Boundary and Distributed Control for a Nonlinear Three‐Dimensional Euler‐Bernoulli Beam Based On Infinite Dimensional Disturbance Observer

Abstract

Control problems in spatially distributed systems are challenging because the disturbance is of infinite dimensions. To this end, this paper discusses an infinite dimensional disturbance observer design, which is illustrated based on a partial differential equation (PDE) model of a nonlinear three-dimensional Euler-Bernoulli beam. The basic idea of the observer design is to modify the estimations based on the difference between the estimated output and actual output. Moreover, an auxiliary parameter system is established to help with the analysis. Then a Lyapunov function candidate consisting of the energy of the system, the observer error and an auxiliary term is given. After a series of analyses of the function, distributed controllers and boundary controllers based on the proposed observer are given to restrain vibration. Finally, by numerical simulations, the convergence of the observer is demonstrated, and the efficacy of control performance is also shown.

Vibration control for a flexible satellite with adaptive actuator fault-tolerant and input quantization

“…In Liu et al (2018b), a backstepping method is used for an Euler–Bernoulli beam subject to bounded input, bounded output, and external disturbances. In Jiang et al (2016), an infinite dimensional disturbance observer is designed of a nonlinear three-dimensional Euler-Bernoulli beam which is based on a PDEs model. In Ji et al (2018), a vibration control scheme is designed for a nonlinear three-dimensional Euler–Bernoulli beam under input magnitude and rate constraints.…”

Adaptive fault‐tolerant control for a nonlinear flexible aircraft wing system

“…The PDE dynamic model of the flexible aircraft wing system consists of several PDEs and ODEs. Due to the actuator and sensor limitations, boundary control is a preferred control method in various flexible structure systems [13][14][15][16][17][18][19][20]. In addition, boundary control is easier to be implemented in practical engineering applications.…”