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 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. 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 spring mass model, and a finite element model of a tetrahedral truss structure. 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.