Multi-model Robust Control Design

Yves Piguet, Ulf Holmberg, LONGCHAMP Roland

Simulations have shown that pole-placement design based on one nominal model results in a large sensitivity of the closed-loop poles. To take into account the parametric variations of the process, a multi-model approach is being explored. Dominant poles for models corresponding to various working conditions are placed approximately (in the least-squares sense). Through pole weighting, the relative errors in locating dominant and non-dominant poles can be controlled. This results in a fixed controller that achieves a trade-off in performance between all of the models.

Multi-model weighted pole placement has highlighted the interest in using multiple models to represent large parametric system uncertainties or variations in operating conditions. However, this approach is difficult to use in an automatic set-up. Instead of using the closed-loop poles, the various specifications can be considered directly, such as templates on the modulus of sensitivity functions and on time responses. A single scalar performance index, which is the smallest factor the specifications must be multiplied by to ensure their fulfillment, is minimized. This results in a minimax problem. Although the optimization can be trapped in local minima, examples show that this method can improve significantly existing controllers and facilitate the choice of a compromise between the various objectives.

Piguet Y., U. Holmberg and R. Longchamp. Instantaneous Performance Display for Graphical Control Design Methods. IFAC World Congress, Beijing, China (July 1999), L-5c-01-4, 403-408

Piguet Y., U. Holmberg and R. Longchamp. A Minimax Approach for Multi-Objective Controller Design Using Multiple Models. International Journal of Control, special issue entitled “Multiple Model Approaches to Modelling and Control”, 716-726

Piguet Y., U. Holmberg and R. Longchamp. Multi-Model Weighted Pole-Placement Design. European Journal of Control, Vol. 3, pp. 216-226 (1997).

Piguet Y., U. Holmberg and R. Longchamp. Multiobjective Controller Design Using Multiple Models. 2nd IFAC Symposium on Robust Control Design (ROCOND’97), Budapest, Hungary, pp. 253-258 (June 25-27, 1997).