Optimal, Coupled-Modal Control of Distributed Parameter Systems With Discrete Actuators

Optimal control of flexible continuous structures subjected to arbitrary time-varying distributed loads is considered. The control is to be implemented by discrete sets of sensors and actuators that monitor the response and apply the necessary forces. The dynamics of the uncontrolled structure is assumed to be governed by a linear, self-adjoint partial differential equation. The control forces at any time are determined on the basis of minimization of the total energy of the system at that time. This leads to a causal optimal algorithm whereby control forces are determined solely on the basis of information available up to the time at which control is being implemented. The effectiveness of the algorithm is demonstrated by applying it to a beam subjected to an impulse.