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**Optimal actuators placements for the active control of flexible structures.**
*(English)*
Zbl 0551.73084

The problem of actuators placements in systems for active control of generalised deflection of mechanical structures is considered. Given the equation of motion of a single degree of freedom mechanical construction: Mẍ(t)\(+C\dot x(t)+Kx(t)=p(t)+w(t)\), where p and w are the externally excited and the control vectors, and M, C and K are the mass, the damping and the stiffness matrices, resp. The problem is to determine the B matrix in the standard state space form of this equation (i.e. the most appropriate positions for placement of a limited number of actuators) under quadratic performance index. The solution is based on the use of the transfer matrix between the applied controls and the natural modes of the mechanical structure. Examples of a flexible prismatic beam and a simply supported plate are discussed.

Reviewer: S.Patarinski

### MSC:

74P99 | Optimization problems in solid mechanics |

74H50 | Random vibrations in dynamical problems in solid mechanics |

93B05 | Controllability |

70J99 | Linear vibration theory |

93B07 | Observability |

### Keywords:

actuators placements; systems for active control; generalised deflection of mechanical structures; equation of motion; single degree of freedom; matrix in the standard state space form; quadratic performance index; transfer matrix between the applied controls and the natural modes; flexible prismatic beam; simply supported plate
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\textit{O. Ibidapo-Obe}, J. Math. Anal. Appl. 105, 12--25 (1985; Zbl 0551.73084)

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### References:

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