Off-line robustness improvement of predictive control laws in state-space description

Through many industrial applications, predictive control has proven its ability to give better performance while keeping its implementation relatively easy. From the basic version, several approaches have been developed to robustify an initial predictive law towards unstructured uncertainties. However, most of them provide high robustness bounds but penalize the disturbance rejection performance, and are built under the transfer function formalism difficult to extend to multivariable systems. To overcome these difficulties, this paper presents a methodology for enhancing the robustness of a GPC controlled system by convex optimization of the Youla parameter. This methodology, completely formulated with the state-space representation, starts with the design of an initial stabilizing GPC controller; this controller is then robustified off-line using LMI techniques to find the best trade-off between stability robustness and nominal performance, which represents the original contribution. The developed robustified GPC controller is finally applied to the velocity control of an induction machine, aiming at reducing the impact of additive unstructured uncertainties on the system, while respecting a time-domain template for the disturbance rejection.