Abstract
In this chapter, the stabilization issue for UMSs is considered. The strategy employed is based on the classification of Seto and Baillieul for these systems. The authors of this classification proposed a systematic control design procedure of backstepping type for the chain structure only. We are therefore concerned here with the problem of synthesizing control laws for each of the structures of this classification; thus, providing a general treatment of all the UMSs. For this, we shall firstly extend the procedure of Seto and Baillieul to a subclass of the tree structure that can be transformed to a chain structure under some conditions. Next, a procedure to control the remaining tree structure that cannot be transformed into a chain structure is presented. Finally, the control of the isolated vertex structure, which is the most difficult structure to control, is proposed.
…A control theorist’s first instinct in the face of a new problem is to find a way to use the tools he knows, rather than a commitment to understand the underlying phenomenon. This is not the failure of individuals but the failure of our profession to foster the development of experimental control science. In a way, we have become the prisoners of our rich inheritance and past successes.
Y.C. Ho (1982)
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Choukchou-Braham, A., Cherki, B., Djemaï, M., Busawon, K. (2014). Control Design Schemes for Underactuated Mechanical Systems. In: Analysis and Control of Underactuated Mechanical Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-02636-7_5
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DOI: https://doi.org/10.1007/978-3-319-02636-7_5
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