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.

本文提出了一种新的多目标算法，用于多变量柔性动力系统的同时路径跟随控制（PFC）并保持横向振动效应的有界性。此方法是专门为控制复杂的动力学系统而设计的，在该系统中，很难或无法获得描述振动和平移动力学的精确数学模型。为了简化控制任务，建议的方案应构造为仅使用系统动力学的刚性近似值就能将闭环系统稳定，同时将振动影响视为非结构性不确定性。这使设计人员可以放弃繁琐的任务，即对柔性振动系统进行精确建模和数值分析，优先考虑重要的路径跟随和闭环稳定性特征。所提出的控制算法结合了基于输入边界的计算而构建的离散滑模控制（DSMC）方案。由于控制输入的生成不直接取决于开关功能，因此该方法不会产生额外的抖动效果。非结构性不确定性是使用一步近似技术估算的，这消除了使用现有文献中使用的困难技术的需要。控制算法以两种不同的模式构造，第一种以适当的路径跟随为目标。除非分配的成本函数停留在可接受的时间间隔内，否则第二种控制模式将停止跟踪任务，从而逐渐降低振动效果的强度。^®机械APDL环境。尽管与现有工作相比使用了相当简单的过程，但所获得的结果仍表明了控制算法的准确性和效率。