The effects of linear-quadratic index and controllability criterion on actuator placement of cantilever beam vibrating systems

This paper considers the problem of actuator placement for a smart cantilever beam using two different placement indices, namely the controllability criterion and the linear-quadratic index. The relationship between linear-quadratic index and controllability criterion is investigated by theoretical analysis and numerical simulations. It is proved in theory that the larger the controllability criterion is, the smaller the linear-quadratic index is. It is observed from the simulation results that there is a good agreement between the results obtained using the two placement indices for actuator placement on a smart cantilever beam. In addition, both theoretical analysis and numerical simulations results show that the better control performance can be achieved with the increase of controllability criterion.