Control of self -adjoint distributed-parameter systems

A method for the optimal control of self-adjoint distributed-parameter systems is presented. The method assumes that the distributed system eigensolutions are known with reasonable accuracy, at least the eigensolutions associated with the modes to be controlled. To extract the modal amplitudes from the system response, the concept of modal filters is introduced. It is shown that when modal filters are used, control of the actual distributed-parameter system is possible, and no discretization is necessary. The control scheme is based on the concept of independent modal-space control, leading to a set of independent second-order matrix Riccati equations. The method requires as many actuators as the number of controlled modes. The number of sensors needed to implement the modal filters depends on the mode participation in the overall response. A sensitivity analysis reveals that small variations in the system parameters have no adverse effect on the closed-loop system stability.