Optimal Control of a Semi-Active, Frictionally Damped Joint

Abstract

Dry or Coulombic friction is a dominant source of damping in many jointed structures. This paper investigates the enhancement of friction damping by controlling the normal loads acting at the frictional interfaces. The resulting frictional joint is termed since the control input is used only to vary the passive damping properties of the interface. The semi-active frictional joint is designed using a system consisting of two flexible beams are connected using a semi-active frictional pin joint. Two different control schemes are developed. The first is a sub-optimal state feedback controller which is obtained by implementing the linear optimal state feedback gains and restricting the control input to be passive. The second control scheme determines the optimal normal force to the frictional interface using a numerical optimization routine. Both schemes are compared to a simple collocated output feedback control design. The performance of the optimal and sub-optimal control designs is seen to be much better than that of the collocated control. It is also found that the performance of the sub-optimal control is very close to that of the optimal control.