基于LQR性能和形状计算的最优执行器设计
Optimal actuator design for vibration control based on LQR performance and shape calculus
AI总结：
本文基于LQR性能和形状计算，研究了振动控制问题中执行器形状的优化设计，通过拓扑导数和水平集方法提出了一种抽象框架，用于解决无限维优化问题，并通过欧拉-伯努利梁模型进行了数值示例。
摘要：
针对振动控制问题，计算了最优执行器设计。根据所得到线性二次调节器（LQR）闭环性能和执行器尺寸的惩罚项，对执行器形状进行优化。通过形状计算和LQR性能指数的拓扑导数，找到最优执行器形状。提出了一种基于无限维优化理论的抽象框架，用于优化执行器形状和相关控制问题。通过水平集方法对执行器形状的最优性条件进行了数值实现。给出了一个示例，展示了针对欧拉-伯努利梁模型的执行器设计。
英文摘要：
Optimal actuator design for a vibration control problem is calculated. The actuator shape is optimized according to the closed-loop performance of the resulting linear-quadratic regulator and a penalty on the actuator size. The optimal actuator shape is found by means of shape calculus and a topological derivative of the linear-quadratic regulator (LQR) performance index. An abstract framework is proposed based on the theory for infinite-dimensional optimization of both the actuator shape and the associated control problem. A numerical realization of the optimality condition is presented for the actuator shape using a level-set method for topological derivatives. A Numerical example illustrating the design of actuator for Euler-Bernoulli beam model is provided.
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