A nonlinear PI controller for a system with a mismatched and unknown external
disturbance is proposed in the present paper. A Sigmoidal function is proposed to be used
in the nonlinear integral element to attenuate the disturbance effect. Formally the controller
forces the state to a positively invariant set around the origin. As an application, the
nonlinear PI controller is used as a virtual controller for the upper subsystem in the frame of
Backstepping control approach for the DC motor system. In this Backstepping controller
design the restriction about the disturbance form in the upper system is relaxed. The results
show the effectiveness of the nonlinear PI controller to attenuate the effect of unknown and
varying disturbance torque and force the angular velocity to follow the desired reference.
Finally a reduced order observer is designed to estimate the armature current used in the
designed controller for the DC motor system.