Adaptive boundary control for flexible three‐dimensional Euler‐Bernoulli beam with input signal quantization

Abstract

SummaryThis paper proposes an adaptive boundary control scheme for the flexible three‐dimensional Euler‐Bernoulli beam with input signal quantization. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the flexible system are represented by partial differential equations and ordinary differential equations. Input signals in modern control systems are often quantized before being transmitted through communication channels in technology engineering. Logarithmic quantitative controllers are designed to suppress the vibration of the beam. It is proved that the proposed control scheme can be guaranteed in handling the vibration of the beam and input signal quantization simultaneously. Finally, numerical simulations illustrate the effectiveness of the results.

Active boundary control of vibrating marine riser with constrained input in three-dimensional space

“…In this article, we consider the input saturation which is widespread in actual industrial field. The input saturation function is described as follows [27]:…”

Event-triggered boundary quantization control for flexible manipulator based on partial differential equations dynamic model

“…Remarkable achievements have been made in quantization control for nonlinear systems. An adaptive boundary control scheme for a flexible three-dimensional Euler-Bernoulli beam with input signal quantization is designed to suppress the vibration of the beam (Ji and Liu, 2018). A decentralized output-feedback adaptive control scheme is proposed for a class of interconnected nonlinear systems with input quantization to guarantee global stability of the overall closed-loop system regardless of the coarseness of the quantizers and the existence of interactions among subsystems (Wang et al, 2017).…”

Quantization control for flexible manipulators with PDE model

“…Compared with the single‐link flexible system with horizontal motion, previous quantization control studies in previous studies [21–24] based on nonlinear system models markedly differ from the distributed parameter system established by PDEs. Previous researchers have also studied distributed parameter systems in effort to eliminate deformation in Yun et al [19] but have not realized joint angle tracking with input signal quantization.…”

“…The objective of a quantization control scheme is to ensure the stability of the system and to satisfy the necessary control accuracy with at the lowest possible communication rate. Through quantization, control, and communication are combined to solve the signal transmission problem via information technology, in Ji and Liu [21], an adaptive boundary control scheme for a flexible 3-D Euler-Bernoulli beam with input signal quantization is designed to suppress the vibration of the beam. In Wang and Lin [22], logarithmic quantizers are applied in double inverted pendulums to improve hysteresis for nonlinear systems in an attempt to improve quantization effects.…”