On a generalization of the PI-controller

PI-controllers are known to achieve output regulation on a constant signal, in spite of sufficiently small but otherwise arbitrary linear plant perturbations. The structure of this controller is rather simple and, in view of the internal model principle, it implements the minimum dynamic extension required to achieve structural stability. If the reference signal is not constant, the PI-controller is no longer adequate. In this note a structurally stable controller that, mutatis mutandis, has the same simplicity of the PI-controller is then introduced to deal with the exogenous signal generated by a finite dimensional linear system. Its applicability to output regulation of nonlinear systems is also discussed and illustrated by considering the approximate regulation of the output of a rigid robot on a periodic joint trajectory