Optimal boundary control of systems of elastically connected parallel beams

摘要

The optimal control of a distributed host structure consisting of two Euler-Bernoulli beams coupled in parallel with boundary controllers is considered. Ail index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving boundary control forces. The minimization of the performance index over these forces is subject to the equation of motion governing the structural vibrations, the imposed initial conditions as well as the boundary conditions. A maximum principle is derived for such a system and then the optimal control law is obtained using this maximum principle and the applicability of the results is demonstrated. The effectiveness of the proposed control mechanism is illustrated numerically.