Improving adaptive feedforward vibration compensation by using “ Integral+Proportional ” adaptation

Abstract

Analysis of various adaptive feedforward vibration compensation schemes has shown that a strictly positive real (SPR) condition has to be satisfied in order to guarantee the stability of the whole system (Jacobson, Johnson, Cormick, & Sethares, 2001; Landau, Airimiţoaie, & Alma, 2011a; Landau, Alma, & Airimiţoaie, 2011b; Wang & Ren, 1999). Filters have to be implemented in order to satisfy this condition. The problem becomes even more crucial in the presence of the internal mechanical coupling between the compensator system and the reference source (a correlated measurement with the disturbance) since some information is not available when adaptation starts (see Landau et al., 2011b). It is therefore very important to relax the SPR condition at least in the initial phase, and in the same time to improve the adaptation transients. It is shown, in this paper, that adding a proportional adaptation to the standard integral type parametric adaptation, the SPR condition can be relaxed and the adaptation transients are improved. Theoretical developments are enhanced by real time experimental results obtained on an active vibration control (AVC) system.