihail Abrudean
Keyword(s):  
Experimental Data ◽  
Fractional Order ◽  
Model Identification ◽  
Step Response ◽  
Robotic Arm ◽  
Positioning System ◽  
Order Model ◽  
Integer Order ◽  
Fractional Order Model ◽  
The Mean

This paper presents a fractional model identification for a billet unloading robotic arm’s positioning system. First, an integer order model is obtained using a graphical identification method based on a set of experimental data. The experimental data represents the robotic arm’s position, measured using an encoder, at a constant billet displacement. The integer order model was obtained based on the overall performances of the measured robotic arm’s step response. The mean square error between the measured data and the model step response is high, thus, in order to decrease the error and to obtain a more accurate model, a fractional order model is determined using an iterative procedure.

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