Robust natural control of distributed systems

The effect of having both parameter uncertainties and errors arising from spatial discretization on the performance of control systems is analyzed for distributed structures. It is shown that having errors in the system parameters, as well as errors due to a finite element type of discretization, is the equivalent to implementing the control laws by a set of admissible functions instead of by the actual eigenfunctions. It is shown that if natural control is considered in conjunction with modal filters and an adequate number of sensors, implementation of the control action by admissible functions leads to a stable closed-loop system. Using GerschgoriiTs disks, the deviation of the desired closed-loop eigenvalues is determined.