Parametric uncertainty modeling for robust control: a link to identification

The dynamic behaviour of a non-linear process can often be approximated with a time-varying linear model. In the presented methodology the dynamics is modeled non-conservatively as parametric uncertainty in linear lime invariant models. The obtained uncertainty description makes it possible to perform robustness analysis on a control system using the structured singular value. The idea behind the proposed method is to fit a rational function to the parameter variation. The parameter variation can then be expressed as a linear fractional transformation (LFT), It is discussed how the proposed method can be utilized in identification of a nominal model with uncertainty description. The method is demonstrated on a binary distillation column operating in the LV configuration. The dynamics of the column is approximated by a second order linear model, wherein the parameters vary as the operating point changes. It is shown that a diagonal PI control structure provides robust performance towards variations in feed flow rate or feed concentrations. However including both liquid and vapor flow delays robust performance specifications cannot be satisfied with this simple diagonal control structure. (C) 1999 Elsevier Science Ltd. All rights reserved.