Inversion based feedforward control for higher-dimensional parabolic systems with spatially distributed control input

The article presents a novel approach for designing an inversion based control for a distributed parameter system (DPS) described by a higher-dimensional inhomogeneous second order partial differential equation (PDE). The tracking task is to drive the output along a desired trajectory with a control input acting spatially distributed on the whole domain of the DPS via a fixed spatial characteristic. For the controller design we propose a transformation that homogenizes the heat equation by splitting the DPS into a homogeneous boundary controlled PDE and a set of ordinary differential equations. Subsequently the transformed system representation is used for the computation of the feedforward control in order to track desired output trajectories. Requirements of the proposed method for higher-dimensional heat equations are investigated. Furthermore the performance of the proposed approach is presented by showing and discussing simulation results.