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首页> 外文期刊>IEEE Transactions on Automatic Control >Reduced-order model feedback control design: numerical implementation in a thin shell model
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Reduced-order model feedback control design: numerical implementation in a thin shell model

机译：降阶模型反馈控制设计：薄壳模型中的数值实现

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摘要

Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (POD) reduced-basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actuators. Donnell-Mushtari equations, modified to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full-order model. Reduced-basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances. Numerical examples illustrating the features of the reduced-basis methods are presented. As a first step toward investigating the behavior of the methods when implemented in physical systems, the use of reduced-order model feedback control gains in the full order model is considered and numerical examples are presented.
机译：提出了降阶模型，该降阶模型在系统的数值逼近和反馈控制中采用了拉格朗日方法和流行的适当正交分解（POD）降基方法，并进行了数值测试。所考虑的系统是带有表面安装压电陶瓷驱动器的薄圆柱壳。修改为包括Kelvin-Voigt阻尼的Donnell-Mushtari方程用于对系统动力学进行建模。由三次样条张量的傅立叶多项式构造的基函数用于全阶模型的Galerkin展开。然后，根据在不同时间获取的外生受激壳的全阶近似值，形成降基元素。给出了说明减基法方法特点的数值例子。作为研究方法在物理系统中实现时行为的第一步，考虑了在全阶模型中使用降阶模型反馈控制增益，并给出了数值示例。

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