We examine an H$∞ mixed sensitivity design problem formulated to achieve good disturbance rejection and tracking properties as well as robust stability. A two degree-of-freedom controller is used, then, as is well known, the tracking objectives can be considered separately. A major concern in H∞ design is the selection of weighting functions to satisfy the design specifications. In this paper we give conditions on the weights which guarantee the optimization problem is well-defined; describe how a constrained optimization can be posed so that improper and unstable weights can be used; describe the effect the weights have on various design objectives; show how an appropriate selection of weights can reduce a 2-block optimization problem (requiring an iterative solution) to a 1-block problem (with a closed-form solution); give an illustrative example. In particular we show how the pole-zero cancellation phenomenon in H∞ design can be exploited or prevented by a suitable choice of weight, and how an optimal controller with a given frequency roll-off can be obtained.
|Number of pages||6|
|Publication status||Published - 1991|
|Event||Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control - Tallinn, USSR|
Duration: 1990 Aug 13 → 1990 Aug 17
|Other||Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control|
|Period||90-08-13 → 90-08-17|
All Science Journal Classification (ASJC) codes