Feedback compensation of the in-domain attenuation of inputs in diffusion processes

This paper addresses the problem of compensating for the in-domain attenuation of inputs for a class of process control applications. Specific examples include the challenge of maintaining uniform temperatures or through-cure during thick-film radiative drying and curing processes in the face of the effective input's variation with film depth due to the so-called Beer-Lambert effect. These distributed parameter control problems are modeled with parabolic PDEs for the diffusion processes along with an in-domain input with a spatial attenuation function. The approach presented in this paper involves transforming the original model to an equivalent boundary input problem to which existing output feedback backstepping boundary control design methods can be applied. The resulting compensation scheme includes a mechanism for tuning the closed-loop performance. The performance of this scheme is compared with a controller designed via modal approximation of the PDE.