Optimal switching policy of smart actuators in flexible structures

The dynamics of intelligent actuators utilized in vibration control of flexible structures may exhibit nonlinear behavior under extreme environments and/or prolonged/repeated usage. When transitions to nonlinearities are not accounted for in the controller design, they might compromise controller performance and even destabilize the very system they are designed to control. A novel approach that addresses the issue of actuator nonlinearities is presented here. Specifically, the actuators considered are those that at some initial period exhibit linear behavior and enter a nonlinear regime thereafter. The method studied here only utilizes these actuators while on their linear behavior by proposing an optimal activation sequence of these actuators. At a given time interval of fixed length, only a single actuator is activated while the remaining ones are kept dormant. The reason is to ensure that at each time instance. a single actuator with linear dynamics is active. When the active actuator is about to become nonlinear, then the algorithm switches to and activates the next available actuator in an optimal fashion. The optimality of switching is with respect to the minimal cost of an associated LQR performance index that corresponds to each actuator. In the proposed algorithm, a control logic is incorporated that only selects the next actuator to be activated from the set of the remaining actuators that are considered healthy(linear); an example of this would be SMA actuators that had enough time to cool down and thus when activated again can exhibit linear dynamics.