Feedback control of flexible four-bar linkages: a numerical and experimental investigation

Abstract

A control scheme for a four-bar linkage with all the links flexible is proposed and tested both numerically and experimentally. The control strategy consists in selecting a reduced number of measurable variables through which performing position and vibration are controlled independently. The controlled variables are the crank angle and the link curvatures, which provide an adequate description of the temporal evolution of the mechanism position and vibrational phenomena. Position control is performed through a proportional integral and differential (PID)-like regulator while proportional controllers are employed to damp the fundamental components of the link oscillations. A force of gravity compensator is introduced to increase the control system performances and appropriate devices are proposed to avoid coupling effects among the controlled variables. The control scheme is first tested and tuned in simulation, where the dynamic behaviour of the flexible linkage is reproduced through a fully coupled non-linear model based on the finite element theory. The performances of the control scheme are assessed by studying the step response of the closed-loop system. The numerical results attained prove that the proposed control scheme achieves efficient positioning and vibration suppression performances. The experimental validation of the control scheme is carried out on an instrumented prototype of the flexible four-bar linkage. Experimental recordings are in good agreement with the numerical results therefore confirming both the effectiveness of the control scheme and the accuracy of the dynamic model.