A numerical algorithm for the optimal placement of actuators and sensors for flexible structures

The objective of this investigation is to present a methodology for obtaining the optimal location of actuators and sensors in systems which describe the dynamics of flexible structures. First an optimal state feedback gain, parametrized by the unknown actuator locations, is found by minimizing an appropriately chosen (control) performance index. Minimization of the optimal value of the quadratic cost is then performed with respect to (spatial) locations in order to obtain the optimal actuator location. The incorporation of partial measurements, which introduces the sensor location(s) into the control problem, achieves the sensor location in a similar fashion, namely by minimizing the optimal value of a dynamic compensator index with respect to locations. Numerical examples with simulation results are presented to support this investigation.