Complex-order Reset Control System

Abstract

According to the well-known loop shaping method for the design of controllers, the performance of the controllers in terms of step response, steady-state disturbance rejection and noise attenuation and robustness can be improved by increasing the gain at lower frequencies and decreasing it at higher frequencies and increasing the phase margin as much as possible. However, the inherent properties of linear controllers, the Bode's phase-gain relation, create a limitation. In theory, a complexorder transfer function can break the Bode's gain-phase relation; however, such transfer function cannot be directly implemented and should be approximated. This paper proposes a reset element and a tuning method to approximate a Complex-Order Controller (CLOC) and, through a simulation example, shows the benefits of using such a controller.

An examination of complex fractional order physical phenomena in IOPD controller design

“…As the result, Equation (29) gives the gain of the plant's frequency response with integrator and Equation ( 30) gives the phase of the plant's frequency response with integrator.…”

“…In this direction, a systematic study of the generalized KdV-Burgers-Kuramoto equation using the symmetry method is presented in a previous study [23], a new (3 + 1)-dimensional KdV equation and MKdV equation with their corresponding fractional forms are presented in another study [24], and the modified Gardner type equation and its time fractional form is studied by Wang and Wazwaz [25]. Researchers are now investigating the use of complex order differ-integral operators in control theory and system modeling [26][27][28][29][30][31][32][33][34][35][36]. Although not exactly the same as this paper, there can be found studies in the literature aiming to provide frequency specifications.…”