Stabilization of Unstable Mechanical Systems

A. M. Formalskii ()
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A. M. Formalskii: Moscow Lomonosov State University

Journal of Optimization Theory and Applications, 2010, vol. 144, issue 2, No 3, 227-253

Abstract: Abstract The set of states (controllability domain) from which an unstable object can be steered to a desired operational regime is bounded in the phase space, if the control resources are restricted. Under admissible (with given resources) feedback control, the basin of attraction of the desired regime belongs to this controllability domain. The problem of control design to maximize the basin of attraction is discussed in this paper. Several systems with underactuation degree one are studied. A system of gyroscopic stabilization of the unstable upright position of a two-wheel bicycle is described also. An active field of research exists, due to the applications of underactuated systems.

Keywords: Mechanical systems; Control; Instability; Unstable equilibrium; Maximization of basin of attraction; Pendulum; Wheel; Flywheel; Bicycle; Gyroscopic stabilizer (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-009-9600-x

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