Integrated design of system parameters, control and sensor/actuator placement for symmetric mechanical systems

In this paper, we address the problem of integrated design of output feedback control, structural damping parameters, and sensor/actuator placement to satisfy an upper bound on the closed-loop H^¿ or H² norm performance of externally symmetric systems. By combining results on the upper bound of the closed-loop norm for externally symmetric systems with a homotopy-like approximation of an optimization problem, we provide a formulation of the integrated design problem of minimizing the upper bound H^¿ or H² norm via iterative LMI optimization problems. In this formulation, the corresponding decision variables are the structural damping parameters, the static rate feedback gain, and the sensor and actuator locations. By iteratively solving the approximated LMI problem, a locally optimal solution is obtained. The method is validated on a numerical example of active collocated vibration control of a simply supported beam.