Design of vibration controllers for flexible beams using the Mechatronic Design Quotient (MDQ) approach

When using linear dampers for the suppression of vibration in flexible structures, their mounting locations and the damping coefficients have to be chosen properly. In this article, an approach to the optimal design of linear dampers for vibration control in flexible beams based on the mechatronic design quotient (MDQ) is presented. This approach strives to make the optimal concurrent design of the dampers come as close as possible to the performance of an optimal sequential design of uncoupled subsystems. The MDQ approach provides a practical way to evaluate the performance of multi-criteria design. It also provides an insight into the performance degradation of various subsystems caused by dynamic coupling effects in the overall system. In the approach developed here, a cost function, based on the modal settling times, is first established from the design objective. Next, the optimal performance indices from the sequential and concurrent designs are obtained by selecting the coefficients and locations of the vibration dampers. These performance indices are used to determine the design corresponding to the highest MDQ value, which gives the overall optimal design. For performance evaluation, optimal design of active vibration controllers is carried out, using the linear quadratic regulator (LQR), and its MDQ value is established. The results from two case studies show that optimal linear dampers designed using the MDQ approach can achieve the performance of an optimal active controller. This approach can also provide an insight into the performance degradation in each subsystem (or sub-problem) due to the dynamic coupling effects in the overall system.