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Content available Application of Newton's Method to Analog and Digital Realization of Fractional-order Controllers
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Tepljakov A. , Petlenkov E. , Belikov J.
International Journal of Microelectronics and Computer Science
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2012
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tom Vol. 3, nr 2
45-52
EN
In this paper, a method for approximating a first-order implicit fractional transfer function, that corresponds to a frequency-bounded fractional differentiator or integrator, is presented. The proposed method is based on a modification of the well-known Newton's method for iterative root approximation. First-order implicit fractional transfer functions have several applications in modeling and control. This type of transfer function is the basis for the fractional lead-lag compensator. In the following, we provide the description of our algorithm, that enhances the existing technique, and illustrate its use in analog and digital implementations of fractional-order systems and controllers with relevant examples and comments.
2
Content available remote Fractional-order digital filter approximation method for embedded control applications
100%
Tepljakov A. , Petlenkov E. , Belikov J.
International Journal of Microelectronics and Computer Science
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2014
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tom Vol. 5, nr 2
54--60
EN
Fractional-order calculus presents a novel modeling approach for systems with extraordinary dynamical properties by introducing the notions of derivatives and integrals of noninteger order. In system theory this gives rise to extensions to linear, time invariant systems to enhance the description of complex phenomena involving memory or hereditary properties of systems. Standard industrial controllers, such as the PID controller and lead-lag compensator, have also been updated to benefit from the effects of noninteger integration and differentiation, and have advantages over classical controllers in case of both conventional and fractional-order process control. However, given the definitions of fractional operators, accurate digital implementation of fractional-order systems and controllers is difficult because it requires infinite memory. In this work we study the specific implementation of a fractional-order PID controller and fractional-order lead-lag compensator based on an infinite impulse response (IIR) filter structure obtained by applying the Oustaloup recursive filter synthesis technique. Software for generating digital fractional-order is developed and tested on an Atmel AVR microcontroller. The results are verified using a MATLAB/Simulink based real-time prototyping platform.
3
Content available FOMCOM: a MATLAB toolbox for fractional-order system identification and control
100%
Tepljakov A. , Petlenkov E. , Belikov J.
International Journal of Microelectronics and Computer Science
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2011
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tom Vol. 2, nr 2
51-62
EN
FOMCON is a new fractional-order modeling and control toolbox for MATLAB. It offers a set of tools for researchers in the field of fractional-order control. In this paper, we present an overview of the toolbox, motivation for its development and relation to other toolboxes devoted to fractional calculus. We discuss all of the major modules of the FOMCON toolbox as well as relevant mathematical concepts. Three modules are presented. The main module is used for fractional-order system analysis. The identification module allows identifying a fractional system from either time or frequency domain data. The control module focuses on fractional-order FID controller design, tuning and optimization, but also has basic support for design of fractional lead-lag compensators and TID controllers. Finally, a Simulink blockset is presented. It allows more sophisticated modeling tasks to be carried out.
4
Content available Tuning and digital implementation of a fractional-order PD controller for a position servo
100%
Tepljakov A. , Petlenkov E. , Belikov J. , Astapov S.
International Journal of Microelectronics and Computer Science
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2013
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tom Vol. 4, nr 3
116--123
EN
Fractional-order calculus offers flexible computational possibilities that can be applied to control design thereby improving industrial control loop performance. However, before theoretical results can be carried over to an industrial setting it is important to study the effects of fractional-order control by means of laboratory experiments. In this paper, we study the practical aspects of tuning and implementing a fractional-order PD controller for position control of a laboratory modular servo system using FOMCON (“Fractional-order Modeling and Control”) toolbox for MATLAB. We provide an overview of the tools used to model, analyze, and design the control system. The procedure of tuning and implementation of a suitable digital fractional-order controller is described. The results of the real-time experiments confirm the effectiveness of used methods.
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