Vibration Reduction in a Flexible-Link Mechanism through Synthesis of an Optimal Controller

In this paper reduction of vibration of a flexible planar mechanism is achieved through synthesis of an optimal controller. A finite element model based on the equivalent rigid-link system theory is used to accurately describe the dynamic behavior of the system. The model which accounts for geometric and inertial nonlinearities of the mechanism has been fully validated through experimental tests. In order to be able to employ the classical optimal control theory a suitable linear model has been derived from the original one by means of a suitable linearization procedure. Vibration reduction can then be obtained by first defining an adequate performance index which accounts for vibration amplitude then by solving Riccati's equation in order to find the controller that minimizes the performance index i.e. the optimal controller. The results of several tests that have been carried out are also reported to show the effectiveness of the synthesized control system.