Generic model control of diffusion-reaction systems

Late lumping controller design for distributed parameter systems presents a significant challenge. This paper extends the generic model control technique to diffusion-reaction systems governed by semilinear parabolic equations, focusing on controlling an output defined as a spatially weighted average of the system state. Both distributed and boundary control approaches are thoroughly investigated. While the design for distributed control is straightforward, boundary control necessitates the use of the extended operator concept. This concept allows to convert the boundary control problem into a pointwise one, a particular case of distributed control, which simplifies the controller design. The effectiveness of the proposed controllers in tracking and disturbance rejection is validated through numerical simulations using a case of a heated rod.