A Global Control Strategy for Efficient Control of a Braille Impact Hammer

Abstract

A combined control scheme relying on feedback-based local control in the vicinity of periodic system responses and global control based on a coarse-grained approximation to the nonlinear dynamics is developed to achieve a desirable dynamical behavior of a Braille printer impact hammer. The proposed control methodology introduces discrete changes in the position of a system discontinuity at opportune moments during the hammer motion while the hammer is away from the discontinuity, thereby exploiting the recurrent contacts with the discontinuity to achieve the desired changes in the transient dynamics. It is argued that, as the changes in the position of the discontinuity affect the motion only indirectly through changes in the timing and state at the subsequent contact, the control actuation can be applied over an interval of time during the free-flight motion as long as it is completed prior to contact. A forced, piecewise smooth, single-degree-of-freedom model of a Braille impact hammer is used to illustrate the methodology and to yield representative numerical results.