Stable Finite-Dimensional Control of Linear DPS Using Very Low-Order Residual Mode Filters

Abstract Exponential closed-loop stability for distribute parameter systems (DPS) can be achieved by using a reduced order modal controller with the addition of a sufficiently large dimensional residual mode filter. In this paper we prove that by using only the closed-loop unstable modes in the residual mode filter design one can still achieve the same exponential stability for the DPS. The modified filter dimension is substantially reduced. Two DPS examples: A simply-supported Euler-Bernoulli beam and a Space Based Laser (SBL) beam expander are presented to illustrate the application of this concept.