Linear fractional order controllers; A survey in the frequency domain (original) (raw)
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Fractional order (FO) differentiation is a generalization of classical integer differentiation to real or complex orders. The origin of this concept dates back to the early days of classical differential calculus, although its inherent complexity postponed its use and application to the engineering world. In the last decades, the developments in computing technologies combined with the unique advantages of FO differ-integrals in modeling complex phenomena, have led to ongoing research interest towards using fractional calculus (FC) as an optimal tool to describe the dynamics of complex systems. Apart from this, FC is currently gaining more and more popularity in the engineering community. Nowadays, the adoption of FC in control engineering has been gaining more and more momentum, both in modeling, identification, and controller design. The aim of this special issue is to promote further development of FC in control engineering, stability analysis of FO systems, solutions for fractional order continuous-time linear systems, signal processing, approximations for fractional B Cristina I. Muresan
International Journal of Engineering and Technology
In this paper, a new comparative approach has been proposed for reliable controller design. Scientists and engineers are often confronted with the analysis, design, and synthesis of real-life problems. The first step in such studies is the development of a 'mathematical model' which can be considered as a substitute for the real problem. The mathematical model is used here as a plant. Fractional integrals and derivatives have found wide application in the control of dynamical systems when the controlled system and the controller are described by a set of fractional order differential equations. Here the stability of fractional order system is checked at the different level and it is found that the stability region is large in the complex plane. This large stability region provides the more flexibility for system implementation in the control engineering. Generally, an analytically or experimentally approaches are used for designing the controller. If a fractional order controller design approach used for a given plant then the controlled parameter gives the better result.
Time and Frequency Domain Analysis of the Linear Fractional-order Systems
International Journal of Advanced Computer Science and Applications, 2012
Recent years have seen a tremendous upsurge in the area related to the use of Fractional-order (FO) differential equations in modeling and control. FO differential equations are found to provide a more realistic, faithful, and compact representations of many real world, natural and manmade systems. FO controllers, on the other hand, have been able to achieve a better closed-loop performance and robustness, than their integer-order counterparts. In this paper, we provide a systematic and rigorous time and frequency domain analysis of linear FO systems. Various concepts like stability, step response, frequency response are discussed in detail for a variety of linear FO systems. We also give the state space representations for these systems and comment on the controllability and observability. The exercise presented here conveys the fact that the time and frequency domain analysis of FO linear systems are very similar to that of the integer-order linear systems.
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www.ijacsa.thesai.org Time and Frequency Domain Analysis of the Linear Fractional-order Systems
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— Recent years have seen a tremendous upsurge in the area related to the use of Fractional-order (FO) differential equations in modeling and control. FO differential equations are found to provide a more realistic, faithful, and compact representations of many real world, natural and man-made systems. FO controllers, on the other hand, have been able to achieve a better closed-loop performance and robustness, than their integer-order counterparts. In this paper, we provide a systematic and rigorous time and frequency domain analysis of linear FO systems. Various concepts like stability, step response, frequency response are discussed in detail for a variety of linear FO systems. We also give the state space representations for these systems and comment on the controllability and observability. The exercise presented here conveys the fact that the time and frequency domain analysis of FO linear systems are very similar to that of the integer-order linear systems. Keywords- Fractional...
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Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.