{'fraction_non_alphanumeric': 0.029796511627906978, 'fraction_numerical': 0.005087209302325582, 'mean_word_length': 5.375, 'pattern_counts': {'":': 0, '<': 1, '<?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}}
Dynamics and control of underactuated mechanical systems: analysis and simple experimental verification

Underactuated mechanical systems are systems with fewer control inputs than the degrees of freedom, m < n, the relevant technical examples being e.g. cranes, aircrafts and flexible manipulators. The determination of an input control strategy that forces an underactuated system to complete a set of m specified motion tasks (servo‐constraints) is a demanding problem. The solution is conditioned to differential flatness of the problem, denoted that all 2n state variables and m control inputs can algebraically be expressed, at least theoretically, in terms of the desired m outputs and their time derivatives up to a certain order. A more practical formulation, motivated hereafter, is to pose the problem as a set of differential‐algebraic equations, and then obtain the solution numerically. The theoretical considerations are illustrated by a simple two‐degree‐of‐freedom underactuated system composed of two rotating discs connected by a flexible rod (torsional spring), in which the pre‐specified motion of the first disc is actuated by the torque applied to the second disc, n = 2 and m = 1. The determined control strategy is then verified experimentally on a laboratory stand representing the two‐disc system. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)