PID filter-shaped optimal PI tracker, state estimator, and EID estimator for continuous-time systems

This paper proposes a proportional–integral-differential (PID) filter-shaped optimal PI tracker for on-line robust optimal tracking control of a system with unknown disturbances. The proposed optimal PI tracker consists of both a modified state estimator and the newly modified equivalent input disturbance (EID) estimator. The main contributions of this paper are: (1) The conventional EID estimator is significantly modified to improve the tracking performances of a system with unknown disturbances; and (2) The improved EID estimator can be simply regarded as a plug-in component of the compensator, to perform on-line optimal tracking control of square/non-square servo systems with unknown disturbances.