{'fraction_non_alphanumeric': 0.015482695810564663, 'fraction_numerical': 0.0, 'mean_word_length': 5.209039548022599, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Optimal Input Shaping with Finite Resolution Computed from Step-Response Experimental Data

The purpose of this work is the computation of optimal input signals for output tracking of a dynamic system, where knowledge of the dynamic system is only given in the form of step response-data. The starting point is a (non-optimal) input signal given in the form of a simple step input and the measurement of the resulting output. The computation of infinite precision optimal input signals are based on linear programming (LP) solutions that can be specialized to mixed integer linear programming (MILP) solutions with an integer parametrization to enforce possible finite resolution solutions for the input shaping signals. The approach of input shaping based on step-response data is illustrated on experimental data obtained from a class IV LASER system with varying pulse length and a laboratory experiment of a mechanical vibration system. In the latter case, computed optimal input signals were tested experimentally to verify the effectiveness of the input shaping to reduce residual vibrations.