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，因为存在着无限多的模式。即使控制器的目的是影响较低的模式，控制信号和干扰也会影响较高的模式。如果没有正确处理较高模式的影响，这可能会导致性能下降，有时还会导致不稳定。结构等控制系统的执行器和传感器的位置通常是可以选择的，由于系统性能取决于这些位置，因此需要使用将控制器设计与执行器/传感器选择相结合的机电一体化方法。通常，在此步骤中必须使用近似值。不幸的是，随着近似阶数的增加，并不是所有的数值格式或控制器设计方法都能产生一致的结果。我计划开发一种算法，使用有限元等近似方法来设计具有最佳执行器/传感器位置的控制系统。

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.