Robust shape control of beams with load uncertainties by optimally placed piezo actuators

The shape of a laminated beam is controlled by an optimally placed piezo ac tuator so as to minimize its maximum deflection. The locations and magnitud es of the external loads are not known a priori and belong to a specified l oad uncertainty domain. The optimal actuator location is obtained for any l oad combinations and locations which are determined so as to produce the ma ximum deflection corresponding to the worst case of loading. In this sense, loading uncertainties lead to an anti-optimization problem which is couple d to the optimization problem via the design parameter and loading. The res ulting coupled problems are solved simultaneously to compute the optimal ac tuator location and the least favourable loading condition. Multiple load c ases are also considered. Numerical results are given to assess the effect of load uncertainty and actuator length on the actuator location and the de sign efficiency which is defined with respect to the corresponding uncontro lled beam.