Robust Self-Tuning Control under Probabilistic Uncertainty using Generalized Polynomial Chaos Models

A robust self-tuning controller for a chemical process is developed based on a generalized Polynomial Chaos (gPC) model that accounts for probabilistic time-invariant uncertainty. Using this model, it is possible to calculate analytical expressions of the one-step ahead predicted mean and variances of controlled and manipulated variables. The key idea is to consider these predicted values for performing online robust tuning of the controller through a quadratic optimization procedure. The gPC model is also used to identify overlap between consecutive probability density functions (PDFs) of manipulated variables and to find trade-offs between the aggressiveness of the self-tuning controller and robustness to uncertainty based on this overlap. The proposed methodology is illustrated by a continuous stirred tank reactor (CSTR) system with stochastic variations in the inlet concentration. The efficiency of the proposed algorithm is quantified in terms of control performance and robustness. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.