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We present here a multi-objective control algorithm based on the use of Youla parameterization and an independent Lyapunov function for each objective. We choose to consider two constraints: one with the H2 norm and one with the H8 norm. The general optimisation problem is presented with the LMI expression of the constraints, followed by the presentation of the AMB machine model. The model we use has been developed as follows: we consider that the rigid and flexible behaviour of the system are independent. Thus, we develop a nodal state space model of the flexible shaft, reduced into a modal model. The rigid equations of the system lead to a second state space model. The two parts are used conjointly in order to build a complete model of the AMB suspended system. We introduce the matrix manipulations that lead to the final LMIs and the general algorithm as detailed in [6] and [7]. The controller we obtain is analysed and compared to the initial one.

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Booktitle: Proceedings of ISMB9