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The control of the popular magnetic levitation system is addressed from the viewpoint of adaptive control based on fast, on line, algebraic parameter estimation, exact linearization and generalized proportional integral (GPI) output feedback control. The GPI controller guarantees an asymptotically exponentially stable behavior of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The online algebraic parameter estimation approach estimates, quite accurately, and in a very short period of time, the unknown parameter or the magnetic levitation system. The proposed adaptive controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilization and trajectory tracking tasks.