Feedback control of systems with multiple time scales

结构振动和声波等系统的控制是具有挑战性的，因为存在无限数量的模式。即使控制器旨在影响较低的模式，控制信号以及干扰也可以影响较高的模式。如果没有正确处理高阶模式的影响，这可能会导致性能下降，有时甚至不稳定。用于控制系统（例如结构）的致动器和传感器的位置通常可以被选择，并且由于系统性能取决于这些位置，因此期望使用将控制器设计与致动器/传感器选择集成的机电一体化方法。 通常，在此步骤中必须使用近似值。不幸的是，并不是所有的数值方案或控制器设计方法产生一致的结果作为近似的阶数增加。 我计划开发算法，使用近似，如有限元设计控制系统的最佳执行器/传感器的位置。

The control of systems such as structural vibrations and sound waves is challenging due to the presence of an infinite number of modes. Even though the controller is intended to affect the lower modes, the control signal and also disturbances can affect higher modes. This can lead to a decrease in performance, and sometimes instability, if the effect of the higher modes is not handled correctly. The location of actuators and sensors for control systems such as structures can often be chosen and, because system performance depends on these locations, it is desirable to use a mechatronic approach that integrates controller design with actuator/sensor selection. Generally, an approximation must be used during this step. Unfortunately, not all numerical schemes or controller design methods yield consistent results as the order of the approximation is increased. I plan to develop algorithms that use approximations such as finite elements to design control systems with the best actuator/sensor locations.