Robust control and tuning problem for distributed parameter systems

In this paper robust multivariable controllers for parabolic distributed parameter systems will be discussed. The purpose of a robust controller is to achieve output regulation, disturbance rejection and insensitivity against some perturbations in the system's and controller's parameters. The robust controller consists of two parts: the unstable servo-compensator and the stabilizing compensator. The servo-compensator will be fixed on the basis of the spectrum of the reference and disturbance signals. The purpose of the stabilizing compensator is to stabilize the extended unstable system that consists of the stable plant and the servo-compensator. In this paper it is proved that the stabilizing compensator can be decomposed into a scalar gain and a matrix gain. A simple sufficient condition for finding stabilizing matrix gains will be given and a straightforward way to compute the gains will be presented. The proposed method is practical in the sense that the dimension of the controller is finite and small, output feedback is used and tuning the controller can be done with the information that can be measured from the stable plant with input-output measurements. To the authors' knowledge, the main results are new even for finite-dimensional systems.