臂架起重机的建模与控制
Modelling and Control of a Knuckle Boom Crane
摘要：
起重机有各种尺寸和设计来执行不同的任务。根据它们的动态特性，它们可以分为龙门起重机和旋转起重机。在本文中，我们将集中在所谓的“折臂”起重机，这是最常见的类型的旋转起重机。与其他类型的起重机（如动臂起重机、塔式起重机、桥式起重机等）相比，铰接起重机的研究仍处于早期阶段，文献中提出的此类起重机的控制策略很少。虽然机械上相当简单，但从控制的角度来看，关节式起重机存在几个挑战。本文的第一个结果是第一次提出了一个完整的数学模型，这种起重机，它可以控制起重机的三个旋转（称为俯仰，回转和悬臂运动），和电缆长度。该模型的唯一简化假设是将缆索视为刚性。在此模型的基础上，我们提出了一个非线性控制律的基础上，能源的考虑，这是能够执行的起重机的位置控制，同时积极阻尼负载的振荡。相应的稳定性和收敛性分析仔细证明使用LaSalle的不变性原理。所提出的控制方法的有效性已在仿真中与现实的物理参数和模型失配的存在下进行了测试。
英文摘要：
Cranes come in various sizes and designs to perform different tasks. Depending on their dynamic properties, they can be classified as gantry cranes and rotary cranes. In this paper we will focus on the so called 'knuckle boom' cranes which are among the most common types of rotary cranes. Compared with the other kinds of cranes (e.g. boom cranes, tower cranes, overhead cranes, etc), the study of knuckle cranes is still at an early stage and very few control strategies for this kind of crane have been proposed in the literature. Although fairly simple mechanically, from the control viewpoint the knuckle cranes present several challenges. A first result of this paper is to present for the first time a complete mathematical model for this kind of crane where it is possible to control the three rotations of the crane (known as luff, slew, and jib movement), and the cable length. The only simplifying assumption of the model is that the cable is considered rigid. On the basis of this model, we propose a nonlinear control law based on energy considerations which is able to perform position control of the crane while actively damping the oscillations of the load. The corresponding stability and convergence analysis is carefully proved using the LaSalle's invariance principle. The effectiveness of the proposed control approach has been tested in simulation with realistic physical parameters and in the presence of model mismatch.
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