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Galerkin approximation in modeling of controlled distributed-parameter flexible systems. (English) Zbl 0783.73082
Summary: Numerical study of control problems for linear distributed-parameter flexible mechanical systems requires finite-dimensional modeling of the system. We study the conditions for \(H_ \infty\) convergence of the transfer functions of finite-dimensional Galerkin approximations. This convergence ensures that control problems can be solved by using a Galerkin model. A stabilization problem for the angular position of a Bernoulli-Euler beam illustrates the theoretical consideration. The beam with an inertial drive represents a flexible manipulator link.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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