The computer-controlled stabilization of a noisy two-dimensional hyperbolic system

The computer-controlled stabilization of a noisy two-dimensional hyperbolic system is described. A meter-square flexible wire mesh, suspended vertically in tension by rigid boundaries, supported transverse deflections about a planar equilibrium which were destabilized by the application of a transverse electrostatic bias. The number of open-loop unstable deflection modes was adjustable with bias strength. Using information from up to nine electrostatic deflection sensors, a minicomputer manipulated nine electrostatic deflection actuators so as to stabilize the mesh. Linear-quadratic-Gaussian control laws, based upon a truncated normal mode system description and modified to include rate-limited deflection integration, were implemented throughout. Experiments are reported in which the open-loop system stability, the number and location of actuators and sensors used, and the computer sampling rate were variable. Three open-loop unstable modes were stabilized at an electrostatic bias pressure nearly three times that required to initially destabilize the mesh. The limits of this stability, regime and the resulting mesh surface tolerances were found to be consistent with theory. Spillover was experimentally observed to be a predictable cause of mesh deflection destabilization.