Control of a flexible beam actuated by macro-fiber composite patches: I. Modeling and feedforward trajectory control
Control of a flexible beam actuated by macro-fiber composite patches: I. Modeling and feedforward trajectory control
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DOI：
10.1088/0964-1726/20/1/015015
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发表时间：
2011-01-01
影响因子：
4.1
通讯作者：
Kugi, Andreas
中科院分区：
文献类型：
--
作者：
Schroeck, Johannes;Meurer, Thomas;Kugi, Andreas
本文研究了由压电宏纤维复合材料（MFC）贴片驱动的柔性悬臂梁的运动规划和前馈控制设计的系统方法。为了实现精确的前馈跟踪控制，必须特别注意这些执行器固有的非线性滞后和蠕变行为。为了考虑这些影响，应用了适当的补偿器，使我们能够在线性无限维模型的基础上执行跟踪控制器设计。对非线性执行器行为以及补偿器设计和整体实验验证的详细分析在配套论文（Schrock et al . 2011 Smart Mater）中提出。Struct. 20015016)。利用扩展的哈密顿原理确定了滞回补偿悬臂梁和蠕变补偿悬臂梁的运动控制方程。这使我们能够以一种直接的方式考虑贴片驱动器对底层梁结构力学性能的影响，并得到一个具有空间变化系统参数的模型。针对运动规划和前馈控制问题，提出了一种基于平面度的方法。第一步，用有限维模型近似mfc驱动的柔性悬臂的无限维系统，其中所有系统变量，即状态、输入和输出，都可以用所谓的平坦输出参数化。第二步，数值模拟表明，这些参数化随着有限维模型的系统阶数的增加而收敛，从而可以直接计算前馈控制输入以实现规定的输出轨迹。
This paper considers a systematic approach for motion planning and feedforward control design for a flexible cantilever actuated by piezoelectric macro-fiber composite (MFC) patches. For accurate feedforward tracking control, special attention has to be paid to the inherent nonlinear hysteresis and creep behavior of these actuators. In order to account for these effects an appropriate compensator is applied which allows us to perform the tracking controller design on the basis of a linear infinite-dimensional model. A detailed analysis of the nonlinear actuator behavior as well as the compensator design and the overall experimental validation is presented in the companion paper (Schrock et al 2011 Smart Mater. Struct. 20 015016). The governing equations of motion of the hysteresis and creep compensated cantilever are determined by means of the extended Hamilton's principle. This allows us to consider the influence of the bonded patch actuators on the mechanical properties of the underlying beam structure in a straightforward manner and results in a model with spatially varying system parameters. For the solution of the motion planning and feedforward control problem a flatness-based methodology is proposed. In a first step, the infinite-dimensional system of the MFC-actuated flexible cantilever is approximated by a finite-dimensional model, where all system variables, i.e. the states, input and output, can be parameterized in terms of a so-called flat output. In a second step, it is shown by numerical simulations that these parameterizations converge with increasing system order of the finite-dimensional model such that the feedforward control input can be directly calculated in order to realize prescribed output trajectories.