the observabilty range space extraction (orse) algorithm used to identify a an initially overparameterized discrete-time state-space model for a single-link flexible manipulator. a controller named pdpc is designed to control rigid body motion, have a zero tracking error and minimum vibration.--abstract.the observability range space extraction (orse) algorithm is successfully applied to identify an initially overparameterized discrete-time state-space model for a single-link flexible manipulator. several critical issues related to the experiments and the implementation of the orse algorithm are addressed. a new model reduction and updating technique is proposed and applied to reduce the identified models. to quantify the contribution of individual modes to the responses, a new measure referred to as modal response magnitude (mrm) is developed and successfully applied to obtain a lower-order model by retaining the most significant modes. to correct errors caused by the model reduction, either the reduced input or output matrix is recalculated by a least squares solution. based on the updated reduced-order models, a controller named as pdpc is designed to ensure a good tracking accuracy and robustness to payload changes. the experimental results show that the pdpc control structure is effective in controlling rigid body motion to have a zero tracking error and the minimum vibration as well.