Control of an elastic manipulator using the Timoshenko beam model. (Russian, English) Zbl 1116.74044

Zuev, A. L.

Prikl. Mekh., Kiev 41, No. 12, 107-115 (2005); translation in Int. Appl. Mech. 41, No. 12, 1418-1425 (2005).

The author studies a controlled mechanical system in the form of a Timoshenko beam with loading which describes the motion of a flexible manipulator. For particular equations of motion, a Galerkin approximation is constructed based on the solution of an appropriate Sturm-Liouville problem. The author establishes conditions of local controllability of Galerkin approximation in a neighbourhood of equilibrium. Stabilizability of the equilibrium state is proved, and an explicit synthesis of control with feedback is proposed.

Reviewer: A. N. Chernienko (Kyïv)

MSC:

74M05	Control, switches and devices (“smart materials”) in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
70E60	Robot dynamics and control of rigid bodies

Keywords:

Galerkin approximation; Sturm-Liouville problem; feedback