(357a) Optimal Placement of Actuating Devices for Transport-Reaction Systems in the Presence of Uncertainty

The issue of actuator choice and placement has long been recognized as an important controller design aspect. The location of the actuator is especially critical for a large number of industrially important chemical processes which exhibit both variation in space and excitation due to disturbances of the process variables. Such processes can be categorized as transport-reaction processes and examples include chemical vapor deposition reactors and plasma etching processes as well as the more traditional thermal processes. Mathematical models can be derived from dynamic conservation equations and usually involve parabolic partial differential equation (PDE) systems. The traditional approach to actuator placement is to select the locations based on open-loop considerations to ensure that the necessary controllability, reachability or power factor requirements are satisfied.

The present work considers the optimal placement of actuators for transport-reaction processes, mathematically modeled by linear parabolic partial differential equations in the presence of disturbance. Using modal decomposition to discretize the spatial coordinate, and based on the definitions of spatial and modal controllability, the infinite optimization problem is formulated as a nonlinear optimization problem in appropriate L₂ spaces. Standard optimal search algorithms are subsequently used to obtain the optimal locations. The method presented here is successfully applied to a representative diffusion process, modeled by a one-dimensional parabolic PDE, where one actuator is placed at a position to preferentially counter the effects of disturbances for the processes. Concurrently, minimum requirements on spatial controllability, modal controllability and spillover suppression are explicitly satisfied.