Based on the exit temperature in the aluminium extrusion process, the quality of the aluminium bars is obtained in the industries. Control of temperature plays a significant role to obtain the quality of the aluminium...
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Based on the exit temperature in the aluminium extrusion process, the quality of the aluminium bars is obtained in the industries. Control of temperature plays a significant role to obtain the quality of the aluminium bars or rods. Problems are still encountered in the design of proper temperature control schemes in the industries. A new control scheme is presented here, to address the temperature control in the aluminium extrusion process. spider-based fractional-order PID controller scheme is simulated for the aluminium extrusion plant using MATLAB and its toolbox. It gives the improved result for reducing the time delay, rise time and settling time in the process. Integral square error performance criteria are considered an objective function. The minimization of objective function gives good results. Comparisons of the presented control scheme with the conventional control methods are presented.
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values (i.e., either asymptotic or critical values) escape on disjoint rays. The constructio...
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We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values (i.e., either asymptotic or critical values) escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional Teichm & uuml;ller space, analogously to classical Thurston's Topological Characterization of Rational Functions, but for an infinite set of marked points. We concentrate on the case when different escaping singular orbits do not come arbitrarily close to each other-this allows to avoid excessive technicality of constructions (almost with no restriction of generality). As in the proof of Thurston's Characterization theorem, we define a map o- acting on a specially chosen Teichm & uuml;ller space and look for fixed points of o- . But unlike in the classical theorem, the Teichm & uuml;ller space is no longer finite-dimensional, which leads to a completely different approach. The core of this article is the construction of a compact o--invariant subset in the Teichm & uuml;ller space. Then from strict contraction of o- on this subspace follows the existence of a fixed point of o- . (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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