Auto-regressive moving average with exogenous excitation model based experimental identification and optimal discrete multi-poles shifting control of a flexible piezoelectric manipulator

Auto-regressive moving average with exogenous excitation (ARMAX) model based experimental identification and vibration suppression of a flexible piezoelectric manipulator are conducted. Experimental identification based on ARMAX models with different orders is conducted. To remove the spurious modes that do not correspond to structural modes, a balanced model reduction method based on the Hankel singular value is employed. After balanced transformation and model reduction, the identified ARMAX model with a high order is transformed into a reduced-order controllable and observable system. Comparative experimental results show that the identified reduced-order model matches closely with the system dynamics. Therefore, an optimal discrete multi-poles shifting controller, which combines the multi-poles recursive shifting method and linear quadratic regulator (LQR) control, is proposed. The first complex conjugate poles pair of the system is shifted to some desired positions by solving a discrete algebraic equation. The weighting matrixes of the LQR are determined based on the solution of the discrete algebraic equation. Then, multi-poles of the identified model are shifted through recursive applications of the reduced-order poles shifting method. Experimental results show that vibrations of the manipulator are significantly diminished. Consequently, the effectiveness of the proposed controller is proven.