This project addresses the development of a practical robust control technique for flexible mechanical systems with an infinite number of vibration modes. The technique uses approximate models for control analysis and design, but purports to guarantee closed loop performance for the infinite order closed loop system. It is based on an approach developed for single-input single-output cases, and intends to show that the Nyquist plot of the infinite dimensional system lies within a certain error bound about a known, approximate, and easy to compute plot. Based on such plots, the performance of a particular design will be guaranteed within a certain bound related to the approximation error. The technique will be experimentally verified.