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On weight adjustment in H$_\infty$ control design

Project members: X.J.A. Bombois, B.D.O. Anderson and A. Lanzon (Australian National University and National ICT Australia, Australia)

In recent years, H$_\infty$ control design has become a well-known method to design a model-based controller satisfying a number of constraints expressed by amplitude bounds (weights) on the "to-be-designed" closed-loop transfer functions. This method has known numerous applications for control design on real-life systems. The design of a controller using H$_\infty$ control design generally follows an iterative procedure. In a first step, only the sensitivity function is effectively constrained (i.e., the constraints on the other transfer functions are chosen in such a way that they remain ineffective). A first controller is obtained in this way. However, this controller has generally an unsatisfactory performance with respect to the closed-loop transfer functions for which the constraints were (in this first step) too loose to be effective. Consequently, in a second step, the weights on these closed-loop transfer functions are adapted in order to improve the closed-loop behaviour of the controller and a second controller is computed using these adapted weights. This procedure is pursued until the obtained controller is judged satisfactory enough. The way with which the weights are adapted at each ``iteration'' is generally purely heuristic. It is consequently very interesting to build some insights about the influence of a weight modification on the obtained (central) controller and, more importantly, on the obtained closed-loop transfer functions in order to be able to improve the way H$_\infty$ control design is performed.


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