Simultaneous path-following and vibration control for uncertain nonlinear flexible mechanical systems without dependency on oscillatory mathematical model

Abstract

In this paper, a novel multiobjective algorithm for simultaneous path-following control (PFC) of multivariable flexible dynamical systems and maintaining boundedness of transverse vibrational effects is proposed. This method is specifically designed for control of complicated dynamical systems where obtaining precise mathematical models describing vibrational and translational dynamics is difficult or unattainable. To facilitate the control task, the proposed scheme is constructed such that it would be capable of stabilizing the closed-loop system solely using a rigid approximation of system dynamics while considering vibrational effects as unstructured uncertainties. This permits the designer to forgo the troublesome task of precisely modeling and numerically analyzing the flexible vibrational system, prioritizing important path-following and closed-loop stability characteristics. The proposed control algorithm incorporates a discrete sliding mode control (DSMC) scheme constructed on the basis of calculation of input bounds. This method does not introduce additional chattering effects as generation of control inputs is not directly dependent on switching functions. Unstructured uncertainties are estimated using one-step approximation technique which removes the need for employing difficult techniques used in the existing literature. The control algorithm is constructed in two distinct modes, the first of which considers appropriate path following as its objective. The second control mode halts the tracking task unless an assigned cost function resides in an acceptable interval, resulting in gradual reduction of intensity of vibrational effects. The control algorithm is numerically simulated in ANSYS® Mechanical APDL environment. The obtained results express the accuracy and efficiency of the control algorithm despite the use of considerably simpler procedure in comparison with existing works.