The μ-Synthesis and Analysis of the Robust Controller for the Active Magnetic Levitation System

Over the centuries object suspension has stunned and interested most of the people including famous scientists such as Benjamin Franklin and Robert Goddard. In 1842 Ernshaw came up with the idea of the suspension of an object in the magnetic field created by permanent magnets. He also proved that permanent magnets cannot reach a stable levitation in all 6DOF [5] which requires new methods to be applied. The stable levitation is achieved by adjusting an object position and/or velocity feedback which creates the appropriate magnetic field. Active Magnetic Levitation System (AMLS) is a perfect example of a structurally unstable object. The control task is to maintain a ferromagnetic object in a desired position by generating an appropriate magnetic field which disposes of gravity and counteracts other accelerations. In various magnetic levitation applications e.g. in high-speed trains and magnetic bearings [13,4] we face a problem of keeping the system stable even in the presence of parameters variations and other perturbations. Very common problem can be the control task of magnetic vehicles when the mass of passengers is variable. The synthesis and analysis of the robust controller for the AMLS with variable load one can find in [12,15]. Systems that can tolerate plant variability and uncertainty are called robust. The problem of stabilising the uncertain linear dynamic systems has been discussed and analysed for almost 3 decades. The main issue with control systems are differences between the actual system and its nominal model which is used in control system design. Every practising control engineer should take into account a real-world systems vulnerability to various types of perturbations like non-ideal sensors, actuators, external noises, parametric uncertainties, unmodelled non-linearities and many others. Methods based on modern feedback H∞ optimisation theory [7,9,18] deal with robustness much more directly than other approaches.