Optimal output fast feedback in two-time scale control of flexible arms

Control of lightweight flexible arms moving along predefined paths can be successfully synthesized on the basis of a two-time scale approach. A model following control can be designed for the reduced order slow sub-system. The fast subsystem is a linear system in which the slow variables act as parameters. The flexible fast variables which model the deflections of the arm along the trajectory can be sensed through strain gage measurements. For full state feedback design the derivatives of the deflections need to be estimated. The main contribution of this work is the design of an output feedback controller which includes a fixed order dynamic compensator, based on a recent convergent numerical algorithm for calculating LQ optimal gains. The design procedure is tested by means of simulation results for the one link flexible arm prototype in the laboratory.