A systematic procedure for modeling and robust control of a multivariable magnetic levitation system is described. Our previous study revealed that an observer‐based LQ controller can stabilize the system, but generates spillovers in the presence of an impulse disturbance. To solve this problem, we apply an H∞ control to suppress the spillovers caused by unmodeled dynamics which we estimate using closed loop identification. First, an exactly linearized model is obtained to compensate for nonlinearities in the system, followed by estimation of the unmodeled dynamics using closed loop identification. Second, this information is used to design a two degree of freedom H∞ servo system for suppressing the spillover while tracking a step reference input. Finally, the desired robust performance of the resulting servo system is confirmed theoretically by γ‐analysis and also experimentally.

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In this paper we treat a three-inputs/three-outputs magnetic levitation system with three electromagnets and a Y shape iron plate as a levitated vehicle without mechanical contact. In general, the magnetic levitation system possesses nonlinearity, natural frequency, and parameter variations inherently, so that we design a decoupled attitude control system in order to compensate nonlinearity and sensor noise. In this paper we compensate the nonlinearity by using a method of exact linearization and design the control system by using ILQ design method. This design method can achieve decoupling and specified time responses, which is important in this multivariable control system, and we can reduce sensor noise by choosing the design parameters appropriately. In this paper we first derive two linear models by using a method of exact linearization as well as 'a usual method of linearization around an equilibrium point. Next we design control systems by using ILQ design method and show the effectiveness of both the design method and two linearization methods by simulations and experiments. Finally we show that with exact linearization method, 1) the derivation of the model is easier, 2) some parameter variations can be treated in the framework of quadratic stabilization problem or /1 synthesis, 3) the selection of the design parameters does not depend on operating points, and 4) ILQ design method can eliminate some parameter variations by tuning certain design parameters.

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