Adaptive self-organizing fuzzy sliding mode controller for a nonlocal strain gradient nanobeam

Abstract

In this investigation, an adaptive self-organizing fuzzy sliding mode controller (ASFSC) has been developed for vibration control of an Euler-Bernoulli nanobeam with immoveable ends, imposed by a centralized external force. Considering the mid-plane stretching effect, the governing ordinary differential equation (ODE) of the considered nanobeam is derived based on nonlocal strain gradient theory and using Galerkin projection. In order to overcome the problem of choosing inappropriate parameters in the self-organizing part, a self-organizing fuzzy sliding mode controller is constructed to modify the parameters. Another fuzzy controller is designed and has the role of imposing controller output to regulate the system response. The sliding surface and its changes are determined as the controller signal inputs for obtaining a better performance. An adaptive law is used to validate the stability and improve the system's performance by modifying the fuzzy controller coefficients and reducing the chattering phenomena and overcoming the issue of dead-zone. Furthermore, Lyapunov stability proof is presented, and the numerical simulations are the showcase of the superior performance of the proposed controller.