In this paper, a fuzzy disturbance observer and a high-gain disturbance observer based on a variable structure controller are applied to deal with imprecise multi-shaft with web materials linkage systems taking into account the variation of the moment of inertia. Specifically, a high-gain disturbance observer and an adaptive fuzzy algorithm are separately applied to estimate system uncertainties and external disturbances. The high-gain disturbance observer is designed with auxiliary variables to avoid the amplification of the measurement disturbance, and the fuzzy disturbance observer has the advantage that it does not depend on model information. The convergence properties of the tracking error are analytically proven using Lyapunov’s theory. The obtained numerical results demonstrate the validity and the adaptive performance of the proposed control law in case the system is exposed to uncertainties and disturbances. Important remarks on the design process and performance benchmarks of the two observers are also demonstrated.
Nonlinear characteristics of fused silica, solid-core photonic crystal fibers (PCFs) with a square array of air holes are studied numerically. We present a novel design that emphasizes the difference in air hole diameters in the photonic cladding. These PCFs have the advantages of flat dispersion, high nonlinearity, and low attenuation. Based on simulation results, three optimal structures, denoted #F1, #F2, and #F3, having anomalous and all-normal dispersions in the near-infrared range are selected to investigate characteristic properties at the pump wavelength. Such PCFs open up many possibilities for nonlinear optical applications, especially supercontinuum generation.
Due to the nonlinearities and dynamical properties of multisection web machines, it is essential to accomplish an appropriate mathematical model as well as design a compatible control scheme. A generalized fully driven web winding model is constructed taking unpredictable changes of moment of inertia and radius of rolls into consideration. In this article, a fractional‐order sliding surface algorithm‐based hierarchical control frame is applied to multisection web machines to deal with matched and mismatched uncertainties and disturbances. In addition, the Radius Basis Function neural network is deployed to estimate necessary system dynamics and the proposed control scheme taking advantage of first‐order low‐pass filters to produce virtual control signals without complicated calculation and attenuate the explosion of terms phenomenon. Finally, the semi‐global stability of the entire system is determined using Lyapunov's stability theory. The simulation results are presented to clarify the superior performance of robust control algorithm and approximation law in the presence of nonideal elements.
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