Generalization of the IDA-PBC method for stabilization of mechanical systems

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We generalize and strengthen the method of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for the stabilization of mechanical systems. First, we replace the skew symmetry property of the interconnection matrix with the energy conservation property, and introduce a gyroscopic force replacing the interconnection sub-matrix that is usually denoted by J2. Second, we derive a new set of matching conditions where the new kinetic matching conditions are simpler than those in the literature. Third, we provide a necessary and sufficient condition for Lyapunov/exponential stabilizability by IDA-PBC for the class of all linear mechanical systems. Last, we give a necessary and sufficient condition for Lyapunov/exponential stabilizability by IDA-PBC for the class of all mechanical systems with one degree of underactuation. These conditions are easy to verify without solving any PDE's. Our results comprehend and extend most results on IDA-PBC in the literature. © 2010 IEEE.
Publisher
Mediterranean Control Association
Issue Date
2010-06
Language
English
Citation

18th Mediterranean Conference on Control and Automation, MED'10, pp.226 - 230

DOI
10.1109/MED.2010.5547672
URI
http://hdl.handle.net/10203/227800
Appears in Collection
EE-Conference Papers(학술회의논문)
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