Robust control design is one of the main branches of research activity in modern control theory. This is determined by special practical importance of the issues discussed here and the necessity to create new effective methods and algorithms for robust control design based on modern capabilities of digital computers. The main goal of robust control design is to provide some desired robust properties of the closed loop system, such as stability and quality of control processes, while the mathematical model can vary within given admissible limits. In the paper the problem of robust control design for magnetic levitation plant is considered. This system has an inaccurate mathematical model, because it has essentially nonlinear dynamics and very difficult approximate description of the agnetic field. Two different optimization approaches for control design are proposed. The first of them is based on the use of predictive models and the second one is the modification of a linear-quadratic synthesis, where additional constraints in the frequency domain are introduced. The corresponding computational algorithms for real-time implementation of a control laws are given. These algorithms are compared by illustrative examples of magnetic levitation system control.