Inversion based tracking control for a distributed parameter system with spatially distributed control input

The article presents an approach for designing an inversion based feedforward control for a distributed parameter system (DPS) described by a linear heat equation. The tracking task is to drive the output along a desired trajectory with the control input acting spatially distributed on the DPS via a fixed spatial characteristic. The inversion is derived from the zero dynamics of the DPS, which is required to be asymptotically stable. To account for unknown initial conditions, the control scheme also includes a proportional feedback. The feedforward and feedback part are combined in a two degree of freedom structure. Results for stability and numerical simulation are given.