SUB-OPTIMAL FINITE DIMENSIONAL OBSERVER-BASED BOUNDARY CONTROLLER DESIGN FOR DISTRIBUTED PARAMETER SYSTEMS ON A PLANAR DOMAIN

摘要

In this paper, a certain class of distributed parameter systems is considered. We propose a three-step design method for finding finite dimensional observer-based boundary feedback controllers. The first step is called the boundary-equation normalization, which transforms the boundary and system equations into a normal form. The second step is called the boundary input transformation, which integrates the boundary input equation into the system equation, and forms a type of distributed parameter system called the general boundary input system. The final step is to design the desired finite dimensional controller, based on the general boundary input system model. The design procedure utilizes the finite dimensional linear quadratic optimal control theory, so well-developed computation tools can be applied. Though the acquired controllers are only sub-optimal for the distributed parameter systems, an estimation of the performance degradation from that of the ideal case is derived for comparison purpose.