The single-link flexible beam is an infinite-dimensional system. Many researchers have proposed controlling such a beam using atl approximate model consisting of a finite a number of modes. But the number of modes that one should retain in the model for the purpose of controller design is not clear. The authors begin with a full-order model containing all the modes of the system within the bandwidth of the actuator and sensors. Control design based on such a model would result in a high-order controller that may not be feasible to implement in practice. Hence, a low-order model for the system is obtained using Hankel-norm minimisation. This procedure gives an excellent reduced-order model in the sense that the reduced model is close to the original system in the graph topology. A controller is designed for the flexible beam on the basis of the reduced-order model thus obtained. Experimental results show that a controller designed for the reduced-order model guarantees effective vibration control of the flexible beam.