Session: VIB-13-01: Passive and Active Control of Vibration, Shock, and Noise

Paper Number: 89788

89788 - Multi-Input Shaping for a Multi-Mode Vibratory Structure Using Deadbeat Control Theory 

A general approach of the multi-input shaping for an underdamped flexible structure with multiple modes of vibration is developed using the deadbeat control theory, which states that a discrete-time system can be made to reach the desired position  in  a minimum time by placing all the poles at the origin of z-plane. For the generation of deadbeat control, discrete-time state space model is developed assuming a Zero-Order-Hold. The sampling period is used as a design parameter to achieve a desired level of input magnitudes. It is shown that this theory can also be used  to minimize  sensitivities to uncertainties in natural frequencies and modal damping ratios.  Numerical results are presented for a two-degree of freedom  spring mass model with two force inputs, and a finite element model of a tetrahedral truss structure with four modes of vibration and three inputs. These examples deal with cases of number of inputs being equal to number of modes, and also non-integer ratio of numbers of states and inputs.  When the number of inputs is equal to the number of modes, it is found that the coupled modal approach yields better results than the independent modal input shaping. Also, an optimization approach is presented to determine a suitable sampling period for input shaping.

Presenting Author: Alok Sinha Pennsylvania State Univ

Presenting Author Biography: Alok Sinha is a Professor of Mechanical Engineering at The Pennsylvania State University, University Park, PA.

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