Pham Phuong-Tung, Nguyen Quoc Chi, Yoon Mahnjung, Hong Keum-Shik
Department of Mechatronics, Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology (HCMUT), VNU-HCM, Ho Chi Minh City, Vietnam.
School of Mechanical Engineering, Pusan National University, Busan, 46241, South Korea.
Sci Rep. 2022 Aug 15;12(1):13811. doi: 10.1038/s41598-022-16973-y.
This paper addresses a control problem of a nonlinear cantilever beam with translating base in the three-dimensional space, wherein the coupled nonlinear dynamics of the transverse, lateral, and longitudinal vibrations of the beam and the base's motions are considered. The control scheme employs two control inputs applied to the beam's base to control the base's position while simultaneously suppressing the beam's transverse, lateral, and longitudinal vibrations. According to the Hamilton principle, a hybrid model describing the nonlinear coupling dynamics of the beam and the base is established: This model consists of three partial differential equations representing the beam's dynamics and two ordinary differential equations representing the base's dynamics. Subsequently, the control laws are designed to move the base to the desired position and attenuate the beam's vibrations in all three directions. The asymptotic stability of the closed-loop system is proven via the Lyapunov method. Finally, the effectiveness of the designed control scheme is illustrated via the simulation results.
本文研究了三维空间中具有平移基座的非线性悬臂梁的控制问题，其中考虑了梁的横向、侧向和纵向振动以及基座运动的耦合非线性动力学。控制方案采用施加到梁基座的两个控制输入来控制基座的位置，同时抑制梁的横向、侧向和纵向振动。根据哈密顿原理，建立了一个描述梁和基座非线性耦合动力学的混合模型：该模型由表示梁动力学的三个偏微分方程和表示基座动力学的两个常微分方程组成。随后，设计控制律以使基座移动到期望位置并衰减梁在所有三个方向上的振动。通过李雅普诺夫方法证明了闭环系统的渐近稳定性。最后，通过仿真结果说明了所设计控制方案的有效性。
