Repetitive control of bilinear systems with application to semi-active isolation of vibration

Abstract

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, ...