Vibrational control of mechanical systems with piecewise linear damping and high-frequency inputs

Abstract

This paper discusses averaging and vibrational control of mechanical control-affine systems with piecewise linear damping and high-frequency inputs. The results are used for dynamic analysis and vibrational control of a three-degree-of-freedom, planar, horizontal pendulum. The system has non-symmetric, linear viscous damping, and the pivot point of the pendulum moves along a prescribed elliptical path with “high” frequency. The dynamic analysis shows that the presence of non-symmetric damping results in change of periodic orbits or equilibria of the system or instability of an otherwise stable system. This paper presents the stability conditions of the system in terms of the physical parameters of the pendulum and the prescribed path. Using the results of dynamic analysis, the paper also discusses vibrational control of the system of horizontal pendulum. The analysis can be extended to mechanical control systems with nonlinear viscous forces, dry friction, or inviscid flow forces.