Topic
Transfer function
About: Transfer function is a research topic. Over the lifetime, 14362 publications have been published within this topic receiving 214983 citations. The topic is also known as: system function & network function.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the fundamentals of fractional derivatives and integrals with arbitrary real or complex orders, fractional transfer functions and their approximations, identification of fractionAL transfer function models from experimental data, first-and second-generation Crone controller, and fractional proportional-integral-derivative (PID) control.
Abstract: This is a tutorial study to introduce fractional control to a reader with a background in control theory. Fractional controllers are those making use of fractional-order derivatives and integrals, and have been receiving increased attention over the last few years because of the robust performance (in the face of plant gain variations and even plant uncertainties in general) they can achieve. The study covers the fundamentals of the theory of derivatives and integrals with arbitrary real or complex orders, fractional transfer functions and their approximations, identification of fractional transfer function models from experimental data, first- and second-generation Crone controller, fractional proportional-integral-derivative (PID) control and third-generation Crone control.
128 citations
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TL;DR: The global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints.
128 citations
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TL;DR: In this article, the authors investigated the usefulness of the Bode diagram in calculus including classical and fractional derivatives and proved that fractional derivative with continous kernel are best to model real world problems, as they do not inforce a nonsingular model to become singular due to the singularity of the kernel.
Abstract: The paper is devoted to investigate three different points including the importance, usefulness of the Bode diagram in calculus including classical and fractional on one hand. On the other hand to answer and disprove the statements made about fractional derivatives with continuous kernels. And finally to show researchers what we see and we do not see in a commutative world. To achieve this, we considered first the Caputo–Fabrizio derivative and used its Laplace transform to obtain a transfer function. We represented the Bode, Nichols, and the Nyquist diagrams of the corresponding transfer function. We in order to assess the effect of exponential decay filter used in Caputo–Fabrizio derivative, compare the transfer function associate to the Laplace transform of the classical derivative and that of Caputo–Fabrizio, we obtained surprisingly a great revelation, the Caputo–Fabrizio kernel provide better information than first derivative according to the diagram. In this case, we concluded that, it was not appropriate to study the Bode diagram of transfer function of Caputo–Fabrizio derivative rather, it is mathematically and practically correct to see the effect of the kernel on the first derivative as it is well-established mathematical operators. The Caputo–Fabrizio kernel Bode diagram shows that, the kernel is low past filter which is very good in signal point of view. We consider the Mittag–Leffler kernel and its corresponding Laplace transform and find out that due to the fractional order, the corresponding transfer function does not exist therefore the Bode diagram cannot be presented as there is no so far a mathematical formula that help to find transfer function of such nature. It is therefore an opened problem, how can we construct exactly a transfer function with the following term ( i w ) α ( i w ) α + b for instance? We proved that fractional derivative with continous kernel are best to model real world problems, as they do not inforce a non-singular model to become singular due to the singularity of the kernel. We show that, by considering initial time to be slightly above the origin then the Riemann–Liouville and Caputo-power derivatives are fractional derivatives with continuous kernel. We considered some interesting chaotic models and presented their numerical solutions in different ways to show what we see or do not see if a commutative world. To end, we presented the terms to be followed to provide a new fractional derivative.
128 citations
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TL;DR: The analysis results show that the nonlinearity parameter plays a crucial role in the system performance and has higher control efficiency than the linear ADRC but reduces the stability margin of the system.
Abstract: Active disturbance rejection control (ADRC) is a new design concept that shows promising power in dealing with the uncertainties of control systems. However, most of the previous work has been numerical time-domain development and frequency-domain analysis for the linear framework. This paper focuses on the frequency-domain analysis of the nonlinear ADRC behavior using the describing function method and characterizes the effect of the ${\rm fal}$ nonlinearity parameter on the performance of the closed-loop system. Both the describing function of the nonlinearity and the transfer function description of the system's linear portion are derived. The stability, dynamic stiffness, and tracking performance are analyzed for a second-order single-input single-output plant. The analysis results show that the nonlinearity parameter plays a crucial role in the system performance. The nonlinear ADRC has higher control efficiency than the linear ADRC but reduces the stability margin of the system. Using the fast tool servo case, simulations and hardware experiments are conducted, and the results further support the analysis.
127 citations
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TL;DR: In this paper, the problem of the derivation of simple transfer function models from high-order state variable models is reviewed, and methods of reduction are classified according to whether they involve 1) the computation of the time or frequency responses, 2) the derivations, as an intermediate step, of a transfer function which is the ratio of two polynomials, the denominator being of the same order as the state variable model, or 3) a set of characterising functions.
127 citations