The first ever oscillation phenomenon of a copper wire embraced inside a self‐powered liquid metal machine is discovered. When contacting a copper wire to liquid metal machine, it would be swallowed inside and then reciprocally moves back and forth, just like a violin bow. Such oscillation could be easily regulated by touching a steel needle on the liquid metal surface.
The main objective of this paper is to revisit one of the key steps of immersion and invariance stabilizing controller design. Namely, the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behavior. Towards this end we invoke contraction theory principles and propose two alternative procedures to carry out this step: (i) to replace attractivity of the manifold by virtual contraction of the off-themanifold coordinate and (ii) to ensure the attractivity of the manifold rendering it horizontally contractive. This makes more systematic the design with more explicit degrees of freedom to accomplish the task. Several examples, including the classical case of systems in feedback form, are used to illustrate the proposed design.
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