Recursive surface structure for fixed-time convergence with applications to power systems

In this study, a novel idea is proposed for fixed-time recursive surface structure design for arbitrary-order system. The stability of controller design methodology is verified by using Lyapunov analysis. The primary benefit behind formulating the proposed surface structure is in achieving fixed-time convergence during sliding. Moreover, the control structure is designed to get fixed-time convergence during reaching as well. The approximate convergence time has been calculated mathematically and is verified using simulations. The sliding mode control is formulated for single-input-single-output non-linear dynamical systems. The proposed control scheme is robust and the singularity is avoided. The conditions to ensure stability during reaching phase are derived and are shown to depend only on the design of surface parameters. The detailed simulation results of a general third-order dynamic system show the efficacy of the proposed scheme. Finally, the proposed method is implemented for automatic generation control (AGC) of a multi-area interconnected power system while considering the non-linearity in the dynamic system. For the first time, fixed-time convergence is assured for AGC. To the best of the authors' knowledge, no such structure is proposed yet for AGC. The results are also compared with the traditional proportional-integral controller.