Stabilization of a Timoshenko Beam With Disturbance Observer‐Based Time Varying Boundary Controls

Abstract

This paper is concerned with the boundary feedback stabilization for a Timoshenko beam with external disturbances in the boundary inputs. Based on the idea of active disturbance rejection controls, extended state observers with the time‐varying gains are designed to estimate disturbances and then a control strategy is presented by canceling the disturbances via the feedback channels. The well‐posedness of the resulting closed‐loop system is proved by the dual theory and admissibility theory, and the relationship between the stability and the disturbance is interpreted by Lyapunov's second method. At the end, the numerical experiment illustrate the effectiveness of the proposed control strategy.

A Non-Local Non-Homogeneous Fractional Timoshenko System with Frictional and Viscoelastic Damping Terms

“…On the other hand, it is known that the geological environment and surrounding (geological medium) with properties of a fractal nature can be described in terms of fractional calculus [21] by fractional-order equations with parameters, depending on the fractal dimension of the geomedium. For some other fractional-and integer-order Timoshenko systems, the reader can refer to [22][23][24][25][26][27]. For some other fractional and integer order Timoshenko systems, the reader can refer to [28][29][30][31][32][33][34][35].…”

On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms

“…The Timoshenko system has found broad applications in various engineering disciplines, such as civil, mechanical, and aerospace engineering, due to its ability to more accurately represent the physical behavior of elastic structures compared to classical models like the Euler-Bernoulli beam Equation (see [2][3][4][5][6][7]).…”

New results on the robust stability of control systems with a generalized disturbance observer

“…Over the past several decades, disturbance rejection control has been one of the major issues in control engineering because of the growing demand for high performance [1][2][3]. Several methods such as adaptive feedforward control, [4] output regulation via the internal model principle, [5] and disturbance observer (DOB)-based control, [6,7] have been proposed to achieve high precision control in the presence of various plant uncertainties and disturbances. [8] DOB, which is proposed in, [9] is a robust control tool used to estimate external disturbance, plant uncertainties, and even plant fault.…”