Controller Parametrization for Offset-free Control Using Set-Based Feasibility Methods

Achieving a new set point and maintaining it with a desired precision is a common control problem. In case the reference is not fixed, or a priori unknown disturbances are present, the problem is often referred to as offset-free control. We consider the problem of finding suitable controller parameters to obtain an offset-free control up to a certain degree. We tackle the problem in two steps: first, we find controller parameters to steer the controlled system in the neighborhood of the desired reference; second, we identify controller parameters such that the system is robustly controlled invariant with respect to the desired neighborhood of the reference value. For each subproblem we determine the set of parameters that guarantee the desired behavior despite bounded uncertainties. We employ a set-based feasibility formulation which is able to handle nonlinear systems with set constraints. The approach is illustrated with an example.