Switching Optimal Modal Control of Linear Time-Invariant Model of a Structural System

Dynamic response of a structural system in frequency domain can be calculated by summing the frequency response of dynamic sub-models. However depending on the frequency content of external disturbance, some dynamic sub-models might be more active; these dynamic sub-models can be identified by calculating the cost-to-go to return to the origin. These cost-to-go to return to the origin for each dynamic sub-model was calculated by solving Lyapunov equation. Then comparing these cost-to-go to return to the origin, a novel switching rule was designed to switch to the dynamic sub-model with the highest cost-to-go to return to the origin. This particular dynamic sub-model was regulated by the associated modal controller. Thus it has been shown that dynamic sub-model with the highest cost-to-go to return to the origin at any time can be controlled instead of controlling all modes of motion of the structural system and the consequence of this switching control concept is minor from the controller perspective.

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