Feedback control of systems with multiple time scales

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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.