Independent Modal Space Control With Positive Position Feedback

Abstract

This study presents an Independent Modal Space Control (IMSC) algorithm whose modal control forces are generated based on a Positive Position Feedback (PPF) strategy. This is in contrast to conventional modal controllers that rely in their opeation on negative feedback of the modal position and velocity. The proposed algorithm combines the attractive attributes of both the IMSC and the PPF. It maintains the simplicity of the IMSC as it designs the controller of a complex structure at the uncoupled modal level. At the same time, it utilizes only the modal position signal to provide a damping action to undamped modes. The paper presents the theory behind this algorithm when using first order filters to achieve the PPF effect. The optimal time constants of the filters are determined. The performance of the algorithm is enhanced by augmenting it with a “time sharing” strategy to share a small number of actuators between larger number of modes. The effectiveness of the algorithm in damping out the vibration of flexible structures is validated experimentally. A simple cantilevered beam is used as an example of a flexible structure whose multi-modes of vibration are controlled by a single actuator. A piezo-electric actuator is utilized, in this regard, as a part of a computer-controlled active control system. The performance of the active control system is determined in the time and the frequency domains. The results are compared with those obtained when using the IMSC, PPF with second order filters, the Psuedo-Inverse (PI) and a Modified Independent Modal Space Control (MIMSC). The experimental results suggest the potential of the proposed method as a viable means for controlling the vibration of large flexible structures.