Suboptimal feedback vibration control of a beam with a proof-mass actuator

A clamped-free beam, damped by a proof-mass actuator, is selected for small scale model research of flexible structures in space. The dynamic behavior of this system is strongly influenced by the constraints on the motion of the proof-mass and by the maximum control forces available. An optimal solution is presented, using a linear programming algorithm. Then, a simplified feedback control is utilized, based on modern control theory, to obtain optimal low-frequency performance, and classical control theory to bound the high-frequency modes. By special consideration of the constraints, satisfactory control is achieved, even in the nonlinear region when the proof-mass approaches its stops.