Integrating an Input Shaper with a Quantitative-Feedback-TheoryBased Controller to Effectively Reduce Residual Vibration in Slewing of a Two-Staged Pendulum with Uncertain Payload

Abstract

In this study, a control system was proposed consisting of an outside-of-the-loop input shaper and a feedback controller based on quantitative feedback theory. The input shaper convolves the reference input with a properly designed impulse sequence to generate a shaped reference input that reduces the excitation in the system’s modal frequencies, resulting in less residual vibration. Recently, the input shaper has been placed inside-of-the-loop to attenuate noise-induced vibration under hard nonlinearity. However, this setting cannot reduce the vibrations induced from plant-input and plant-output disturbances as well as from plant model uncertainty. A controller was designed to meet various disturbance rejection specifications, when plant uncertainty is also taken into account. The input shaper was then designed using the closed-loop natural frequencies and damping. Together, the proposed control system could effectively reduce residual vibrations especially those induced from disturbances and uncertainty. The control system was applied to a two-staged pendulum where all masses were lumped together to create a simplified model used in controller design, and the inertia forces of both links and payload were treated as plant-input disturbance. Simulation and experimental results indicated that the control system was very effective in residual vibration reduction in the presence of uncertainty and disturbances.