Implementation of ℋ<inf>∞</inf> Modified Positive Position and Velocity Feedback controllers for active vibration control of flexible structures in multimode

Abstract

In this paper, ℋ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> Modified Positive Position Feedback (HMPPF) and ℋ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> Modified Positive Velocity Feedback (HMPVF) controllers are developed as two novel controllers for active vibration suppression in flexible structures. The controllers use the concept of positive feedback and are enhanced by the powerful optimization ability of the ℋ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> to provide effective vibration suppression. After performing the numerical simulations, an aluminum cantilever beam is used to experimentally evaluate the performances of the two controllers. The objective of the HMPPF controller is to suppress vibration displacement amplitude, when all fundamental modes are active. In this case, considering the first three modes of the flexible structure, overall vibration displacement is reduced to 38% of the uncontrolled value. The HMPVF on the other hand, uses the control energy to reduce the vibration velocity to the lowest possible value in order to prevent the fatigue failure. Vibration velocity amplitude is reduced to almost half using HMPVF for the multimode experiment, which is a satisfactory result for suppression of velocity in multimode.