Higher-Order Sinusoidal-Input Describing Function Analysis of Fractional-Order Hybrid Integrator-Gain Systems
S.A. Hosseini (TU Delft - Mechatronic Systems Design)
L.F. van Eijk (TU Delft - Mechatronic Systems Design)
M.B. Kaczmarek (TU Delft - Mechatronic Systems Design)
S. Hassan HosseinNia (TU Delft - Mechatronic Systems Design)
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Abstract
In this paper, the higher-order sinusoidal-input describing function (HOSIDF) of the fractional-order hybrid integrator-gain system (HIGS) is derived analytically. The HIGS element, designed as a nonlinear component, aims to overcome limitations inherent in linear control, such as the waterbed effect. The HIGS element has been generalized by replacing the integer-order integrator with a fractional one. Here, a modified version of the fractional-order HIGS (FO-HIGS) is introduced with the aim of shaping the nonlinearity at low frequencies. Additionally, this paper demonstrates that obtaining an analytical solution for the HOSIDF of the FO-HIGS enables us to gain better insight into the tuning of the control architecture.
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