Flatness-based feedforward control for parabolic distributed parameter systems with distributed control

This paper deals with distributed parameter systems being described by inhomogeneous parabolic partial differential equations in one space dimension with a distributed control. The distributed control is presented by the right part of an equation, i.e. the source function. The source function can depend on the time as well as spatial variable. The approach for design of a feedforward control for the purpose of exact output tracking is presented. The design of the feedforward control is based on the examination of inverse system dynamics. The proposed technique utilizes the method of the variables separation and the representation of a solution by the power series in the time domain. Some examples and numerical simulations are included and demonstrate the efficiency of the proposed approach for developing the feedforward control.