Behavior and robustness study of fractional controllers based on RLC cells

In this article, we will study the behavior of the RLC cells for the four configurations that we have presented in [1]. We will propose an electric circuit that will be used to study the fractional behavior and robustness of these RLC operators and compare their responses to the behavior of the fractance which is an ideal fractional operator [2]. This analysis will be studied for both natural and forced responses. In more details, we will neglect the initial conditions of the capacitors and inductances in the first case and we will take them into consideration in the second one. The number of initial conditions will be related to the number of RLC cells used. For example, if we are using 10 RLC cells, we will have 21 initial conditions (as we have 11 conductors and 10 inductances). Also, the robustness of all arrangements will be analyzed when varying the unsteady parameter value of the same system used to study the fractional behavior. The non-steady parameter will be represented by an inductance in the electrical circuit. This inductance represents a different variable parameter in each field of application. For example, in the hydropneumatic domain, this inductance refers to the mass of the vehicle as the mass has the main influence on the speed and robustness when using the suspension. A conclusion will sum up the results for all four arrangements and show that the phase constancy and robustness are preset for both modes.