Narrow Results

We study the principle of least (stationary) action for mem-elements. The least action principle allows us to derive relationships between the electrical variables for each of the six mem-elements. The principle of least action from modern physics is a natural environment to characterize mem-elements, including various one-period loops in the context of periodic circuits. The time-integrals of Lagrangian lead to the action and coaction quantities and a full characterization of mem-elements with periodic control variables.

In this paper, Lagrangian-based method has been proposed for tuning the parameters of fractional order $P{I}^{\alpha }{D}^{\beta }$ controller. In this method, the five parameters ($K_p$, $K_i$, $K_d$, $\alpha$ and $\beta$) of fractional order $P{I}^{\alpha }{D}^{\beta }$ controller (FOPID) are suitably optimized, and successfully applied to a benchmark stable second-order feedback system. To prove the performance of the proposed method, several state-of-the-art approaches were compared. The computational complexity, robustness and stability analysis has been performed to investigate the performance of all these algorithms. Moreover, the precision and flexibility analysis among all these approaches has also been carried out in this paper. The closed loop response of the second-order bench mark stable plant in Simulink has also been depicted in this paper.