Exact modeling for control of flexible manipulators

This work presents the dynamic modeling and active vibration control of planar multilink manipulators having flexible links. Since the eigenvalue problem of such continuous structures is strongly dependent on the posture configuration, at first an efficient matrix formulation is provided in order to derive exact natural frequencies and mode shapes of a robot in its general posture. The analytical modal data are used to develop the forced vibration model; this is accomplished through the analytical decoupling of the modal coordinates of the manipulator; to this latter end, orthogonality conditions of modal shapes sets of planar multilink manipulators are demonstrated. The suppression of vibrations is challenged through a full-state linear quadratic regulator controller by optimally placing collocated sensor/actuator pairs. An optimal stochastic observer is designed in line with the noise-corrupted truncated model, i.e. the continuous Kalman-Bucy filter. The simulation results demonstrate that the presented matrix formulation for deriving exact modal data is effective, and the designed control method, along with the forced vibration solving strategy, is feasible and efficient.