Robust multivariable PI-controller for infinite dimensional systems

A robust multivariable controller is introduced for a class of distributed parameter systems. The system to be controlled is given as in a Banach space. The purpose of the control, which is based on the measurement , is to stabilize and regulate the system so that as , where yris a constant reference vector. Under the assumptions that operator generates a holomorphic stable semigroup, is linear and bounded, is linear and -bounded, and the input and output spaces are of the same dimension; a necessary and sufficient condition is found for the existence of a robust multivariable controller. This controller appears to be a multivariable PI-controller. Also, a simple necessary criterion for the existence of a decentralized controller is derived. The tuning of the controller is discussed and it is shown that the I-part of the controller can be tuned on the basis of step responses, without exact knowledge of the system\´s parameters. The presented theory is then used as an example to control the temperature profile of a bar, with the Dirichlet boundary conditions.