Mechanical structures are modelled in general with a high number of degrees of freedom, in order to properly describe their behavior. H∞ techniques are commonly used to design vibration controllers, but for the usual techniques the controller order is the same of the plant model, rendering solutions difficult to implement and often infeasibility. One obvious way to deal with this problem is to design a fixed (reduced) order controller. But, due to the rank restriction, the reduced order controller design is a non-convex problem. A methodology to design a fixed order H∞ controller is presented here, and experimental results applied to a cantilever beam are reported. To overcome the difficulties, the Augmented Lagrangian method allows the problem to become a convex one, and linear matrix inequalities are used to solve it. Based on the Finite Element Method, a cantilever beam truncated model is used to design the controllers. It is known to be a very difficult task to assure stability and performance to vibration controllers, due to the several sources of modelling uncertainties. Adequately designed weighing filters are used to attain the necessary robustness of the controller, preventing the excitation of the uncertain modes and so avoiding the spillover phenomenon (Balas, 1990). Using the methodology, two types of H∞ controllers were designed, of complete and fixed order, and implemented over an experimental testbed. Simulated and experimental results are presented and compared. These results permit to conclude that the method achieves the objectives of reducing the vibration level, maintaining robust stability and performance, even for a first order controller. [ABSTRACT FROM AUTHOR]