Best achievable performance: Non-switching compensation for multiple models

This paper presents a solution to the best achievable performance problem f or a family of process models that are simultaneously stabilized by a non-s witching LTI compensator. Specifically, a method is presented that can quan tify the best dynamic performance achievable by a dynamic feedback compensa tor, for a finite family of process models. Closed-loop dynamic performance is quantified through a new performance measure that guarantees performanc e with respect to all allowable disturbances and allows for closed-loop res ponse shaping with respect to fixed disturbances. The simultaneous performa nce problem is then formulated as a quadratically constrained minimax optim ization problem that is non-differentiable and infinite dimensional. It is shown that the simultaneous performance problem can be solved through the i terative solution of appropriately constructed finite-dimensional nonlinear programming problems. A method that identifies E-globally optimal solution s to this type of problems is presented. Finally, the proposed approach is demonstrated through an illustrative numerical example problem. (C) 1999 Jo hn Wiley & Sons, Ltd.