Optimization of oscillation damping modes of spatial double pendulum. II. Solving the problem and analyzing the results

Abstract

This paper is a continuation of the article «Optimization of oscillation damping modes of spatial double pendulum. I. Formulation of the problem», in which the problem formulation of the optimal oscillations damping of double pendulum with joint axes not collinear to each other was given. Passive damping (viscous friction) is considered separately, and the possibility of additional accounting of active impacts (collinear control) is also discussed. Two optimization criteria are adopted that characterize the efficiency of the damping processes of system movements: first, the degree of stability is maximized, and then the integral energy-time criterion is minimized. The optimal values of the parameters of the considered damping options are determined according to both criteria in the course of the exact solution of the problem within the framework of a linear model. The obtained results are presented in the form of visual graphic illustrations which allow to establish their main qualitative and quantitative features. The conclusions can be useful in studying the movements of manipulators and various robotic structures.

Keywords:

spatial double pendulum, viscous friction, collinear control, optimization criterion, degree of stability, energy-time criterion