An algorithm for the selection of linearisation points in non-linear systems: a diesel air-path case study

Abstract

One typical approach to implement model predictive control in relatively fast sample rate applications utilises linearised plant models to simplify the online optimisation problem in the presence of limited computation budget. A number of linearisation points may be used to account for the variation in the non-linear plant over the entire operating domain, leading to potential switched linear time-invariant (LTI) or linear time-variant (LTV) implementations. The choice of these linearisation points, and the regions over which they are considered valid, can have a significant impact on the closed loop performance of the overall controller. In this work, in the presence of a high-fidelity digital twin of a non-linear plant, a numerical algorithm for the selection of linearisation points is proposed. The approach makes use of the concept of disturbance sets to determine both the linearisation points and the domain to which each linearisation point applies. The use of disturbance sets provides an implicit connection to closed-loop controller performance if robust model predictive control algorithms are implemented. The proposed approach is implemented for the challenging problem of diesel air-path control, with simulation results on a high-fidelity mean value engine model used to demonstrate the efficacy of the approach.