This work deals with the LQG control problem of a flexible beam clamped at one end and with a point mass at the free end, where a boundary control force can he applied. A class of finite-dimensional control laws is proposed here, derived on the basis of the Euler-Bernoulli infinite-dimensional beam model. By means of this approach it is possible to take into account also the higher order modes that are indeed neglected in the more usual methods based on a finite-dimensional model of the beam. The main motivation for the approach followed here is that it naturally allows lo overcome the phenomenon of spillover. occurring when unmodeled modes are excited by the control law itself. The finite-dimensional control law here proposed is derived by a Galerkin approximation of the solution of the LQG control problem, in a proper Hilbert space setting. In particular, the novelty of the approach is the definition of an implementable Galerkin approximation scheme based on generalized eigenfunctions of the Euler-Bernoulli model instead of the usual splines. It is here proved that, for any given finite time horizon, the evolution of the system state driven by the proposed control input converges, in L2 norm, to the optimal LQG evolution, as the order of the approximation scheme increases. The strong stability of the closed loop system is guaranteed for any order of the approximation scheme. Moreover, it is proved that the proposed compensator guarantees modal stability of the closed loop system also in the presence of stiffness inertia parameters uncertainties

Germani, A., Manes, C., Palumbo, P. (2006). A robust approximation scheme for the LQG control of an undamped flexible beam with a tip mass. EUROPEAN JOURNAL OF CONTROL, 12(6), 635-651 [10.3166/ejc.12.635-651].

A robust approximation scheme for the LQG control of an undamped flexible beam with a tip mass

Palumbo, P
2006

Abstract

This work deals with the LQG control problem of a flexible beam clamped at one end and with a point mass at the free end, where a boundary control force can he applied. A class of finite-dimensional control laws is proposed here, derived on the basis of the Euler-Bernoulli infinite-dimensional beam model. By means of this approach it is possible to take into account also the higher order modes that are indeed neglected in the more usual methods based on a finite-dimensional model of the beam. The main motivation for the approach followed here is that it naturally allows lo overcome the phenomenon of spillover. occurring when unmodeled modes are excited by the control law itself. The finite-dimensional control law here proposed is derived by a Galerkin approximation of the solution of the LQG control problem, in a proper Hilbert space setting. In particular, the novelty of the approach is the definition of an implementable Galerkin approximation scheme based on generalized eigenfunctions of the Euler-Bernoulli model instead of the usual splines. It is here proved that, for any given finite time horizon, the evolution of the system state driven by the proposed control input converges, in L2 norm, to the optimal LQG evolution, as the order of the approximation scheme increases. The strong stability of the closed loop system is guaranteed for any order of the approximation scheme. Moreover, it is proved that the proposed compensator guarantees modal stability of the closed loop system also in the presence of stiffness inertia parameters uncertainties
Articolo in rivista - Articolo scientifico
Flexible structures; LQG regulator; Infinite-dimensional systems
English
2006
12
6
635
651
reserved
Germani, A., Manes, C., Palumbo, P. (2006). A robust approximation scheme for the LQG control of an undamped flexible beam with a tip mass. EUROPEAN JOURNAL OF CONTROL, 12(6), 635-651 [10.3166/ejc.12.635-651].
File in questo prodotto:
File Dimensione Formato  
2006 EJC - LQG control of Flexible beam.pdf

Solo gestori archivio

Dimensione 3.93 MB
Formato Adobe PDF
3.93 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/246667
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
Social impact