This paper compares Generalised Minimum Variance and Pole-placement techniques for the control of a lightly damped cantilever beam smart structure. Saturation of the control signal can lead to limit cycles in Pole-placement control. Saturation compensation can remove these limit cycles, allowing disturbances of the beam to be rejected, but introduces a low amplitude, higher frequency vibration effect. Control sensitivity functions used to investigate these limit cycles show that certain Pole-placement controllers are sensitive to frequencies in the 50Hz range. The sensitivity of a Generalised minimum variance (GMV) controller is shown to be less than that of the Pole-placement controller. This GMV controller is applied to the vibration control of the smart beam. The controller weightings of the cost function limit excessive control signals. Previous work allows a plant model to be generated that produces results that closely match experimental data. Control results shows that the GMV technique is highly effective in reducing both the decay time and amplitude of vibration for free and forced vibrations respectively.