The CRONE Control of Resonant Plants: Application to a Flexible Transmission

Oustaloup, Alain; Benoit, M.; Lanusse, Patrick

doi:10.1016/s0947-3580(95)70014-0

Cited by 378 publications

(179 citation statements)

References 3 publications

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“…1), [7,11]. However, by limiting the frequency range of application for the CPE, one can design a module composed of a finite number of components such as a finite ladder by truncating the CFE [22] that can approximately work as a CPE for the specific range of interest, and eventually become a practically-acceptable FOD [20,21] for various applications.…”

Section: Theory and Realization Of Fractional-order Elementsmentioning

confidence: 99%

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

Gonzalez¹,

Dorčák

Monje

et al. 2014

Fract Calc Appl Anal

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In 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 PI λ D μ ) 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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Section: Theory and Realization Of Fractional-order Elementsmentioning

confidence: 99%

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

Gonzalez¹,

Dorčák

Monje

et al. 2014

Fract Calc Appl Anal

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show abstract

“…However, in the recent years, emergence of effective methods in differentiation and integration of non-integer order equations makes fractional-order systems more and more attractive for the A New Approach to Design Smith Predictor Based Fractional Order Controllers Khosro Khandani and Ali Akbar Jalali systems control community. The TID controller [10], the CRONE controllers [11], [12] and [13] and the fractional lead-lag compensator [14] and [15] are some of the well-known fractional-order controllers. In some of these papers it is verified that the fractional-order controllers can have better disturbance rejection ratios and less sensitivity to plant parameter variations compared to the traditional controllers [16].…”

Section: Fractional Calculus and Fractional Controlmentioning

confidence: 99%

A New Approach to Design Smith Predictor Based Fractional Order Controllers

Khandani¹,

Jalali²

2010

IJCEE

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I. INTRODUCTIONDead times, or time delays, are found in many processes in industry. Dead times are mainly caused by the time required to transport mass, energy or information, but they can also be caused by processing time or by the accumulation of time lags in a number of simple dynamic systems connected in series [1]. Compared to processes without delays, the presence of a delay in the process greatly complicates the analytical aspects of the control system design, making it more difficult to achieve a satisfactory level of control [2]. Time-delay has been a common phenomenon to overcome whenever we close a feedback loop for the purpose of controlling any system. Recent increase of control applications in the variety gives more importance to systematic methods to cope with time delay. In order to compensate the negative effects of time delay, a well-known and highly effective dead-time compensator for stable processes is Smith predictor [3]. In this predictor scheme, a mathematical model of the process is implemented in an internal feedback loop around a conventional controller. The distinctive scheme was proposed by O.J.M.Smith approximately 50 years ago, and is still attracting much attention for its usefulness. The major advantage of the Smith predictor is that delay issues can be ignored when designing the controller.Fractional-order dynamic systems and controllers, which are based on fractional-order calculus have been gaining attention in several research communities since the last few years [4]. A few recent works in this direction as well as

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“…This is mainly due to the fact that many real-world physical systems are better characterized by fractionalorder state equations [22], i.e., equations involving the so-called fractional derivatives and integrals. On the other hand, with the success in the synthesis of real noninteger differentiator and the emergence of new electrical circuit element called "fractance" [17], [31], fractional-order controllers [20], [23], [25], [32] have been designed and applied to control a variety of dynamical processes, including integer-order and fractional-order systems, so as to enhance the robustness and performance of the control systems.…”

Section: Introductionmentioning

confidence: 99%

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

Chen

2013

fcaa

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This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.MSC 2010 : Primary 26A33; Secondary 34A08, 34D10, 93C73, 93D09, 93D21

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The CRONE Control of Resonant Plants: Application to a Flexible Transmission

Cited by 378 publications

References 3 publications

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

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

A New Approach to Design Smith Predictor Based Fractional Order Controllers

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

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