Optimal FIR Input Shaper Designs for Motion Control With Zero Residual Vibration

This paper considers the design of input shaping filters used in motion control of vibratory systems. The filters preshape a command or actuation signal in order to negate the effect of vibratory modes. A class of finite impulse response filter satisfying a set of orthogonality conditions that ensure zero residual vibration is introduced. Filter solutions having minimum quadratic gain, both with and without the inclusion of non-negativity (peak gain) constraints, are presented. Unlike impulse-based shapers, the filters have impulse responses with no singularities and therefore automatically remove discontinuities from an input signal. Minimum duration impulse response solutions are also presented. These contain singularities but may also have smooth components. Discrete-time designs can be obtained numerically from system modal parameters, accounting for all modes simultaneously so that convolving single-mode solutions, which leads to suboptimality of the final design, is not required. Selected designs are demonstrated experimentally on a flexible link planar manipulator.