Design of Robust Vibration Controller for a Smart Panel Using Finite Element Model

Abstract

This paper presents a model reduction method and uncertainty modeling for the design of a low-order H∞ robust controller for suppression of smart panel vibration. A smart panel with collocated piezoceramic actuators and sensors is modeled using solid, transition, and shell finite elements, and then the size of the model is reduced in the state space domain. A robust controller is designed not only to minimize the panel vibration excited by applied uniform acoustic pressure, but also to be reliable in real world applications. This paper introduces the idea of Modal Hankel Singular values (MHSV) to reduce the finite element model to a low-order state space model with minimum model reduction error. MHSV measures balanced controllability and observability of each resonance mode to deselect insignificant resonance modes. State space modeling of realistic control conditions are formulated in terms of uncertainty variables. These uncertainty variables include uncertainty in actuators and sensors performances, uncertainty in the knowledge of resonance frequencies of the structure, damping ratio, static stiffness, unmodeled high resonance vibration modes, etc. The simplified model and the uncertainty model are combined as an integrated state space model, and then implemented in the H∞ control theory for controller parameterization. The low-order robust controller is easy to implement in an analog circuit to provide a low cost solution in a variety of applications where cost may be a limiting factor.

Active vibration control of a slewing spacecraft’s panel using H∞ control

“…Moreover, controller design for MIMO systems and simultaneous suppression of multiple modes can be easily achieved through a unified and systematic procedure. Effective vibration control of piezoelectric smart structures using H∞ has been demonstrated in number of studies; however, the applications have been chiefly limited to constraint structures [7][8][9][10][11][12][13]. Moreover, vibration reduction is achieved for arbitrary excitation source without considering relative modal responses of controlled modes.…”

A new approach to suppress spillover instability in structural vibration control

“…Vibration control of flexible structures has been extensively studied in the literature [1][2][3][4][5]. Flexible structures are usually lightly damped and have clustered vibration modes.…”

An intelligent active-passive vibration absorber using hierarchical fuzzy approach

“…Hence, the upper level controller monitors these differences and causes the supervisory decision to be fed to the lower level. The weight factors 1 w and 2 w generated by the supervisory fuzzy logic controller are multiplied with the local controls 1 u and 2 u . These are then summed to form the total control F u for feeding back to the flexible beam.…”

“…Recent advances in piezoelectric actuators, based on the converse piezoelectric effect, have great potential for the active control of vibrations, especially for suppressing or isolating vibrations [1,2,3,4].…”