Stability analysis of a discrete-time limit cycle model predictive controller

Abstract

Recently, a novel discrete-time nonlinear limit cycle model predictive controller for harmonic compensation has been proposed. Its compensating action is achieved by using the dynamics of a supercritical Neimark-Sacker bifurcation normal form at the core of its cost function. This work aims to extend this approach's applicability by analyzing its stability. This is accomplished by identifying the normal form's region of attraction and final set, which enables the use of LaSalle's invariance principle. These results are then extended to the proposed controller under ideal conditions, i.e., zero-cost solutions with predictable disturbances. For nonideal scenarios, i.e., solutions with unpredictable disturbances and cost restrictions, conditions are developed to ensure that the closed-loop system remains inside the normal form's region of attraction. These findings are tested under nonideal conditions in a power systems application example. The results show successful power quality compensation and a satisfactory resilient behavior of the closed loop within the margins developed during this work.