Stabilization of a chaotic oscillator via a class of integral controllers under input saturation

Abstract

This work presents the straightforward design of an integral controller with an anti-windup structure to prevent undesirable behavior when actuator saturation is considered, and the proposed controller improves the performance of the closed-loop dynamics of a class of nonlinear oscillators. The proposed integral controller has an adaptive control gain, which includes the absolute value of the named control error to turn off the integral action when it is saturated. Closed-loop stability analysis is performed under the Lyapunov theory framework, where it can be concluded that the system behaves in an asymptotically stable way. The proposed methodology is successfully applied to a Rikitake-type oscillator, considering a single input-single output (SISO) structure for regulation and tracking trajectory purposes. For comparison, an equivalent fixed gain integral controller is also implemented to analyze the corresponding anti-windup properties of the proposed control structure. Numerical experiments are conducted, showing the superior performance of the proposed controller.

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

“…The objective of this work is to implement the above approach to achieve better control over the dynamics of microgrids during transients under different load conditions. Fractional error feedback, Error Function (ERF) feedback and Proportional Integral (PI) feedback have been extensively proven efficient in handling disturbances in a variety of systems with various applications (Alotaibi et al 2021;Howard et al 2022;Aguilar-López et al 2013). The efficiency of different configurations of delayed modes such as fractional error, ERF and PI forms of feedback in overcoming the effect of transient events and thereby achieving efficient control are investigated.…”