Computation of optimal H∞ controllers and Approximations of fractional order systems: A tutorial review

This paper briefly reviews the recent techniques in the field of fractional order systems, and concentrates on the design of 'H00 optimal controllers for a magnetic suspension system model, derived in (25). The plant involves infinite dimensional terms, including a time delay and a rational function of y's. The recent formulation in (36) is used for the controller design, solving the mixed sensitivity minimization problem for unstable infinite dimensional plants with low order weights, and the result is verified with the old design procedure of (44). For simulation purposes, various implementation methods are performed, and a new approximation method is proposed.