Topic
Differentiator
About: Differentiator is a research topic. Over the lifetime, 3973 publications have been published within this topic receiving 45176 citations.
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TL;DR: In this paper, an order of the maximal differentiation error to the square root of the maximum deviation of the measured input signal from the base signal from Lipschitz's constant of the derivative was proposed.
1,958 citations
TL;DR: In this article, the state-of-the-art on generalized (or any order) derivatives in physics and engineering sciences is outlined for justifying the interest of the noninteger differentiation.
Abstract: The state-of-the-art on generalized (or any order) derivatives in physics and engineering sciences, is outlined for justifying the interest of the noninteger differentiation. The problems subsequent to its use in real-time operations are then set out so as to motivate the idea of synthesizing it by a recursive distribution of zeros and poles. An analysis of the existing work is also proposed to support this idea. A comprehensive study is given of the synthesis of differentiators with integer, noninteger, real or complex orders, and whose action is limited to any given frequency bandwidth. First, a definition, in the operational and frequency domains, of a frequency-band complex noninteger order differentiator, is given in a mathematical space with four dimensions which is a Banach algebra. Then, the determination of its synthesized form, by a recursive distribution of complex zeros and poles characterized by complex recursive factors, is presented. The complex noninteger differentiation order is expressed as a function of these recursive factors. The number of zeros and poles is calculated to be as low as possible while still ensuring the stability of the synthesized differentiator to be synthesized. A time validation is presented. Finally, guidelines are proposed for the conception of the synthesized differentiator.
1,361 citations
TL;DR: It is shown that a general uncertain single-input-single-output regulation problem is solvable only by means of discontinuous control laws, giving rise to the so-called high-order sliding modes, and homogeneity features significantly simplify the design and investigation of a new family of high- order sliding-mode controllers.
822 citations
TL;DR: A recently developed robust exact differentiator being applied, robust output-feedback controllers with finite-time convergence are produced, capable to control any general uncertain single-input-single-output process with relative degree 2.
760 citations
TL;DR: In this paper, a class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, is presented.
Abstract: The effective application of sliding mode control to mechanical systems is not straightforward because of the sensitivity of these systems to chattering. Higher-order sliding modes can counteract this phenomenon by confining the switching control to the higher derivatives of the mechanical control variable, so that the latter results are continuous. Generally, this approach requires the availability of a number of time derivatives of the sliding variable, and, in the presence of noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, could be helpful both in reducing the number of differentiator stages in the controller and in dealing with unmodelled actuator dynamics. In this paper different second-order sliding mode controllers, previously presented in the literature, are shown to belong to the above cited class, and some cha...
648 citations