Modelling and Control of a Hydraulically Actuated Shaking Table Employed for Vibration Absorber Testing

Abstract

This paper presents an activity concerning the modelling and control of an unidirectional electro-hydraulically actuated table adopted to test vibration isolators. The test rig consists of a hydraulic actuation system that drives a sliding table mounted on linear bearings. The system is characterized by nonlinearities such as valve dead zone and frictions. A nonlinear model is derived and then employed for parameters identification procedure. The results concerning the model validation are illustrated. They fully confirm the effectiveness of the proposed model able to capture the system behavior. The testing procedure of the isolation systems is based on the definition of a target displacement time history of the table and, consequently, the precision of the table positioning is of primary importance. In order to minimize the positioning error, a suitable control system has to be adopted. The system non-linearities limit highly the performances of the classical linear control, so a non-linear one is proposed. The sliding table mathematical model is employed for a non-linear control design able to minimize the error between the target position and the current one. The controller synthesis is made taking into account no isolator under test. The proposed approach consists in a non-linear optimal control based on the state-dependent Riccati equation (SDRE). Numerical simulations have been performed in order to evaluate the goodness of the designed control with and without the specimen under test. The results confirm that the performances of the proposed non-linear controller are not invalidated because of the presence of the specimen and highlight the controller robustness.