New techniques for H2 optimal control of a flexible beam

One method of controlling a flexible beam is H₂ optimal compensation, which minimizes the mean square tracking error for a particular reference input. However, for many flexible beams the H₂ optimal compensator requires plant input magnitudes that are unrealizable. To avoid this difficulty, constrained H₂ optimal compensation is used which requires that the plant input not exceed a certain value. An algorithm based on stable factorization and a Lagrangian multiplier has been developed to solve this problem. A further difficulty in controlling flexible beams is that the usual output definition of the beam does not have a well defined model. Previous work has shown that an alternative output definition does have a well defined model. Experimental results indicate that by applying the algorithm to either model an excellent controller can be obtained