Adaptive order and parameter estimation in fractional linear systems by approximate gradient and least squares methods* *M. Rapaic and Z.D. Jeličić acknowledge the financial support of Serbian Ministry of Science and Education, grants no. 32018 and 33013 A. Pisano has been supported by the Italian Ministry of University and Research (MIUR) under PRIN project “Non integer order systems in modeling and control”, grant no. 2009F4NZJP.

Web processing systems rely on accurate lateral positioning to achieve high processing speeds and improved product quality. Due to physical constraints in some processing lines placement of the edge sensor near the web guide is not possible. As a result, large lateral oscillation and/or web instability have been observed. A new model is developed for lateral web dynamics. Experimental verification has justified the structure of the model. A parameter estimation scheme is used to tune the model for imperfections not originally incorporated. State estimation is then used to predict lateral web position on a downstream sensor. Desirable control is achieved and is further improved with the use of the feedforward sensor. Predicted and experimental results are compared.

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Conceptual design of a selectable fractional-order differentiator for industrial applications

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0195-z ◽

2014 ◽

Vol 17 (3) ◽

Cited By ~ 30

Author(s):

Emmanuel Gonzalez ◽

Ľubomír Dorčák ◽

Concepción Monje ◽

Juraj Valsa ◽

Felicito Caluyo ◽

...

Keyword(s):

Conceptual Design ◽

Fractional Order ◽

Industrial Applications ◽

Modeling And Control ◽

Integer Order ◽

Research Areas ◽

Fractional Order Differentiator ◽

Main Components ◽

And Control ◽

Fractional Order Pid

AbstractIn the past decade, researchers working on fractional-order systems modeling and control have been considering working on the design and development of analog and digital fractional-order differentiators, i.e. circuits that can perform non-integer-order differentiation. It has been one of the major research areas under such field due to proven advantages over its integer-order counterparts. In particular, traditional integer-order proportional-integral-derivative (PID) controllers seem to be outperformed by fractional-order PID (FOPID or PIλDμ) controllers. Many researches have emerged presenting the possibility of designing analog and digital fractional-order differentiators, but only restricted to a fixed order. In this paper, we present the conceptual design of a variable fractional-order differentiator in which the order can be selected from 0 to 1 with an increment of 0.05. The analog conceptual design utilizes operational amplifiers and resistor-capacitor ladders as main components, while a generic microcontroller is introduced for switching purposes. Simulation results through Matlab and LTSpiceIV show that the designed resistor-capacitor ladders can perform as analog fractional-order differentiation.

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