Control of a flexible link by shaping the closed loop FRF through optimized feedback filters

A frequency domain method is presented to design a closed-loop control for vibration reduction flexible mechanisms. The procedure is developed on a single-link flexible arm, driven by one rotary degree of freedom servomotor, although the same technique may be applied to similar systems such as supports for aerospace antennae or solar panels. The method uses the structural frequency response functions (FRFs), thus avoiding system identification, that produces modeling uncertainties. Two closed-loops are implemented: the inner loop uses acceleration feedback with the aim of making the FRF similar to that of an equivalent rigid link; the outer loop feeds back displacements to achieve a fast positioning response and null steady state error. In both cases, the controller type is established a priori, while actual characteristics are defined by an optimisation procedure in which the relevant FRF is constrained into prescribed bounds and stability is taken into account.