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该文研究了多变量刚柔耦合的机械臂操作柔性负载系统的镇定问题。系统动态特性由偏微分方程表示的分布参数模型描述,避免了集中参数模型导致的溢出问题。基于柔性负载的能量动态分析和正实引理,利用Lyapunov函数提出了一种动态反馈控制方法。控制器由补偿控制和动态反馈两部分构成,其中动态反馈部分的传递函数是严格正实的。通过线性算子半群理论和LaSalle不变集原理,证明了闭环系统在期望位置邻域内的渐近稳定性。
In this paper, we study the stabilization problem of manipulative flexible load system with multi-variable rigid-flexible coupling. The system dynamics is described by the distributed parameter model represented by partial differential equations, avoiding the problem of spillover caused by the centralized parameter model. Based on dynamic analysis of energy and positive real leveraging of flexible loads, a dynamic feedback control method based on Lyapunov function is proposed. The controller consists of compensation control and dynamic feedback. The transfer function of the dynamic feedback part is strictly positive. The asymptotic stability of the closed-loop system in the neighborhood of the expected position is proved by the linear operator semigroup theory and the LaSalle invariant set principle.