Reliable Beam Modeling in Control Problems
The approaches to modelling and optimization of controlled dynamical systems with distributed elastic and inertial parameters are considered. The general integro-differential method for solving wide class of boundary value problems is developed and criteria of solution quality are proposed. The numerical algorithm for discrete approximation of controlled motions is worked out and applied to design the optimal control law steering an elastic system to the terminal position and minimizing the given objective function. The polynomial control of plane motions of a homogeneous cantilever beam is investigated. Such type of system disturbances can induce essential elastic deflections and lead to sufficient computational difficulties when the conventional approaches are used. The optimal control problem of beam transportation from the initial rest position to given terminal state, in which the full mechanical energy of the system reaches its minimal value, is considered. The obtained numerical results are analyzed.