REPETITIVE CONTROL OF BILINEAR-SYSTEMS WITH APPLICATION TO SEMIACTIVE ISOLATION OF VIBRATION

A new repetitive control method is presented for semi-active vibration control of machines, such as presses and forge hammers, that are subject to nearly periodic disturbances with known periods. The vibration of the machine is controlled by actuators consisting of a proof mass, a spring, and a damper with variable damping coefficients that are treated as control inputs. The system is approximated by a bilinear state equation involving products of state variables and control inputs. Using optimal control theory a control input vector is synthesized which minimizes an objective function that trades-off the quality of isolation against relative motions of the proof masses and accounts for inequality constraints on the control inputs. The optimal control law calls for a full state feedback and feedforward of a variable dependent on future disturbances. It is therefore proposed to estimate the system disturbance based on measurements from the most recent period and, assuming the disturbance to be repetitive, to use this estimate as a predicted disturbance for the consecutive period. An observer for simultaneous estimation of the state and the disturbance is developed. Although intended for a particular application, the repetitive control theory developed in this paper is general and can be applied to other systems described by bilinear state equations. The results of simulations for a two degree-of-freedom model representing a machine with a semi-active vibration absorber and for a simple distributed parameter structure illustrate the proposed approach.