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Dynamics and control of underactuated mechanical systems: analysis and simple experimental verification
Author(s) -
Blajer Wojciech,
Dziewiecki Krzysztof,
Kołodziejczyk Krzysztof,
Mazur Ze
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910028
Subject(s) - underactuation , control theory (sociology) , flatness (cosmology) , mathematics , simple (philosophy) , torque , differential (mechanical device) , mechanical system , computer science , engineering , control (management) , physics , artificial intelligence , philosophy , cosmology , epistemology , quantum mechanics , thermodynamics , aerospace engineering
Abstract 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)