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首页> 外文期刊>Proceedings of the institution of mechanical engineers >Dynamic modeling and nonlinear boundary control of hybrid Euler-Bernoulli beam system with a tip mass
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Dynamic modeling and nonlinear boundary control of hybrid Euler-Bernoulli beam system with a tip mass

机译：具有尖端质量的混合Euler-Bernoulli梁系统的动力学建模和非线性边界控制

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摘要

This paper presents dynamic modeling and Lyapunov-based boundary control of a hybrid Euler-Bernoulli beam. The beam is hybrid in the sense that it holds both rigid and elastic motions. The beam is equipped with actuators hub at one end and it carries the payload as the tip mass at the free end. The distributed parameter dynamic equations (i.e. partial differential equations governing the hybrid beam motion) are derived using Hamilton's principle. The dynamic model consists of four distributed parameter dynamic equations, representing the beam vibration and rigid motion in the plane, coupled to the discrete dynamic boundary equations. This paper uses the system equations to achieve model-based control laws that asymptotically stabilize the beam vibration while driving the rigid body position and orientation to the desired set point. The control system applies three forces/torque at the hub to regulate the rigid body position/orientation and a transverse force at the free end to suppress the beam vibration. In this regard, the control system only applies actuation and makes measurement at the beam boundary, thus excluding the need for distributed actuators or sensors. Furthermore, the proposed method directly uses the system equations for the control design without model truncation to rule out spillover instabilities. The closed-loop system stability is shown through Lyapunov-based analysis. Numerical simulations demonstrate the effectiveness of the proposed method.
机译：本文提出了一种混合的Euler-Bernoulli光束的动力学建模和基于Lyapunov的边界控制。从既保持刚性运动又保持弹性运动的角度来看，梁是混合的。横梁的一端装有执行器轮毂，其自由端承载有效载荷作为尖端质量。使用汉密尔顿原理导出分布参数动力学方程式（即控制混合梁运动的偏微分方程式）。动力学模型由四个分布参数动力学方程组成，代表了梁在平面内的振动和刚性运动，并与离散的动力学边界方程耦合。本文使用系统方程式来实现基于模型的控制定律，该定律在将刚体的位置和方向驱动到所需的设定点时渐近稳定梁的振动。控制系统在轮毂上施加三个力/扭矩以调节刚体的位置/方向，并在自由端施加横向力以抑制梁的振动。在这方面，控制系统仅施加致动并在光束边界处进行测量，因此不需要分布式致动器或传感器。此外，所提出的方法直接将系统方程式用于控制设计，而无需模型截断以排除溢出不稳定性。通过基于Lyapunov的分析显示了闭环系统的稳定性。数值模拟证明了该方法的有效性。

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