<p>The subject of this thesis is the design of a control law for a magnetic levitation system, which in this case is the system 33-210. The method used is backstepping technique and specifically adaptive observer backstepping due to parameter uncertainties and lack of access to all the states of the system. The second state of the system, the speed of the steel ball, was estimated by a reduced order observer. The model used gave us the opportunity to estimate a parameter which in the literature is denoted virtual control coefficient. Backstepping method gives us a rather straight forward way to design the controlling unit for a system with these properties. Stabilization of the closed-loop system is achieved by incorporating a Lypapunov function, which were chose a quadratic one in this thesis. If thederivative of this function is rendered negative definite by the control law, then we achieve stability. The results of the design were evaluated in simulations and real-time measurements by testing the tracking performance of the system. The simulation results were very promising and the validations in real-time were satisfying. Note that this has been done in previous studies; the new aspect here is the limitation of the voltage input. The real-time results showed that the parameter estimation converges only locally.</p>

The subject of this thesis is the design of a control law for a magnetic levitation system, which in this case is the system 33-210. The method used is backstepping technique and specifically adaptive observer backstepping due to parameter uncertainties and lack of access to all the states of the system. The second state of the system, the speed of the steel ball, was estimated by a reduced order observer. The model used gave us the opportunity to estimate a parameter which in the literature is denoted virtual control coefficient. Backstepping method gives us a rather straight forward way to design the controlling unit for a system with these properties. Stabilization of the closed-loop system is achieved by incorporating a Lypapunov function, which were chose a quadratic one in this thesis. If thederivative of this function is rendered negative definite by the control law, then we achieve stability. The results of the design were evaluated in simulations and real-time measurements by testing the tracking performance of the system. The simulation results were very promising and the validations in real-time were satisfying. Note that this has been done in previous studies; the new aspect here is the limitation of the voltage input. The real-time results showed that the parameter estimation converges only locally.