Flatness‐based deformation control of an Euler–Bernoulli beam with in‐domain actuation

Abstract

This paper addresses the problem of deformation control of an Euler-Bernoulli beam with in-domain actuation. The proposed control scheme consists in first relating the system model described by an inhomogeneous partial differential equation to a target system under a standard boundary control form. Then, a combination of closed-loop feedback control and flatness-based motion planning is used for stabilizing the closed-loop system around reference trajectories. The validity of the proposed method is assessed through well-posedness and stability analysis of the considered systems. The performance of the developed control scheme is demonstrated through numerical simulations of a representative micro-beam.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

“…With above advantages, the boundary control has been successfully applied in the drilling riser 19 and flexible wing. 20 As every coin has two sides, the accuracy and rapidity may not satisfy some requirements of specific situation 21 especially for the small bending stiffness of materials.…”

“…The aim of this work is to design a hybrid temporal-spatial differential controller, which is derived by applying Lyapunov’s direct method and linear matrix inequality (LMI) technology. Compared with the existing results, this paper has potentially achieved the following contributions: a) The proposed control design approach is based on the original Euler-Bernoulli beam model, which can overcome the deficiency of discretized system, 24,25,27 such as, nonlinear truncation order and spillover problem; b) In contrast to the distributed controller design results, 21,26 this paper presents a hybrid control strategy which is involved the spatial cooperation performance of actuators; c) Different with the boundary controller derived by LMI technology, 28–30 the hybrid controller can guarantee the stabilization of Euler-Bernoulli beam with in-domain and boundary actuators.…”

Stabilization of a wave equation with a distributed control

“…Many systems can be described by partial differential equations (PDEs) in engineering fields, and stabilizing these systems is an important and basic problem; therefore, in control theory field, the research of stabilization is very popular and basic, and there are many methods involved in, for example, backstepping method [1], spectral methods [2], linear quadratic regulator (LQR) approach [3], multiplier technique [4], and Lyapunov function method [5]. Among these methods, the backstepping method is a high efficient tool in designing controller for boundary controls of various types PDEs (see previous studies [6][7][8][9][10][11][12][13][14][15] and the references therein), because this method is easy to understand and it does not need the advanced mathematical tools; therefore, it is very useful in designing the stabilization controller of system.…”

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

“…Consequently, many studies have been conducted to study the vibration behaviour of micro/nanobeams [31][32][33][34][35]. Furthermore, the analysis of vibration control is used to prevent the micro/ nanobeams from damage and improve the performance and resolution of beams [36][37][38][39]. However, the measured dimensions of nanobeams may not be exact; therefore, the estimation analysis and robust controllers are useful to enhance the accuracy.…”